University of Nigeria Research Publications

NWAORGU, George Iheoma

Aut

hor

PG/M.Sc/96/22687

Title

Interpretation of 2-D Seismic Reflection Data from Meren Field, Niger Delta

Facu

lty

Physical Sciences

Dep

artm

ent

Physics and Astronomy

Dat

e

December,1998

Sign

atur

e

INTERPRETATION OF 2 - D SEISI REFLECTION DATA FROMMEN FIELD, NIGER DELTA

NVYAORGU GEORGE IHEOMA R E G NO: ~ G / ~ k ? C / 9 6 / Z 2 6 8 7)

DEPARTMENT OF PHYSICS & ASTRONOMY UNIVERSITY OF NIGERIA NSUKKA

INTERPRETATION OF 2 - D SEISMIC REFLECTION DATA FROM MEREN FIELD,

NIGER DELTA

NVA ORGU GEORGE IHEOMA (REG NO: ~ G / ~ S C / 9 6 / 2 2 6 8 7)

I - . '. yL,

ARESEARCHPROJECTPRESENTED TO THE DEPARTMENT OF

PHYSICS AND ASTRONOMY UNIVERSITY OF NIGERIA NSUKKA

IN PARTIAL FULFILMENT FOR THE AWARD OF THE DEGREE OF

MASTER OF SCIENCE IN GEOPHYSICS.

CERTI FlCATlON

MR. NWAORGU GEORGE IHEOMA, a postgraduate student of

the department of physics and Astronomy with registration number

I'G/MSC1/96/22687 has satisfactorily fulfilled the requirement for course and

rese;uxh work for the award of the degree of master of science in

Geophysics.

'I'l~e work embodied in this project is original and has not been

submitted in past or ti111 for any other diploma or degree of this or any other

Ilniversity.

sufiervisor ' Prof. P.N. Okeke

DEDICATION

This research project is dedicated to

LORD MY REDEEMER

And

NWAORGU FAMILY.

ACKNOWLEDGEMENT

The contributions of several people made the completion of this

research project possible. The resource persons consulted have contributed a

lot and others have helped financially and morally.

I wish to express my sincere gratitude to these people especially my

supervisor Dr. J.U. Chukwudebelu. His efficient supervision, advice and

corrections added a great value to this research work. The 2 - D Meren Field

Data Interpreted was supplied by Chevron Nigeria Limited. In the course of

carrying out the research Mr. .N.A. Dada provided guidance and materials.

He is a retired Petroleum Explorationist of Nigeria Agip Oil Company

Limited. May God reward him. The special aid rendered by Dr. P.I.

Obiakor and Calister Odoemena was of immense value. Mr. Felix

Adindu rendered help in well log interpretation while Mr. Toyin Akinosho

made corrections on the interpretation of seismic sections. These are

Petroleum Expplorationists in Chevron Nigeria Limited. I wish to thank

Mr. Taiwo Rasaki of DPR, Lagos, Mr. & Mrs. R.M. Ogbeta for their

moral and financial support. I grateful to Cecilia Anih for the efficient work

done in typing this project. The contributions from the entire members of

Nwaorgu family especially my younger brother Sylvester Nwaorgu and

my mother Mrs. Emilia Nwaorgu are enonnous.

I am indebted to various authors and publishers whose materials have

been consulted in carrying out this work.

I thank all these people and mostly my GOD for giving me the

inspiration to pursue this course.

Nsukka December,l998

NWAORCU GEORGE.

ABSTRACT

The objective of this study is to carryout structural interpretation of 2 - D seismic reflection data. The interpretation is to locate possible structural

traps of hydrocarbon.

The data interpreted is a subset of 2 - D seismic reflection data obtained

fiom Meren field. The field is located in the offshore area of the western

edge of Niger delta basin. The seismic sections were examined and faults

were interpreted. The horizons mapped were selected by well log-to-seismic

correlation. The well log used was derived fiom well M - 73 located in the

survey area. Two horizons were interpreted and timed to produce time

contour maps.

The time contour maps were used to obtain a three dimensional view

of the subsurface layers mapped. It was assumed that, in a layered earth

where velocity is constant or velocity variation is small, the time for seismic

wave to travel to a layer is directly proportional to the depth of the layer.

Time contour maps were therefore used in studying the structures of the

formations mapped.

On horizon 1, six faults and seven closures were identified. The faults

are normal growth faults. The closures include simple rollover anticlines,

faulted anticlines, faulted closures and closures against faults. The faults are

growth faults and concave to the downthrown side. Reflection on seismic

sections and well log data showthat the closures are good hydrocarbon

traps. The locations of these closures were recommended for possible

drilling. Use of 3 -D seismic reflection data and cross sections to further

study the area were also recommended.

TABLE OF CONTENTS

CHAPTER ONE: INTRODUCTION

1.3.3 Structural style of Niger delta ................................

1.3.4 Hydrocarbon trapping mechanism ...........................

1.4 Geology of Meren field ........................................

i . .

"11

. . . 111

iv

v-vi

vii-x

CHAPTER TWO: BASIC THEORY OF SEISMIC WAVE

CHAPTER FOUR: PROCESSING AND INTERPRETATION OF

SEISMIC REFLECTION DATA

Introduction ---------------- ---- ------------------- - ----- ----- ---- -- Data Processing ------------ ---- ...................... - ------------- Fourier transforln ...................................................

Collvolution ............................................. ------------ Correlation ...........................................................

Processing sequence ................................................

Filtering ...............................................................

Delnultiplexing ------ ................................................. Field static comectjon ................................................

Common midpoint sorting ....................................... Velocity malysis/NMO correction ............................... Stacking ------------- ----- ------- --------------- ..................... Residual static correction ....................... ------ ------------- Migration ----------- --------- - .................... ------ -------------- Interpretation of seismic reflection data ........................... Introduction ------ -------------- -- --------------- ----- ------- - --------- Characteristics of seismic events ................................... Hydrocarbon habitats and trapping ................................. Evidence of faulting on seismic section ............................ Seismic stratigraphy ----------- - ---------------- --- ---- ----------- ---- Data used in seismic interpretation ................................. Seismic sections ....................................................... Vertical seismic profile --------- ------------ .......................... Synthetic seismogram ......................... --- ------- -- ----- ------ Base map ......................... ----------- ........................... Well log data -- ................................... - ..................... Seismic data interpretation sequence ............................... Selection of mapping horizons ----------- ........................... Interpretation of seismic sections ................................... Fault mapping and contowing --------------- -- -------- ---- ----------

CHAPTER FIVE: INTERPRETATION OF 2 -D SEISMIC

REFLECTION DATA FROM MEREN FIELD.

CHAPTER ONE

INTRODUCTION

1.1 Introduction

The interpretation of seismic reflection data which is consistent with

the geology of an area using available data is important in Petroleum

exploration. In oil and gas prospecting, the seismic method is more

suitable than other methods because of it's high ability to give details

of structure. Some of the other geophysical methods of exploration

include electrical method, gravity, magnetic and radioactivity

methods. Each method has it's advantages and disadvantages.

In general, seismology has to do with waves resulting from the

vibrations of the earth. Thus seismology involves artificially

generated and natural earthquake waves that penetrate well into the

earth.

In seismic reflection prospecting, sound is artificially produced

at or near the surface of the earth. The sound is produced using

chemical explosives or mechanical vibrators. The echo returned ti-om

the subsurface is recorded by detectors (geophones). The use of

computers makes it easy to record data in either digital or analogue

form.

The data is processed to obtain greater vertical and horizontal

resolution. The repositioning of the data done during processing gives

a better picture of the subsurface. During acquisition and processing,

the unwanted seismic energy reflected (noise) is attenuated by

filtering. The primary reflections (signals) from bedding planes are

enhanced. Seismic data acquisition and processing is done with the

aim of maximizing signal to noise ratio. The seismic reflection data

acquisition technique is an application of the principle of "echo

acoustics" therefore processing and interpretation are based on wave

equation and wave characteristics of seismic events. Reflection

occurs where there is change in acoustic impedance/velocity across

the interface.

The interpreter uses the regional geology, seismic data, well log

data, gravity anomaly and other relevant data to locate hydrocarbon

traps. The alignment of reflections and splitting of wavelets on a

particular horizon is used in delineating anticlines, synclines, faults

and other structures in the survey area. The use of amplitude

preservation processing has given birth to direct detection of

hydrocarbons on seismic section using "bright spots" and "dim spots".

In this regard facie analysis using 3 -D seismic data is very important

in interpretation of seismic data. Interpretation gives information on

the hydrocarbon bearing sand, the structural traps and positions of

faults. This becomes a guide in positioning and drilling of wells.

In this project, based on the available data, "Time contour

maps" are produced for the horizons interpreted from the seismic data.

This was used, to obtain areas of possible hydrocarbon accumulation,

the fault positions and trapping mechanism of the subsurface mapped.

The subsurface geological map is an important instrument for

discovery of hydrocarbons during exploration.

1.2 Obiective and scope of study.

The objective of this study is to carryout the structural

interpretation of an already acquired 2 -D seismic reflection data fiom

Meren field in the offshore Niger Delta basin of Nigeria. The

structural interpretation will give possible location of hydrocarbon

accumulation and leads to recommendation of optimal drilling sites.

The scope of this project is within the area covered by the

seismic sections available. This consists of nine dip lines and four

strike lines which were used for the study. The regional geology of

Niger delta will be combined with the deductions from the interpreted

data to make recommendations and draw conclusion.

1.3 Geolow of N i ~ e r delta

1.3.1 Regional setting and basin formation.

The Niger delta is one of the ten major sedimentary basins of

Nigeria. The others are Abakaliki basin, Anambra Basin, Benue

trough, Bida basin, Bornu-Chad basin, Dahomey basin, Gongola

basin, Sokoto basin and Yola trough. These onshhore basins occupy

about half the total area of Nigeria (Whiteman 1982). The basins are

delineated by three main areas of basement complex. These are

Western end of the Cameroun volcanic zone, Northern Nigeria massif

and the eastern end of West African massif. The basins and basement

complex are shown in figure 1.1 .

The -Niger Delta complex basin is situated on the Gulf of

Guinea on the west coast of Central Africa. It built out into the

Atlantic ocean at the mouth of the Niger-Benue river system during

the tertiary @oust and Omatsola 1990). The maximum sediment

thickness is at the central part of the delta within the greater Ughelli

megastructure. The thickness is about 12 kilometers.

The formation of Niger delta basin and others started with the

break of the central African-south American part of the Gondwana

super continent. This took place in the Mesozoic. It is along a series

of rift zones of different orientations that met in a triple junction on

the present gulf of Guinea. Two of the anns, which followed the

southeastern and southwestern coasts of Nigeria developed into

collapsed continental margins of south Atlantic. The first sediments

of the cretaceous to tertiary cycle accumulated during the rift-fill

phase. Thick successions of marine and marginal marine clastics and

carbonates were deposited in a series of transgressive and regressive

phases. On complete separation of the continent, the sea transgressed

inland to Benue trough which is the third arm due to subsidence of the

continental basement.

The present Niger delta basin is built on the collapsed

continental margins of the south Atlantic. The core of the delta is

located over the site of the triple junction. The bulk of sediment

supply fiom the north and east is through the Niger-Benue river in the

tertiary. The Benue and Cross rivers supplied substantial amount of

volcanic detritus fiom Cameroun volcanic zone since the Miocene . The Niger delta has prograded into gulf of Guinea at a steady rate.

This is due to drainage area, basement subsidence, and eustatic sea

level changes.

Presently the Niger delta is typically wave and tidal dominated.

It appears to be constructive at the centre and destructive at the flanks

(Nedeco 1959)where it is sandy. The lower plain consists mainly of

distributary channels of rivers surrounded by fiesh water swamps.

The destructive part of the delta are salt water mangrove swamps with

greater tidal influence. Long shore currents carry sediments off the

area form sandy beaches, beach bridges and offshore bars along coast

flanks (Burke 1972). The marginal areas of the delta suffer

encroachment due to lack of sediment supply.

The submarine portion of the delta consists of shallow shelf

which gradually merges into a long continental slope. The upper part

of the slope is marked by a zone of faulted sediments, clay walls and

diapirs known as distal belt. This is the outermost portion of the

developed part of the delta.

The trend of development of the Niger delta is a major factor in

the stratigraphy and structure of the region.

1.3.2 Stratigraphy of Niger delta.

The Niger delta is composed of regressive sequence of clastic

sediments developed in a series of offlap cycles. The delta shows a

tripartite lithostratigraphic successions in which regressive sequence

is demonstrated. The well sections in figure 1.2 shows the division of

the overall regressive scheme into gross lithofacies units. Formal

stratigraphic names are given to these unit; thus we have fkom the top,

continental alluvial sand (Benin formation), the paralic clastics

sequence (Agbada formation) and the marine shale (Akata formation).

The Akata formation extends to the basement rock. It is a massive

monotonous marine shale. The paralic facie on top of Akata

formation consists of shallow marine and fluvial sands, silts and clays

which are interbedded. The non marine continental sand on top of

these formations is massive. Pre-deltaic basement indications are seen

Fig 1.2 Well sections showing regressive scheme of the Niger delta @oust and Omat sola 1990).

on seismic data only along the northwestern and north-eastern basin

flanks. It is also seen below the continental rise offshore. The deltaic

facies range in age fiom Eocene in the North to miocene-pliocene in

the south.

The detailed stratigraphy of Niger delta is complex. The delta

is affected by synsedimentary faults, the rate of sediment supply and

subsidence, then tidal waves. These control the progradation of the

delta. The Niger delta is divided into major sedimentary units by the

synsedimentary faults giving rise to depobelts. These depobelts are

shown in figure 1.3 with the age of the deltaic sequence. These are

northern delta depobelt (P450-P560) or late Eocence to oligocene,

Greater ughelli depobelt (P650-P680) or early miocene to middle

miocene, central swamp 1 depobelt (P720-P740) or middle miocene,

central swamp I1 depobelt (P770) or middle miocene, coastal swamp I

depobelt (P 780-P820) or middle miocene to late miocene, coastal

swamp I1 depobelt (P830-P840) or late miocene, offshore depobelt

(P900) or quaternary and the delta edge @oust and omatsola 1990).

In each depobelt, the tripartite regressive sequence forms an integral

delta unit of distinct age. Each depobelt contains one or more

paleontogically distinct transgressive shale horizon. This represents

interruptions in the overall regressive sequence. These transgressive

shale horizons are probabaly related to sea level rises. The lithofacies

do not have distinct boundaries which makes it difficult to define

separate formations.

The major lithofacie units of the Niger delta are shown in

fig. 1.4. It illustrates the diachronous nature of these lithofacies .

LATE

QUATERNARY .-- PLIOCENE

- W Z W

-

-

- OLIGOCENE

LATE

EARLY

PALEOCENE ---

IF>L'J[-- - ------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ---A FACES - - - - - - - - - . - - - - - - - - . - - - - - . . . . . . . . . . . . . . . . . . . . . .

1 I I I u E X T E M OF EROSIONAL TRUNCATDN

Eig 1.4 The tripartite sequence of major lithofacies units ofthe Niger delta @oust and Omat sola 1990).

The Akata formation which is composed of shales, silts and

clays is at the base of the delta sequence. It contains a few streaks of

sand. The sand is turbiditic in orgin and were deposited in the

holomarine environments. The shale ranges from paleocence to

Holocene in age. They crop out offshore in diapirs along continental

slope and onshore in the northeast of the delta (Imo shale). The top of

this formation is the economic Basement for oil. The deeper

formation contains gas dissolved in oil field waters under high

pressure. The onshore is rich in benthonic foraminefera. Sand and

silt beds break the uniform shale.

The Agbada formation is the hydrocarbon prospective sequence. It

consists of sand, silts and clays in various proportions representing

offlap units. They were deposited in delta fronts, delta topset and

fluvio-deltaic environments. The alternation of fine and coarse

clastics provide multiple reservoir seal couplets. This is present in all

the sedimentary units. The age ranges from Eocence to pleistocene.

The sand consists of lignite streaks and limonite. The thickness of

Agbada formation is about 3000m. In this formation pre-Miocene

reservoir rocks are deposited as con ti nu^ sand, point bars and

channel sand. Miocene and younger rocks were deposited as barrier

bars. The Agbada formation lies between Akata and Benin formation

(weber and Dakoru 1975).

The Benin formation is the uppermost unit. It is made up of

massive fresh water bearing sand and gravel. The sand was deposited

in alluvial environment. The Benin formation sand is thinner in the

coastal swamp and in the offshore depobelts. It's maximum thickness

is about 2000m. Little oil is found in this formation (short and stauble

1967, Avbovbo 1978).

One characteristic which distinguishes these formations is the

sand to shale ratio. The top of Agbada formation is the base of fi-esh

water inversion while the base of Agbada formation is the on set of

hard over pressured zone. This marks the top of Akata formation

which continues to the basement rock. A shematic structural section

showing relationships of the tripatite division of the tertiary sequence

is shown in figure 1.5 @oust and omatsola 1990).

1.3.3 Structural style of the N i ~ e r delta.

The dominant direction of movement and involvement of

basement rocks are important in a sedimentary basin. In petroleum

exploration, it dictates the extent sediment is structured into potential

traps and amount of closures at a level. The basement rock influences

the regional and local structural pattern.

The tectonics of Niger delta are limited to extensional

deformation and minor basement involvement. - The most visible

extensional faulting occurs in the paralic clastics (Agbada formation).

The marine shale (Akata formation) has obscure structure while the

continental sand accumulated over each growth fault trend. Growth

faults dominate the structural style. This is attributed to the

movement of over pressured, ductile marine shale combined with

slope instability. The deformation that creates structures capable of

trapping petroleum is cold deformation in which temperature and

pressure are not extreme. Shear failure follows fracture propagation

in an elastically deforming medium. The faults found in the Niger

delta are mainly listric and normal faults.

The growth faults initiate when sand prograde over

uncompacted shale. The local overburden due to density contrast

between shale and their overlying sands creates gravity instability:

causing growth faults. The shales are laterally displaced under

increasing sand weight. Faulting starts as a steep shear plane at the I

upthrown side of the depocentre. The shear plane then separates as

growth faults due to higher sediment infill in the down block of the

structure close to the fault. The dip magnitude increases downward in

a counter fault direction.

Growth fault index = unit thickness of down block

Unit thickness of upblock.

The vertical component of the faulting process is generally

combined with a horizontal displacement of the down block due to

regional delta slope. This gives rise to formation of rollover

anticlines. The Niger delta rollover anticlines shows that the crest

shifts with depth (Evamy et al, 1978). The rollover anticlines shows

as gentle undulations due to differential compaction.

Mud diapirs occur on the landward side of growth faults in each

depobelt. This restricts' sedimentation on the upthrown side of the

fault but enhances sedimentation on the downthrown side. The mud

diapirs located on the ,seaward side of the growth fault produce

collapsed crest structures. This causes variation of sand deposit

thickness in the downthrow. The principal types of structures found

in the various depobelts of the Niger delta are shown in figure 1.6.

The structural style in the depobelts differ a little from each other.

The preponderance of anticlines and faulted anticlines in the older

depobelts gives way to more complex structures like collapsed crests

in the coastal swamp and offshore depobelts. The structural style as

: :! U t-

w 8.9 D

-! Z m m s ;r v :: '3- m 0 c 0 P

U D Z D w

D 1 rn U

6 2 - z 4 x m

U n

I I?

I P 1 0 b r U m 0 2 0 z (I)

D

0

I m

F t 0 4 I n X 2 m U U)

w

(I)

I 4

a n 3 . II (I) 4

P r P M - U

z

observed in various depobelts is shown in figure 1.7. The Northern

delta depobelt and the delta edge westward is dominated by anticlines

and faulted anticlines. In the central delta depobelt, faulted anticlines

dominate with few collapsed crest structures, while in the coastal

swamp and offshore depobelts there are more complex structures of k-

type footwall closures and collapsed crest anticlines.

1.3.4 Hvdrocarbon trapping mechanism.

The sealing capacity of faults in the Niger delta appears to

depend on the amount of the shale smeared into the narrow fault zone.

This depends on the amount of clay layers over the throw of the fault.

A fault is sealing if it has been passed on the down thrown side by an

interval of more than 25% shale @oust and omatsola 1990). Sealing

capacity increases with increase in percentage of shale. In some oil

reservoirs, overpressure makes some rollover anticlines to be full of

oil between demarcating faults. Migration of oil in the Niger delta is

by spilling up through the narrow conductive fault zones. The

blocking off of delta sequence into cells by growth faults cause lateral

and vertical variation of hydrocarbon properties suggesting little

megration.

According to Doust and omatsola (1990), the trapping

structures may be classified into complex structures, anticlinal dip

closures, up thrown fault closures (foot wall) and down thrown fault

closures (Hanging wall). This is shown in fig 1.8.

In anticlinal dip closures, trapping is by means of simple

closure independent of faults. This is of three types, unfaulted simple

dip rollovers, dip closures where fault though present contributes less

than 15metres to the closure and faulted anticlinal closures where dip

closure is these dissected by synthetic and antithetic non sealing

faults. Closure here is limited to dip element.

In down thrown fault closures, trapping- relies on combined

dip/fault closure on the down thrown side of a sealing fault. In this

case the fault plane and sediments dip are in the same direction. This

may be where the fault dependent element exceeds 15m of vertical

column or where the bed is juxtaposed against over pressed shales in

the up thrown block.

Trapping in the up thrown fault closures is by combined

dip/fault closure on the up thrown side of the sealing fault. In this

situation the sediment dip and the fault plane are in opposite

directions. The situation may be where the upthrown side of a north-

dipping antithetic fault lies on the south flank of a rollover structure.

It may also be where the upthrown side of a south -dipping synthetic

fault lies on the northern flank of a rollover structure. Also the

upthrown side of a structure building fault if deep may he below the

structure in the overlying downthrown block.

1.4 Geology of Meren field

The g e o h of Meren field is derived fiom the regional geology

of Niger delta west.

The field is shown on the fault map of Niger delta in figure 1.9.

The field lies in the delta edge at the northwestern flank of the Niger

delta basin. It is an offshore field at the mouth of Benin river. The

field lies outside the two lobes of the southern offshore depobelt of the

Niger delta since it is located at delta edge. The structures in the delta

edge differs fiom the structures within the main offshore depobelt of

the Niger delta at the southern part.

The structural style of the field is dominated by antidinal dip

closures and closures against the downthrow of growth fault found in

the region. This is illustrated in figure 1.7. The structure 'at the delta

edge differs from the complex structural style of the coastal swamp

and southern offshore depobelts. In the coastal swamp, collapsed

crest closure and k-type footwall closures dominate. The trapping

morphology of the field is that of simple unfaulted rollover anticlines

and faulted anticlinal closures. However, the presence of complex

structures within the field cannot be ruled out since it lies offshore.

The stratigraphy follows the tripartite sequence of marine shale

(Akata formation), paralic clastics (Agbada formation) and continental

alluvial sand (Benin formation). In the field, the continental alluvial

sand is thick as in the delta edge. Diapirism is not well pronounced as

in the southern offshore deposbelt hence the absence of complex

structures. There are growth faults which are similar to the faults in

the northern depobelt.

The geology of a given area determines the reflections on the

seismic section. The propagated acoustic wave is reflected at

stratigraphic boundaries. Faults cause diffractions and change

alignment of primary reflections. . Data acquired by transmitting

seismic wave through the earth depends on the nature of the

subsurface. It is therefore imperative to understand the theory of

seismic wave propagation through the earth. This will make data

acquisition and interpretation to be consistent with the geology of the

survey area.

CHAPTER TWO

BASIC THEORY OF SEISMIC WAVE PROPAGATION

Introduction

The elastic theory of waves plays an important role in data

acquisition and processing.

The formulation of wave theory combined with spatial

convolution (signal theory) is significant in processing of seismic

data. Complex seismic response is understood using elastic modeling

schemes. One way elastic wave equation is used, is in wave equation

migration scheme. The acoustic parameters of compressibility and

density which determine propagation velocity are obtained using wave

equation. During acquisition, seismic source and detector positioning

are based on the wave theory of propagation, transmission and

reflection of seismic waves. We now present the general theory of

seismic wave propagation. The treatment given below follows that of

sheriff and Geldart (1982).

2.2 Fundamentals of elastic wave propagation

2.2.1 Theory of elasticity

The elastic behaviour of rocks is described here in terms of

stress and strain. Stress is defrned as force per unit area while linear

strain is defined as extension per unit length.

b Fig 2.1 Components of stress for faces pemendicular to x - axis.

Fig 2.1 shows a small element of a rock under stress. The forces

acting perpendicular to each face of the cuboid respectively give rise

to normal stresses designated as p, p, and p,. P, is the x

component of the stress acting on the face perpendicular to x

direction. P, is the y component of the stress acting on the face

perpendicular to the y direction. P, is the z component of the stress

acting on the face lying in a plane perpendicular to z axis.

Similarly tangential forces acting on the body give rise to

shearing stresses pm, p , p,. P, is the y component of the stress

acting on the side lying in a plane perpendicular to x axis. P, is x

component of stress acting on a side lying on a plane perpendicular to

%axis. P, is x component of stress acting on a side lying on a plane

perpendicular to z axis and P, is the z component of the stress acting

a side lying on the plane perpendicular to y axis.

Under equilibrium condition the stresses are balanced and the I

body is stable. When an external force is applied, the stresses become

unbalanced. They oppose each other causing changes in shape and

size. Opposing shearing stresses give rise to a couple.

For example rotational equilibrium about the z-axis is

I& dydzdx = P,dxdzdy, where dxdydz is an element of volume. It

follows in this case that p, = pm. It can be shown in general that

under equilibrium condition

Pij = i # j

Fig:2.2 .\nnlvsis of 2-D strain. k In fig: 2.2, the rectangle PQRS lies in the x-y plane. When

stresses are applied, the displacement components of PP' are u and v

respectively. In a situation where u and v have different values,

changes in size and shape occur (strain).

Let u=f (x,y) and v = f (x,y); then the cordinates of PQRS and

P'Q'R'S' are as follows:

Q (x+dx,y): Q' (x+dx+u+&dX y+v+& dx) 6x 6x

S (x, y+dy): S' (x+u+&dy, y+dy+v+&dy) 6~ 6~

R (x+dx, y+dy): R' (x+dx+u+&dx+bdy, y+dy+v+6xdx) 6x 6y 6x

In the present discussion we assume that the terms

6m-6~ and 6~ and 642_ are small enough for their powers and 6x 6y 6x 6y products

to be neglected. Hence we make the following deductions.

6d6x and 6v16y are fractional increases in length in the x and y

directions respectively. 61 and 62 are infinitesimal angles equal to

6d6x and 6v16y respectively. The right angle at P decreases by

61 +A and is rotated counter clockwise through 61 -& . The quantities 6dSx = e, and 6vI 6y = e, are normal strains. The s h e e n g strain e, = (6vI6x +6d6y. The rotation of the body about z axis is given by 4 = (GvlSx - 6u by). In 3-D using displacements u,v, and (3, we have e, = 6u/6x, eyy = 6v/6y, ezz = 6W6z ... ...... ... (2- 1

The components of rotation of the body about z axis are

Q = y x S where S= iu +jv + ok.

Dilatation 8, is defined as the change in volume per unit volume. Thus,

Hooke's Law

It states that for small strain, the given strain is proportional to the

stress producing it. When several stresses act, each strain is a linear

function of all the stresses and vice versa.

For elastic energy to be a function of strain, we must have C, = C,

In isotropic solid, only two elastic constants remain since the

coefficients are independent of set of axes chosen. These constants

are denoted by h and p. Where

C12= C13=C21=C23=C2S =C32=C31 = h

= cSS =C(j6 = p

Cll =Cu=C33 = h + 2 p

we can then state Hooke's law as

Pii = he +2&i ................. (2.5)

Pij = p eij ......................... W )

h and p are lame constants. The other elastic constants are youngs

modulus, E, poisson's ratio, a and bulk modulus, k. The relationship

between these elastic constants are given as follows (sheriff and

Geldart 1983).

E = P, /em = p (2p=3h) '/h+p ................ (2.7)

CJ = - e,le, = -e,/ e, =A A jp ............... 0 2 (2.8)

When a solid is subjected to uniform hydrostatic compression, P, = P, = P, = -P and fractional change in volume equals - (e,+e,+e,)or -8.

This shows the changes that occur on the solid when force acts on

it. Forces acting on the layers of the earth causes a change in the

elastic properties. This makes it possible for seismic wave

propagate through the medium. . . -

?* . . - - - - . .

. . . I

The wave equdon. mi-

Fig. 2.3 Stresses on faces perpendicular to X- axis.

Using fig.2.3 we obtain equations of motion in an elastic homogenous

isotropic medium. The stresses on the fiont face are

Pxx + P n +&zx+jXand Pyx + &yx&

6, - 6, 6, The stresses on the rear face are P, , P, and P,. The net unbalanced stresses are therefore P, + 6 b - d)( Pn + Gp,h(and P, + 6padX -

6x 6 x 6 x respectively.

These stresses on the area dy dz and affect the volume dxdydz. The

net force per unit volume in X direction is given by 6pd6x (dxdydz)/ dxdydz

The net force per unit volume along x direction is 6pd6x. Similarly we obtain for y and z directions 6g,&x and 6b&x - respectively. The total force per unit volume in x direction is (6g,+ - 6gz+ 6ga - )

6, 6, 6, For motion along x axis Newton's second law of motion is

e 6 2 ~ - = 60 , + 6g!, + 6gE st2 6x 6y 6z

whereg = density 6g=+ d& + 6p&

st2 6x 6y 6z

es&= 6 h + 6&. + - .............. (2.12) st2 6x 6y 6z Expressing the above equations in terms of strains we obtain

In terms of displacement the force is

In a homogenous isotropic elastic substance we obtain the wave

equation by differentiating equations 2.14, 2.15 and 2.16 with respect to

x,y,z respectively. Summing up we obtain

where a is propagation velocity and z2 916t2 is being propagated. The

wave is dilatational (P) wave. To obtain the shear wave equation we differentiate equations 2.15 and 2.16 w.r.t z and y respectively to obtain.

Subtracting equation 2.18 from 2.19 we obtain

Similarly we obtain R, and R ,. Where P is the propagation velocity of the rotation d RJ6 t? being propagated through the medium. To obtain the solution of the wave equation, we state the standard wave

equation as ti2 Y / v2 6 t? = V ~ Y ........... (2.22).

where Y is the wave function and V is the velocity of the wave. The general

solution for a plane wave travelling along x axis is given by

Y = f (x-vt) + g(x+vt) ................ (2.23).

In spherical co-ordinates the solution is given by

1 62 Y = 1_ ~ ( 2 6 ~ ) + 1 6 ( s i n e w + &Y --

v2 6 t? [6r 6 r sine 6 8 6 8 ~ i n ~ 8 6 4 ~ ... (2 .24)

When the wave motion is independent of 8 and 4, Y becomes a function of r and t, equation 2.24 simplifies to

The general solution of equation 2.25 is

rY = f (r-vt) + g (r+vt) ............ (2.26)

The wave equation can be written in terms of scalar potential of

displacement 4 and vector potential of displacement Y. The use of vector

and scalar potentials enables the wave equation to express displacements u,

v, W and the velocities u', v', and W' in terms of potentials. We have

4 (x,y,z,t) and Y ((x,y,z,t). We express

Using these relations we obtain in the wave equations 2.17 and 2.21 respectively as

The wave equation is easier to analyse for the propagation and

reflection of waves when stated in terms of potential function.

The dilatational wave and shear wave are bodily elastic waves ; they

propagate through the body of the earth. However rotational waves

are not transmitted through a body of zero rigidity such as fluids.

Also P-wave velocity (a) is greater than the shear wave velocity p since a = 843 for materials whose Poisson ratio is above 0.25.

Transmission and reflection of bodily elastic waves.

Fig 2.4 Two laver medium in welded contact.

In fig 2.4, M, and MI represent two layers in welded contact

along a horizontal boundary surface. Consider a plane wave incident

in M and reflected at the boundary. x, y and z are perpendicular to

eachother. The wave is incident in the direction oy and

perpendicular to the direction ox. For a simple harmonic wave, the

solution which corresponds to the waveform is

h l ( z ) = CIexp( -~kS~z )+F~exp( iks~z )

Due to reflection back into the medium and transmission across the boundary, the displacement can be expressed as

Where 4 is the scalar potential and ty is the vector potential. For a

3- D displacement of plane wave, we have

u, v and W satis@ the equations of simple harmonic wave if

ti2 = p 2 v 2 ~ - st2

and

in both media M and MI. The relevant solutions of equation will

contain no term in y. x will enter as a factor of the term e - ' ('*') I

\

Fig 2.5 Reflection of body waves. L . P U N S OF WAVE FRONT

, -.

In fig 2%

= (c2-9) ((At )2

2 tan e = - a2 = c2 - g S ( A ~ ) 2

cose = VAtlc At = v/c

v - - Ccose = Csini ............ (2.34)

1/C is a constant for all waves involved.

cose ==f = c m = cosf, = 1 '. - a P a I P 1 c

The general solution for p waves in medium M is

4 = Ao exp {ik (ztane + x-ct) ............ (2.35)

where k has been used for K, and is given

Ka2xcoselh = K cose ............... (2.36)

Kz = 2nsine/h = ktane ............... (2.37)

For reflected P waves in medium MI the solution is

4 = A exp {ik (-ztane +x -ct)) ............... (2.38)

and

t+ = ~oex&ztane + x-ct)) + Aexp (k(-ztane +x-ct)

for incident P wave.

For incident SV wave we have

y= Bo exp (ik(ztane+x-c-ct) {+ Bexp {ik(-ztane +x-ct}

when SH wave is incident we .............. (2.39)

V = Co exp {ik(ztanf +x-ct))+Cexp{ik(ztane +x-ct)}

When P is incident Bo = Co = 0

When SV is incident Co = Ao = 0

When SH is incident Ao = Bo = 0

To determine the coefficients A,B,C,Ao) Bo and Co

respectively we apply boundary conditions. The conditions apply to

continuity of displacement and stress across boundary at all places and

times.

For incident SH waves Ao = Bo = o and pfo. The boundary

conditions which involve 4 and y then show that A, B, Al and B1

have no dependence an Co and the relevant solution is accordingly of

the form.

In medium M V= Co exp(ik(ztanf +x-ct)) + Cexp (ik(-zatnf +x-ct)

........... (2.41)

and in medium M1

If C L ~ O for continuity of displacement at the boundary

for continuity of stress, we differentiate equations 2.41 and 2.42 wrt z

and put z=o to obtain

from Equations 2.4 1 and 2.42

C - - - -1- C -- co ptanf - pltanfl 2ptanf = ptanf + pltanfl ............... (2.45) using sini = cose = constant. We have v v sini = cose - (2.46) - ............... v P 1

In the case of normal incidence we have

C = -1- C = C', --

............. PP1 -PIP 2PP 1 PPl+ PIP (2.47)

The above solution shows that when incident wave is of SH type, the

reflected and refracted wave can only be of SV and SH type.

We now consider a situation in which P- wave is incident on a free

surface. The reflected waves obtained are P and SV waves.

Fig. 2.6 Incident P - waves on a free surface.

In fig. 2.5 the interface is horizontal and coincides with the x-y plane.

The z axis points in the upward positive direction. We use the elastic

wave equations

The solutions to these equations in medium M are

4 = Ao exp { k (ztan+x-ct)) +Aexp {ik(-ztane +x-ct)) ......... .(2.49)

Y = Bexp {ik(- ztanf + x-ct)) .......... (2.50)

V = Cexp {ik(- ztanf + x-ct)) ........... (2.51)

The boundary conditions are

(1) The stress components PZy , P, and P, must vanish at the boundary.

.... P, = p6v 1 6z = PC(-iktanf) exp {ik(-ztanf +x-ct)) = 0 (2 .52)

By differentiating and equating to zero we obtain

& = A (-iktanep exp (-ik ztane) exp:d(x-ct)) + 6z2 Ao ( ~ k t a n e ) ~ exp (-ik ztane) expid(x-ct)) ....... (2.54)

& = A (ik)2 exp (ik ztane) exp {k (x-ct)) + 6x2 Ao ( ikp exp ( ik ztanf) exp {ik (x-ct)) ....... (2.55)

......... & = B (iktanf)(ik) exp (-ik ztanf) exp {ik (x-ct)) (2.56) 6z6x P, at z=o gives assuming h=p

P, = h { ~ ( i k ) ~ + ~ o ( i k ) ~ +(-iktane)2 A+(ilctane) Ao ) + 2p {A-(iktane)2 + Ao(ktane)' -B(-iktanf)(ik)) = o ... (2.57)

= (Ao+A)+(A+Ao)tan2 e+2(A+Ao) tan2 e + 2B tanf = o

hence

(A+Ao) (l+3 tan2 e)+2Btanf = o

62b = A (-iktane) (ik)exp (-ik tane) exp {ik(x-ct)) + 6z6x

.... +Ao (iktane) (ik) exp (-ik ztane) exp {ik (x-ct)) (2.58)

i& = B (ik) exp (-ik ztanf) exp {ik (x-ct)} ......... (2.59) sx2

a t z = o

p = )J{2(-ik)tane ) (ik)A+2Ao (iktane)(ik)- B(ik)' + B (iktanf) ) = o ...( 2.60)

from Equation 2.57

........ from Eqn 2.60 Ao-A = - ~ ( t a n ~ f - 1) (2.62) 2tane

Adding Equations 2.61 and 2.62 we obtain

Ao = - Btanf - ~ ( t a n ~ f -1) ......... (2.63) 1 +3 tan2e 4 tane

hence

B = - - (4 tane) (1 +3 tan el Ao 4tane tanf + (1+3tan 'e) (tan2 f-1) ............ (2.64)

Using snells law and poission relation

Sini = cose and k =p , a 4 4 3 - v v

We obtain from equations 2.61 and 2.62.

B = Ao

- 4tane (1+3tan2e) 4tane tanf +(1+3tan2e $ . . . . . . . . (2.65)

A = B (ctan2 f-1) (1+3tan2 e) - (4tanf tane))

4 tane (l+3 tan2e)

substituting B in equation (5)

A - - Ao ... ... . (2.66)

2 2 4tane tanf - (1+3 tan e) 4tane tanf +(l+3tan2e )

we note from equations 2.61 and 2.62 that, at normal incidence of P

waves e = d 2 cos2 e = 3 cos2f = o and for grazing incidence e = o, B

= o, in both cases. These are the only conditions in which there is SV

reflected waves*fiom equation 2.66 A vanishes if

(1+3tan2e)l = 4tane tanf

using cos2 e = 3cos2f we see that this equation has two relevant roots

e= 12.8 O and 30 "- For these angles of emergence there are no

reflected p waves.

2.2.4 Surface waves.

In an infinite, homogenous, istropic medium only p and s waves

which are bodily elastic waves exist. When there is a surface

separating media of different densities or elastic properties, surface

waves exist.

Seismic surface waves are guided along the surface of the earth

and the layers near the surface. They do not penetrate into the earth.

Their amplitude decrease with increase in depth from the surface.

Two main types of surface waves are Rayleigh wave and love wave.

Love waves occur when there is general increase in s-wave

velocity with depth. This involves transverse motion (SH) which is

parallel to the surface of the earth. They can only be recorded by

horizontal geophones hence of much less importance in seismic

exploration.

Rayleigh waves propagate close to the surface of a semi-infinite

medium. The particle motion is confined to a vertical plane

containing direction of propagation. The particles describe a

retrograde near the surface of uniform half space. It can therefore be

recorded by both vertical and horizontal seismometers.

In this section, we derive expressions for the propagation of

surface waves along a plane horizontal boundary separating two

homogenous perfectly elastic media in welded contact and apply it to

a situation where Rayleigh waves exist.

Fig 2.7 Two media separated bv a horizontal boundaw in welded

contact.

In fig 27, MI extends upwards infinitely while M extends downwards

infinitely.

Consider a wave travelling in the direction ox in such a condition that

(1) The disturbance is largely confined to the vicinity of the boundary.

(2) At any instant all particles in any line parallel to oy have equal

displacement.

The first condition shows that it is a surface wave while the second

condition shows that it is a plane wave. Therefore all partial derivatives

w.r.t.y are zero.

The assumptions shows that the components of displacement u, v and

W satism Newtons law of motion given in terns of displacement in 2.14,

2.15 and 2.16 hence from 2.26a we see that, u, v and cl> in medium M

hence

we then have

substituting for u and o in terns of potentials (equation 2.26a) we

have

From equation 2.67 we have

From 2.68 and 2.69, equation 2.14 becomes

The above equation is satisfied if the following relations hold in medium M.

similar relations hold for M1 with al, Pl and pl

To solve the above equations we put

+ = f (z) exp {ik ( x-ct)} ............... (2.74)

v = g (z) exp {ik (x-ct)} ............... (2.75)

v = h (z) exp {ik (x-ct)} ........... (2.76)

for medium M. similar relations hold for medium M1 with f, g, and h

replaced with fl, gl and hl. This will lead to a particular solution

corresponding to a group of SH waves of wave length 2 d k travelling

with speed C.

introducing r, s, rl and sl where

substituting 2.74, 2.76 into 2.71 and 2.73 in a typical case for the medium'

M1, we obtain

but v = hl (z) exp {ik (x-ct)}

differentiating v w r t to t we obtain

6v = (-kc) hl (z) exp {ik (x-ct)} - 6t

s2v = (ik)2 h (z) exp {ik (x-ct)} .............. - (2.79) sx2 s2v = k2 c2 hl (z) exp {ik (x-ct)} ........ - (2.80) st2

s2v = - . hl (z) exp {ik (x-ct)} 6z2 8 2

comparing 2.78 and 2.80 we have

k2 c2 hl (z) exp {ik (x-ct)}= p2 {- k2 hl (z) + d2 hl (z) }exp ik (x-ct} &-

............ d A l + (z) hl k2(& 1 ) = o (2.81) d 2 p2

+hl P Sl2 = 0

cb2 solving we obtain

@+ hl Ps12) h1=0

The general solution is

hl p) = Cl exp ( -ik sl z) +Fl exp (ik slz) ......... (2.82)

for the effect to be essentially a surface one hl (z) must diminish

indefinitely with increasing distance from the boundary. This will be

the case if hl (z) contains an exponential factor in which the exponent

is real and negative hence s, r and z are inaginary. Also constants

corresponding to C1 must vanish in medium M1 as those

corresponding to F1 vanish in medium M.

The form of solution in M is therefore

4 = A exp {ik(-rz + x - ct)}

w = B exp {ik(-sz + x -ct)}

V = (exp (ik (-sz + x -ct}

The solution in M1 is of the form

4 =Dl exp {ik (rl z + x -ct)

w = El exp {ik (rl z + x -ct} ........... (2.85)

v = F1 exp {ik (sl z + x -ct} ........... (2.86)

where A, B, C, D, E and F, are constants and r, s, rl and sl are all pure

imaginaries.

The boundary conditions are that displacement at boundary surface

are continuous at all times and places. The stress across boundary surface is

continuous at all times and places

In medium M we differentiate 4 wrt x and wrt z in equations 2.83

and 2.84, then add to obtain at t = o, z = o, x = o

U = Aik - Bisk ... ... ... ... .. (2.87)

In medium MI, similarly using 2.85 and 2.86 at t= o, z = o and x = o

we obtain u = Dl ik + El ik sl . ... ... ... ... ... (2.88)

Equating 2.87 and 2.88 for continuity of displacement

For continuity of o at boundary we have

-Aikr-Bik=D1ikrl-El ik

for continuity of v we have c = F1 ........ . . ........ (2.92)

considering continuity of stress, the stress components involved are P,, P,,

and P, using the stress - strain relation

Pij = + 2pe ij

we obtain in medium M

pzz. = p ( 2 a -& +&) . . . . . . . . . . . . . (2.94) 6z6x 6x2 62

- Pzz - P& ... ... ... .... (2.95) 6z

Substituting from 2.83 and 2.85 into 2.93,2.94 and 2.95 we obtain after

solving, at t = o, z = o x = o

pm = - I Z ~ { h ( 1 + ? ) + 2 ~ ? ) - 2 p ~ P s ... . .. . .. ... . (2.96)

similarly for medium M1 at t = o, z = 0, x = 0,

- PZ - - IZD~ (hl+hl? + 2p1 1: )+ 2p1 E]I? sl ... ... .. . ... (2.97)

using

a2 = h+2p and p2 = p/p P

equation 2.96 becomes

from equation 2.97, we have in medium M1

Equation 2.98 and 2.99 we have for continuity of stress

.......... (2.100)

Similarly,continuity of stress P, in M and MI we have

[ - 2 r ~ - ( l - S ~ ) ~ ] p2 p = [2rlD1- (I-S21)~l] p2 pl

for continuity of stress p,, we have

-pCikS = p1 F1 ikSl

or -SC p2 p = s1 F~ p12 pl ............ (2.102)

since S and Sl are both imaginaries, therefore C and F1 have to be zero for

equation 2.102 to hold. Thus there is no coml onent V of displacement

which shows there is no SH waves.

Rayleigh waves occur when one of the boundaries correspond to a

vacuum and we have a uniform half space. There is no SH wave. In the

absence of stress over the free surface, we equate the other components of

displacement to zero hence 2.100 becomes

{ a2 (I+?)- 2 p 2 ) ~ + 2~ 2~~ = o .............. (2.103)

and for stress 2.10 1 becomes

2rA+(l -s2 )B = o .............. (2.104)

From 2.103 we have

and from 2.104 we have

hence

using Equation 2.77 in which r and s are pure imaginaries with the

bracketed roots being less than one, hence factors under the bracketed

roots become real and positive. Using this 2.106 gives on

simplification

(2- c2l4 = 16 (1-c2 2)( (1-c2) .............. (2.107)

p2 a2 p2 2 2 on expansion and dividing through by C / P we obtain

The velocity c of Rayleigh wave cim be determined fiom 2.108 in its

relation with aand (3 . The equation has two real roots of C ~ h k h lies between zero

and f! under the codition that r and S are imaginaries. This be

found if we substitute the value C = f! and C = 0 on left hand side of

equation 2.108. Tnis type of surface wavz is pohrised with particles

of thz medium moving in vertical plane parallel to the direction of

wave motion. The velocity is less than that of bodily elastic waves in

the s k e medium. During the passage of Rayleigh waves, particles of

ground surface describe an ellipse in re trogade. It is refered to as

38

groundroll. Surface waves are suppressed during acquisition and

processing of seismic reflection data.

The seismic wave theory enables us to understand the

propagation and reflection of different types of seismic waves. This

leads to construction of ray paths geometrically to understand

reflection on plane horizontal and dipping surfaces.

2.3 Geonletrv of sesimic reflection ray Paths

2.3.1 In trodwction

In seismic method of data acquisition, the source wave field

propagates down into the subsurface. It is reflected at the geologic

boundaries. The reflected energy propagates back to the surface. It is then

recorded at the detector positions. The seismic response is determined by a

mixture of propagation and reflection effects. The propagation of primary

waves depends on the physical properties of the subsurface. The regection

depends on the local variations in the density. The subsurface information is

then derived from the reflection. The amount of energy reflected depends

partly on the angle of incidence of incoming wave field. In pre-stack

seismic inversion technique, determination of propagation free angle

dependent reflection is achieved. This information is lost on stacked data

(Berkhout 1987).

The use of geometrical optics is made here to relate arrival time to

offset distance. This is used in obtaining an expression for depth to the

reflecting interface.

' 2.3.2 Single horizontal reflector I

Fig.2.6a. Reflection from a s i n ~ l e horizontal reflector separatin~ two

lavers of inf6lnite thickness.

L Fig 2.65. Two layer medium with horizontal plane interface.

In the diagrams above AB represents the reflecting interface, S the

shot point, h is the depth to the reflecting interface, sc is the incident

wave and CR is the reflected wave. Also a, V, t and x represent angle

of incidence, average velocity, two-way travel time and offset

respectively.

It is easily seen that the following relations hold:

Hence

For the direct wave which forms the first arrival time t~ = x/v

............. (2.112)

The depth of the reflecting bed could be determined by measuring the

travel time (to) for geophone located at the shot point.

Thus at x = o, t = to.

Hence from equation 2.1 10

h = %Vto .......... (2.112)

Using 2.1 12 eqrmtion 2.1 10 becomes

Or t =x2+ to2 v2 .......... (2.113)

The ploting t2 against x2, we obtain a straight line graph with slope

1/v2 and intercept time t20.

To solve equation 2.1 10 for time, we use binomial expansion to

obtain

t = (3) [1+ (3) ] = to[l+l/? (3) - l@14+ ............ ] .......... (2.114) V 2h Vto 8 (Vto )

If tl , and t2 and XI, X2 are travel times and corresponding offset then

where At is the move-out. In a situation where geophone is coincident

with shot point, At is known as normal move-out (NMO).

At, = X .............. (2.116) 2v2to

This equation shows that the reflection curve increases rapidly

with offset but decreases progressively with increasing record time.

The value of normal move-out determines whether an event is a

reflection. When At, differs fiom the calculated value using 2.116 by

more than allowed experimental error, the event is not a reflection.

Dinping reflector. /

Fig. 2.7 Two laver ;medium with dipping interface.

The figure illustrates the geometry of seismic ray path for a

dipping horizon. The angle of dip is 8.

For a dipping plane interface equation 2.1 10 becomes

This gives us

Equation 2.118 is a hyperbola in which the axis of symmetry is

the line X = - 2hsin9 instead o f t axis as in a horizontal layer. This

shows that t has different values for geophones placed symmetrically

on opposite sides of the shot point. It is unlike the case of zero dip.

Setting X = o and 2h >> X in equation 2.1 17 and sloving for t, we

obtain

t = (1+x2 + 4h sine) % ............ (2.119) V 4 h2

Approximating only to the first term we have

t 4 to (1+x2 + 4 a i n e ) ........... (2.120) s h2

To find 8, we use hvo geophones on opposite sides of the shot

point with equal offsetsrm is for updip while + AX is for down dip.

tl and t2are corresponding travel times.

tl to [1+ (AX) + 4hAX sine ] ............. (2.121) 8h2

Ah =tl-t2~t~[1+(AX)2-4hd~sin0] 8h2

to ( s ) z 2AX sine h V

Sin0 = ?h VfAt8) ........... (2.122 Ax

The quantity V Atth is cal!ed dip movement. For small angle, hi 0 ;+: Sine and 0 is directly ?roportional to AtS. Also AtS is directly

propsrtional to AX for a given reflector. The largest LY allodfor is

used in accuiately determining the dip.

2.3.4 Several horizontal layers S+--- ----+R

1 Fig.2.tQRavpath ~eometrv for multilayered structure with several

horizonttll interfiices (Robinson and corugh 1955)

For a multi layered structure equation 2.11 3 becomes 2 2 ............. txp = X + t o.n (2.123)

V n m Where x is the offset and n is the layer of the reflector, V .,, is the

root mean velocity for the material from surface to the reflector and t t,,, is

the two-way vertical travel time to nth reflector. From fig. 2.8 it can be

shown that the following relations hold.

foPl = 2Atl v1

fo2 = a:-+ & = 2Atl +2At2 Vl v2

to,3 = 211-+ & 2h3 = 2Atl +2At2 + 2At3 ....... ( 2.126) v1 v2 v3

where b,l, fo2, to,3 are the two-way vertical travel time to the lst,

2nd and 3rd layers respectively and hl, h2 and h3 are the thickness of

each of the:e layers while V1,V2 and V3 are the average velocities of

the respective layers .

Atl, At2 and At3 are the one way increase in the travel time though the

respective layers.

We then use the root mean square velocity to analyse the travel time

along the offset path through the layers (Robinson and corugh 1988).

In fig. 2-18 the root mean square velocity V,, along the path SAR is

given by

for the path SDBER

The path SF H CIGR gives

Hence for n horizontal layers parallel to each other, the root

mean sq-uxe velocity along an offset path reilected at the nth

boundary is

A plot of arrival time versus effset obtained in a seismic section

enables us to determine the root means square velocity. The ms

velocities for reflection paths to n reflectors are calculated from the

slopes of hypenbolic travel time curves. ,

These velocities are then used with zero - offset time to find the

velocities and thicknesses of individual layers .in the structure.

Using equation 2.124

The vertical travel times Atl = to, 1 and At2 through these layers in terms of zero offset time is

At zero offset reflection i12 = i22 = i13 = iZ3 = i33 = 0 hence COS i12 = 1, then from equation 2.132 we have

........ v2, =[&LJ + v22 fb.2 &dl% (2.133)

to.3 - t o 2

hence

- h3 - V3(to.3- fo,2 )

2 for several n horizontal paralIel layers we have

and hn = Vn (kg - bpl)/2 ... ... ..... (2.140)

The determination of layer velocity and thickness is important

in seismic exploration. The sedimentary rocks of the subsurface are

layered, with different layers having different velocities, as a result of

density variation. The reflection time t, for reflections from nth

interface in a multi-layered horizontal structure is measured, then

using the layer velocities, depth to the interface is calculated.

47

CHAPTER THREE

DATA ACQUISITION IN SEISMTC REllECTION

PROSPECTING

3.1 Introduction

Seismic reflection data acquisition method is an application of

echo acoustics. The medium under investigation is illuminated fiom

the surface with acoustic waves. The incident wave field is reflected

at inhomogeneities in the medium. The reflected wave field is

registered at the surface. The detector records information on the

mechanical properties of the medium. This same principle is applied

in ultrasonic medical imaging and inspection of interior of materials

(Berkhout 1987).

In seismic reflection data acquisition the geologic subsurface is

illuminated from different positions on the surfrrce. The reflected

waves are optimally combined to maximinze signal to noise ratio.

T'nere is also optimization or" both vertical and horizontal resolution.

The field pocedures and operation principles of instruments

used in seismic reflection acquisition are described. The survey

methods are treated based cn their use on land and marine operations.

3.2 Can6 reflection survey

Land survey starts with the survey crew. The crew lays out the lines

to be shot and prepares the base map. Positions and elevations of shot points

and centres of geophone groups are determined. A geophone groups ranges

from three to hundreds connected in series or parallel. The output from each

geophone goes into the single amplifier whose output represents the average

ground motion over the group.

Holes are drilled at the shot points where charges are loaded by

drillers. Trucks, tractors or portable drilling equipment is used depending on

the terrain. To reduce groundroll holes are covered with sand after loading.

The recording unit connects seismic cable geophones in turn as

shooters move from one shot hole to the next to operate the blaster. The

recorders signals the shooters before a blast is released. When surface

energy is used, the source unit moves into place and the signal from the

recorder activates the sources to release energy into the shot point at a proper

time. A monitor record is made in the field either in parallel with recording

on magnetic tape or by play back on the magnetic tape. It is used to

determine weathering corrections and to check equipments.

In modern field procedures, holes where rnisfues occur are not

recorded or reshot. The use of comnon depth point (CDP) coverage has

reduced dependence on individual shot records. In CDP there is continuous

profiling because cables and shot points are arranged so that there is no gap

in the data.

1

k c tor

. Fig: 3.1 Common depth point profile

The CDP illustrated in fig 3.1 shows geophone groups evenly spaced

and numbered by their sequence along the seismic line. When shot A is

fired it gives a subsurface coverage from~f)ghahorizontal reflector. When

shot B is fxed it gives a subsurface coverage fiom b 6 hwhile shot c gives a

subsurface coverage from c to i. This process continues down the seismic

line. Each reflecting point is sampled more than once. The multiplicity

ranges fiom 6 to 24 fold. Many traces are recorded per reflecting point. A

reflecting point sampled 6 times has 600% or 6-fold recording hence six

seismic traces from that reflecting point.

When the bed is inclined, the depth point will be displaced up dip

from it's position midway between shot and receiver. The term common

midpoint (CMP) is used instead of CDP.

The traces from each reflecting point are then combined (stacked)

after removal of normal mow out in the subsequent data processing

operation. Stacking chaits are made to keep track of the many traces

involved. From the stacking charts, traces with the same shot poiat, same

offset, same depth point and same geophone are identified. Stacking charts

are useful in making static and dynamic corrections and to ensure that traces

are stacked properly.

The CDP technique is tlierefoie, designed to cancel noise of large

aparent wavelength such as groundroll, multiples and random noise

regardless of it's origin. This is because as with noise cancellation by means

of arrays, outputs of geophone groups distributed over a distance exceeding

a wavelength are summed.

Different types of spread ixe employed in seismic data acquisition.

The types of spread include split dip, end-on, in-line offset, Broad-L-spread,

cross spread, split dip spread with shot point gap and Broad side-T spread.

This is illustrated in figure 3.2.

(a) Split dip spread xxxxxxxxxxx xxxxxxxxxxxx 61

(b) Split-dip spread with shot point gap 1 12 13 24 XXXXXXXXXXXX (.) XXXXXXXXXXxx

1 24 (c) Brad-L-spread. Xxxxxxxxxxxxxxxxxxxxxxxx

(-1 1 24

(d) In-line off set spread. Xxxxxxxxxxxxxxxxxxxxxxxx (-1

1 24 (e) End-on spread xxxxxxxxxxxxxxxxxxxxxxxx (.)

I (.) W ( f ) Broadside-T spread xxxxxxvxxxxxxxxxxxxxxxxx r* X X x

(g) Cross spread xxxxx~~xxxxx I X

x 1%

. .

33 Fig 3.2 Types of reflection spread (Telford et a1 1976)

In split dip spread,shot point is located at the centre of a line

regularly spaced geophone groups. The disadvantage of this is that

when shot point is close to geophone, it gives rise to noisy trace. For

end-on spread, the shot point is located at the end of the line of active

geopho~e groups.

In Broad side-1 spread, the shot point is located at a point

normal to the cable at one end of active part while in broad side T, the

shot p0ir.t is opposite to the centre of the line of geophone group.

Both in-line and broad side offsets pepnit the recording of one to two

seconds of reflection energy before the groundroll energy arrives at

the spread. Cross spread consists of two lines of geophone groups

roughly placed at 90 degrees to each other and are used to record 3-D

dip information.

3.3 Land survey equinment

Land survey equipment can be classified under drilling, energy

source and recording. For dynamite source, holes are drilled with

rotary drills which are mounted on a truck bed or on a tractor or

amphibious vehicles. Hydraulic pumps are used in marshy areas.

Explosives are important seismic energy sources on land. Two

common types are gelatin dynamite and ammonium nitrate.

Dynamites introduces impulsive seismic signal into the earth. The

amount of dynamite needed for reflection shot varies from less than

2kg to se-/era1 hundred kilograms. This depends on the lithologic

characteristics of the geolgogic section below the shot and the depth

of penetration desired. It's drawback is the cost of drilling holes and

danger to human health. The efficiency of energy transmission

depends on the material, it's moisture content, charge size, hole depth

etc.

Vibrating sources are used to put signals which persist for many

seconds into the earth. An example is vibroseis. Energy is introduced

into the earth over the entire range of seismic frequencies. The

efficiency of the transmission depends on the nature of the subsurface

material. The mzin disadvantage is that the frequency content of the

signal introduced into the earth is not subject to control . Weight

dropping acd land air gun are otiier non dynamite sources which are

used.

Vibroseis data posses a certain noise known as harmonic ghosting by

which a vibrator earth system introduces a frequency that is twice the

fundermental frequency being sent out.

The main instrument used in detection and recording of seismic

energy is the geophone. The other recording equipments include

amplifiers, tape recorders, and computers. The entire recording

process in the field is controlled using computers. I t is also used in

monitoring field operations. The computer is also used for work

station processing and interpretation of 3-D data. The geophone is in

direct contact with the earth it detects aid converts ground motion

into electric signals. The modern geophone is an electromagnetic

instrument. The voltage generated in the geophone is directly

proportional to the velocity of ground motion.

According to sheriff and Geldar-t ( 1 983), a geophone coil in

motion is acted upon by three forces. These are restoring force of the

springs, the force of interaction between the permanent lnag~letic field

and the magnetic field of curfent and the frictional force.

Using Newton's second law of motion, we have that

where x is displacement of the surface and geophone,' x, is

displacement ol'geophone coil relative to permanent, magnet I current

in the coil, z is the mechanical damping factor, s is spring constant, f

is force stretching spring through distance Ax, m is mass, r is radius

and n is number of turns of coil whilc ki is force on coil due to

current, R is resistance, L is inductance.

................. K = 2 n m H (3 3

e.m,f induced in the coil = - d$ /dt (d$ /dxc) (dt)

Differentiating 3.1 and substituting for d ~ J d t the geophone equation of motion becomes.

For a geophone output to be independent of frequency, L must be

equal to zero. However L is a assumed to be negligibly small hence

where dildt represents damping. At zero damping, system becomes

simple harmonic with natural frequency V, given by 'h

Vo=!& = (l) (s3 ............. 27~ 27t m (3 3

with damping we have

............. where Zho, = (dm + K ~ I ~ R ) , h (3.9)

being damping factor.

Equation 3.8 is for damped motion. To get the transient solution, we

set the right side equal to zero.

Assi~ming i=o, di/ dt = IJo al t = o. l ' l ~ e ~ i the soli~tiol~ l~ecomes

for Ii > I (over- clamped)

for 11 = I (critically da~nped) i = Uo/ exp-( {r.o,t)

'I'llcsc: sollllions :IIT I rn~lsic~ll 1)ccarw i avc~lt r~;~lly Oecon~es zero d i~c to

I'or praclical pilrposes [lie geoplio~ie se~lsilivity is, tlcter~nined~

largely by k 11, this iii~plies se~isitivity depe~ids on radius,

nu~l~ber ofttllhs of coil, niagnetic field slrengtli and dampine. 1 11~0.3

Fig.

fiwtor (sheriff and Gcldeart 1983) ' '

These solutions are sllow~l i n fig. 3 ill t e rm of resoliant period TO for

clifl'erenl tlanlping factors 11. For 11 > I, the currellt starts to build up

becar~sc of the sidi faclos, but the11 decreases as the exponential factor

begins to dominate. When 11 < I , llle outpi~t is a clamped sine wave

aid successive peaks occiu at i~~tervals. For 11 - I , the critically

damped case, the output just Sails to be oscillatory.

2 I \ '1'0 =27~/{(00(l-h ) , . . . . . . . . . . . . . . . (3.13)

and ratio of the successive peaks is 2 H iJin +1= exp [2nh (1- h ) ]

where

6 = In(in/in+l-) =21~h(l-h2)"

By measuring 6, h can be obtained when h < 1. To obtain the

geophone response to a driving force, assume that it is subjected to a

harmonic displacement such that the velocity dddt = Vo cosot, then

X = (Volw) sinwt,

d2X/dt2 = - ~ V O sinot, d3x/dt3 =-02Vo cosot.

hence equation 3.8 becomes

d2 i/ dt? + 2hqdiI dt +&t = (-a2 KVOIR) cosot . . . . . . . . . .. (3.15)

The solution of equation 3.13 has two parts. The transient solution is

given by equation 3.12 to 3.14. The second is the solution

representing the forced motion of the geophone resulting from motion

of the ground.

i= (Volz) cos (o t+y) 2 'A where z = @w2kw2) [{ 1 -(w/wo )2}2 + (2ha2/+w0) ] . . . . . . . (3.16)

tany = (2wh/oo) { ( o ~ w , ) ~ - 1) ... ... . (3.17)

Thus the amplitude of i for a given geophone depends on Vo,. o/oo

R, k anC h. When o + a, z -+ R/K and the amplitude of i

becomes i, = Vo KR.

One of the most important characteristics of a geophone is

output voltage per unit velocity of the case. The sensitivity called

geophone transudation constant r is defined by

r = amplitude of output voltage 1 amplitude of geophone velocity

Assuming the geophone is connected to an amplifier with an

infinite input impedance, the output voltage is the voltage across Rs,

which is the shunt resistance. Using equations 3.6 and 3.12 we get

r = Rs(Vo1z)No = Rslz

= K(Rs/R) F(o1oJ

where F (olo,) = o when o = o

= 1 wheno=oo

= %h when o = o,

For practical purposes the geophone sensitivity is determined

largely by K and h, This implies that sensitivity depends on radius and

number of turns of coil, magnetic field strength and damping.

The signals from geophone groups are fed into an amplifier.

This amplifies weak signals. Also signals are compressed to useful

range of amplitudes. The goephone outputs are also filtered to

enhance signal to noise ratio. There are digital and analogue

amplifiers. Seismic signals are generated and recorded in analogue

form beforc Cigitization. In analogue, signal is expressed as a

continous function respresenting the amplitude of the signal as a

function of an independent variable w i c h is often time. Continuous

signal is registered on a magnetic tape having a magnetization

continuously varying along the tape. Modem recording is either by

frequency modulated or pulse- width modulation technique . In

frequency modulation (F.M.), amplitude of output from the amplifier

modulates the frequency of a 3000HZ carrier signal over the seismic

range (10 to 300HZ). Signal is extracted upon play back by

demodulation. In p$e-w& or amplitude modulation (AM), the

signal is impressed directedly upon the tape the magnetization of the

tape is proportional to the strength of the signal up to the limit of the

tape's dynamic range.

In digital recording, the signals from each detector group are

fed into an amplifier (one for each group) using binary gain amplifier,

in which the gain changes in steps of a factor two. The recorded data

is then multiplexed, wliicli converts signal magnitude into a binary

number transcribed onto a magnetic tape. A binary sequence is

obtained after multiplexing and digitization. Sampling is done in the

sample and hold unit. The output from this unit goes into analogue to

digital converter. Tlie signal wliicli emerges is in the form of pulses

having uniform height, The signal passes througli the buffer and

format controller before it is recorded on digital tape.

3.4 Marine reflection survey.

Marine reflection survey is carried out on water, the water

being deeper than about 10m and needing sizable ships, about 50111 in

length. Some land acquisition techniques are applicable to marine

survey. The use of multiple receivers and CDP tecliniqrre is

applicable to marine seismic survey.

In marine exploration, the energy sources introduce a sudden

positive (or sometimes negative) pressure impulses into the water.

The imprllse involves a compression (or rarefaction) of water

particles, creating a sliock wave that spreads out spherically into the

water and then into the earth. When the sliock wave is delayed, there

is an oscillatory flow of water in tlre area around the explosion. This

causes srlbsequent pressure pulses designated as bubble oscillation.

Tlie bubble oscillation determines the properties of the seismic signal

generated by all marine energy sources.

The most widely used energy source in marine survey is the

airgun. This discharges highly compressed air into the water. The

impulsive sources (liydroseis, flexichoc) may be said to be the

converse of the airguns. These initiate a pulse when the hydrostatic

pressure of external water makes the walls of an adjustable evacuated

chamber to collapse on sudden removal of the restraint keeping the

walls apart.

The detectors for marine work are called hydrophones or

pressure phones. They are used 61- detecting seismic signals in

appreciable depth of water. They utilize the phenomenon of

piezoelectricity. This is based on the fact that certain materials

develop electrical charges. When subjected to mechanical stress. The

voltage generated is proportional to the instantaneous water pressure

associated with seismic signal. The pressure is proportional to the

velocity of tlie water particles set into motion by the signal.

The material used in hydrophones is mainly barium titanate. It

is either in disc or hollow cylindrical form. Tlie cylinder form is

closed at both ends with brass caps. When subjected to bending due

to a pressure wave, the outside and inside of the hollow cylinder will

become oppositely charged. The voltage between the surfaces is the

output of the liydroplione which is proportional to the velocity of the

surface. Each hydropone consists of up to 50 series of coupled

elements. Special waterproof cases are designed to permit planting of

moving coil hydropl~ones in marshy ground.

Tlie hydrophones are contained in a tube several kilometers

long, called streamer. The streamer is reeled off and positioned in tlie

water astern- a ship, while the ship is still arriving in the area of work.

This is followed by the seismic source units; shots are fired and

recordings made w h i k the ship is moving.

This is necessary as otherwise the trailing streamer cannot be

kept in position. Detailed monitoring of data quality is not possible

because of the ship's motion. Work proceeds generally on a 24 hour

basis but not all time can be spent shooting. A major problem in

marine operation is to know the ship's position at any instant. Nearly

all energy sources in common use are towed at a distance far enough

from the stern of ship to avoid the possibility of damage to the ship's

hull. The distance between the source and nearest receiver group is

about 30m.

Drifting away (feathering) of cables fiom the line of motion of

the ship and position of hydrophones occur due to cross currents.

This causes detoriation of data in CDP stacking. The tail bouy is

difficult to see but it is designed to be observable on radar screen.

The tail bouy contains a light for visibility atuight so that it's position

will always be known.

3.5 3-d reflection survey rlesim and data acqoisitim

The main aim of 3-D survey is to obtain a three dimensional

migrated wave field. The success of the migration depends on the

stack-quality as well as the accuracy in velocity estimation. The

subsurface is real 3-D, the more complex the subsurface is the greater

the need for 3-D exploration. Better imaging of the subsurfBce can

only be achieved by higher dimension survey and migration. In

moderate complexity of subsurface, 2-D migration is inadequate 3-D

survey is important because migration requires adequate spatial

sampling of the seismic wave field.

3-D surveys are canied out in such a way that the data to be migrated

are obtained in a 3-D volume with closely spaced traces in both in-line

and cross line directions. The detailed overage provides a more

detailed and reliable interpretation.

Land 3- D surveys are commonly acquired with the swath

shooting techniques. In this, the receiver cables are laid out in

parallel lines and shots are positioned in perpendicular direction. The

line spacing in 3-D survey may be 50m unlike 2D which may be

Z O h . The dense coverage in 3-D requires a good knowledge of shot

and receiver location. This shooting pattern provides a wide r a n g of

azimuthal coverage, which is important during velocity analysis.

Swath shooting is economical. The receiver cable sections are moved

up from the rear of the swath to the forward end while shooting

continues. Once one swath is completed, another one parallel to it is

recorded and this procedure is repezted over the entire survey area. It

is usehl in- the entire survey area. It is useful where there is

environmental or topographic restriction. Coverage over a

topographic high can be achieved by shooting vound it. A complete

loop is made with shots and receivers located on the loop.

The size of th2 survey area is not only dictated by the ,*--,-

extent of the target zone in the subsurface, but also by the aperture

size required for adequate migration of the 3-D seismic data volume.

This inctecses the arreal extent of a 3-D seismic survey.

A cell is a rectangular area on the earth's surface and constitutes

the basic element of a grid that covers the entire area of the 3-D

survey. A common-cell gather coincides with the CMP gathers for

swath shooting.

Typical size of a cell is 25x25m for land surveys and

12.5x37.5m for marine surveys. The gathers are used in velocity

analysis and the cell stacks are generated.

A marine 3-D survey involves shooting a number of closely

spaced, parallel 2-D lines (line shooting). In the shallow water

environment, the swath shooting technique for land acquisition is

preferred. The direction in which the ship sails is called in line

direction, the direction perpendicular to it is called cross line. The

receiver cable is subjected to a certain amount of side ways drift

(feathering) from the ideal streamer line due to cross currents. This

causes problem of travel time deviation from a hyperbolic move out

within a common cell gather in 3-D surveys especially where there is

a dipping a event.

The common practice in marine 3-D shooting is to use two ships.

Each ship is equipped with both a source array and a recording cable.

The two ships travel abreast a few hundred meters apart. The two

ships alternate firing their source arrays. In the simplest configuration

for such bvo ship operation, three subsurface profiles are recorded

during the traverse of a line . Subsurface coverage produced by each

ship would be one and one-half times as much as that obtained by the

one ship acting alone. The use of two ships reduces the cost of the

survey.

CHAPTER FOUR

PROCESSING AND INTERPRETATION OF SEISMIC

REFLECTION DATA

4.1 Introduction

The analysis of acoustic waves reflected fiom different rock

layers in the earth's subsurface is the objective of exploration

seismology.

The acquired data is analyzed to obtain information on the

subsurface despite it's complexity. This could have been easy if the

wave suffers only reflection while passing through the earth and it

occurs only on the surface of the geologic boundary. However the

incident wave is affected by absorption, high stress near the shot, peg

leg multiples, diffraction and sequence of reflections from various

layers. 'l3e result is that the reflected wave received has to be

processed to obtain the primary reflection.

Generally the information that c m be obtained from reflection

depends on, (a) The propagation properties of absorption and average

velocity (b) The reflectivity properties of density and elastic moduli.

In each geologically related layer, the average velocity parameters and

the reflecting boundaries have to be delineated. The information

obtained must be clear and precise to give reliable interpretation.

4.2 D:~ta ~ r o c e s s i ~

The data obtained from the field is taken to the processing

centre. At the processing centre the appropriate time shift is made to

correct for static and dynamic variables. Filtering is done to enhance

signal to noise ratio. Using velocity estimates, velocity analysis is

carried out and the stacked sections are produced. The data is

migrated for repositioning in order to align with the position in the

subsurface. The processing stages involves use of signal theory and

mathematical formulations. These are used in obtaining the time

shifts to produce time seismic sections.

The various mathematical theories and stages of processing

include, Fourier transformation, convolution and correlation.

4.2.1 Fourier transformation

The data presented in seismic section can be viewed in two

ways. In one way we study the variation of amplitude of output with

time, in this case we are operating in time domain. The same seismic

record can be viewed as the superposition of many sinusoidal waves

of differing frequency and this corresponds to the fi-equency domain

(sheriff and Geldart 1953).

A function can be transformed fi-om frequency to times domain. Also

the inverse transform can be carried out.

Tlle Fourier series representation of a well behaved function g

(t) of period t is given by

g (t) = C a. Pvnt

where

in the limit of T infinite, we have

a3

g (t) = G (~)ej '"~ ' dv - 00

CO

or G (v) = 1 g (b)ee2KVt dt ............. - CO

(4.4)

The h c t i o n G(v) is Fourier transform of g(t).

Q(t) is in verse transform of G(v)

9 0 ) ct G W

Generally

G(v) =

Hence

g ( 0 =

where

CO

1 A (v) cos [ 2xvt + y(v) ] dv, .... (4.6) - CO

A (v) represe~ts the amplitude spectrum while y(v) represents

the phase spectrum.

a3

R(v) = 1 g(t) cos2xvt dt ......... (4.8) - a3 a3

- x ( v ) = j g ( t ) ~ i n h v t d t .......... (4.9) - c0

X(v) and - X(v) are the cosine and sine transforms respectively.

4.2.2 Convdu t : o ~

Is a time domain operation in which each element of an input

function is replaced with an output function scaled according to

magnitude of input element. The outputs are then superimposed.

Considering a linear system, the output of data sampled at

regular intervals can be calculated if we know the impulse response.

Using 6t as impulse response of discrete data and 6 (t ) as impulse

response of a continuadata, and for successive sampling intervals.

6t - I System f t = [ % , f l , f l ..... J

at t = n, unit impulse, we have

kdt __+ System ____+

............. (4.11)

For series of sampled values, the input can be represented by unit

impulses multiplied by appropriate amplitude factor.

..... Let& = [f = [f,,f 1, f ] be the impulse response of o~ tpu t filter.

and

gt .... - - [g,,gl, g 2 I.. .be the input response.

ht = f i * g t = 5:fk g(.k = Z g l r f t l

for two continuous functions

00

h(t) = f ( t )*g( t )= l f ( r g ( t - r ) d r ............. (4.13) -00

The convolution theorem states that the fourier transform of the

convolution of two functions is equal to the product of the transform

of individual functions.

pt ++F (v) = lF(v) 1 e jy ' (") ............ (4.14)

gt c * ~ l ( v ) = IG(v) ejyg (") ............ (4.15)

............ Ft 'gt - IF($ k ( v ) h J { yf(v)+yg(v) I (4.16)

F (v) and G (v) are amplitude spectra while yf (v) are the phase

spectra

Convolving two sets of data in time domain gives an effect in

frequency domain. The effect is the multiplication of their amplitude

spectra and addition of the phase spectra by symmetry.

........... ft gt - F (v) * G (v) (4.17)

Convolution principle is applied in sampling and aliasing. In

and log-to digital conversion continuous signal is replaced with

discrete values. The wave form on seismic record is a result of

successive convolutions of shot impulse with impulse resgonse of

various layers of the earth.

Deconvolution is a process of convolving with inverse filter.

ft * it = & where i t is the filter and ft is the inverse filter.

Deconvolction is used in removing singing effect of water in marine

survey. The propagated and reflected seismic waves undergo

convolution with the earth in various ways. Xn deconvohtion these

effects are removed during data processing.

4.2.3 Correlation

It is a measure of similarity between two different sets of data.

Let Xt and Yt be two sets of data

............ 4.y ( ~ ) = C X tr YkfT (4.18)

r = displacement of Yt relative to Xt . If 4 , (r) has large negative

value, there will be similarity if one set of data is inverted.

one data set is reversed, then convolved with the other set of data.

X, o X(v) = I x (v) le jv ............ (4.20)

~ ( 3 o Y(V) = I ~ ( v ) le jw ............ (4.21

X- , o X(v) = 1 x (v) le jv ............ (4.22)

$xy (T) ff X(y) y(v) = k(v) I k(v) le ' [v(x) - ~ ( v ) 1 ..... (4.23)

Cross correction in time domain gives in the frequency domain

an effect which is same as multiplying the complex spectrum of

second data by conjugate of the complex spectrum of the first set.

Forming the complex conjugate involves only reversing the sign of

the phase, hence cross correlation is equivalent to muiltipying the

amplitude spectra and subtracting the phase spectra.

Auto correlation. In this case one set of the data is corrected with

itself. It is a measure of repetitiveness of a function.

Auto correlation has it's peak value at zero time shift. If auto

correlation has large value at some time shift not equal to zero, it

indicates the set tends to be periodic with At. For continuous

functions in cross correlation.

a

............. oxy ( 3 = I X ( 0 Y (t+r) dt (4.25) - a3

for auto correlation it be becomes a3

4 (T) = x (t) x ( t + ~ ) dt ............. (4.26) - CO

At zero shift, auto correlation value is called the energy of the trace.

@a (0) = E X; . . . . . . . . . . . . (4.27) k

Correlation functions are applied in processing of reflection data. In

vibroseis. It is also used in sign-bit recording and ~nultichannel

coherence.

4.3 Processing sequence

The use of digital recording and computer processing has

introduced a routine sequence in processing of seismic data. Primary

stages of data processing are filtering, deconvolution, velocity

analysis, stacking and migration, secondary processes are applied at

each stage and that depends on the processing centre.

4.3.1 Filtering

Frequency filtering is carried ortt to attenuate noise whose

frequencies fall outside the signal range. It improves record quality.

Velocity filtering is used in removing organised noise particularly

groundroll from shot record. It can also be performed on Pecords

sorted into shot gather, receiver domain and common midpoint gather

respectively. Filtering in shot domain is preferred using f-k because

signal and noise are separated.

4.3.2 Demultiplexing

Field data is recorded in tnultiplexed mode. It is demultiplexed

in the processing centre. The data is sorted into columns of samples.

The samples i n one column are followed by those in other channels.

Demultiplexing is seen as transposing a big matrix. The columns of

the resulting matrix can be used read as seismic traces recorded at

different offsets from a common shot point. This can then be used for

resampling.

Trace editing

This is the removal or correction of any trace record which in

it's originally recorded form may cause detoriation of the stack. These

include dead trace and strong noise out bursts

Gain recovery.

It is a time variant scaling. This is applied on the data to correct

amplitude effects of wavefront divergence. The amplitude of deep

reflections may be so small that it may not be recognised on the

record. The applied coi-rections compensate for geometric spreading,

absorption and transmission losses. Gain functions are applied at

various stages of processing to bring up weak reflections.

4.3.3 Field static corrections.

It reduces the travel times of the various shot point to a

common datum level. It is used in removing near surface effects. The

two corrections applied are weathering and elevation corrections.

Weathering correction is applied to compensate for changes

along the seismic line on raw reflection time. It arises fi-om variation

in thickness and velocity of the weathered layer.

W, = Weathering correction where d, is the thickness of the

weathered layer, V, is the weathering velocity and V, is the correction

velocity.

Elevation correction is applied to correct topographic effect on raw

reflection time due to elevation of seismic sources and receivers on

the surface. El< = elevation of receiver,

E,s = ED-E, v c

Where En is dutum elevation from sea level, Es is source elevation

from sea level and E, is elevation correction. Field statics correction

is the algebraic sum of weathering and elevation corrections. If t,, is

the field statics time and trrIr is the upliole t h e .

.......... tl)=EcS+Ecl<- t r ~ r 1 = 2 E d - @ , + E ~ ) - - ~ I I I I (4.31)

v, 4.3.4 Deconvolution.

Deconvolution is used in removing filtering effect introduced

by the earth during propagation of tlic wave. The effective source

wavelets contained in the seismic trace are compressed to a spike.

The ideal is that the output h(t) is known and we are to recover the

form of the input signal f(t) before it was modified by the filter.

Suppose the filter response is K(t) a~ld h(t) is passed through it to

recover f(t). K(t) in this case is an inverse filter with respect to

impulse response g(t). The filter response is then cancelled with

another filter. The time domain equation is given by

F(t) = h(t) * L= I#) * K(t) ......... (4.32)

While in the frequency domain it is . . . . . . . . . . (4.33)

F(h), H(n), G(n) and K(n) are frequency spectra of Fourier

transform of the respective Rf), h(t)8$ld K(t) respectively. In

deconvolution long initial wave form of a marine source can be

transformed into a shot wavelet. Land data have an initial short wave

form consisting of shot pulse which is broadened by filtering action of

the earth. Deconvolution brings back the waveform to it's nature

before filtering by the earth.

4.3.5 Common midpoint sortinv.

The purpose of common midpoint (CMP) sorting is to improve

signal to noise ratio by attenuating random noise (sengbush 1953). It

is assumed that the reflection signal on the traces of a CMI) gather are

identical and the random noise is mut.~ally uncorrelated from trace to

trace. The data is transferred from shot receiver cooordinate to

midpoint offset co-ordinate. The three co-ordinates in which

conventional 2-D data exist in space xe time, offset and x co-ordinate

along line of profiling. In stacking, offset co-ordinate is compressed

to zero along midpoint axis. This then gives the CMP sorting. The

traces with same midpoint are grouped together to obtain a CM?

gather. In a horizontal reflector in a dipping reflector they are

different.

4.3.6 Ve!ccity a ~nlvsis/Nrno correction

Normal moveout (NMO) correction is a dynamic correction. It arises

from increase in offset as detector positions are moved farther away

from the source. The initial velocity analysis involves calculation of

normal moveout velocity from measurements of normal moveout

(sheriff 1984). The NMO velocity is the velocity of a constant

homogenous isotropic layer above a reflector which would give

approximately the same offset dependence as actually observed. This

is the value determined in velocity analysis. It is applied to remove

the influence of offset on travel time. The NMO velocity is based on

the small spread hyperbolic travel time. Stacking velocity is based on

the hyperbola that best fit data over the entire spread length. 2

The travel tx time as a function of offset is given by ex = e0 + /v2

At = tx - t,, = (& + 6 V 2 f%- &,where t,, is time at zero offset, At is

moveout, X is offset, V is velocity. These are equations of hyperbolic

trajectory used in velocity analysis.

Application of NMO correction virtually flatten all events

across offset range. Traces are stretched in a time-varying manner

causing a shift in frequency content. This is because it is a dynamic

correction. This mainly affects shallow events and larger offsets.

AElf = Atmd t,,

where f is the dominant fiequency, t, is the vertical travel time at shot- point, X is the offset and V is velocity.

4.3.7 Stnckin~.

Common midpoint stacking is carried out by summing the

events over the offset. It is the combination of two or more traces

together. It is done in different ways depending on the purpose of

stac!&g. Stacking can be used to test NMO correction and to

determine velocities in the subsurface. It can be used to reduce the

amount of processing job by combing adjacent traces.

Traces are normalised after stacking especially in CDP gather, in

which it is divided by the number of traces. In CDP stack the

difference in geometries of primary and ~nultiple reflections is used to

weaken multiples.

4.3.8 Residual static correction

The assumption made during static correction is that tlie travel

path from datum to receiver is vertical. This is not always true. Also

if the crew uses surface sources, only approximate weathering

corrections can be made. This introduces a series of small,

unsystematic errors in the original field static corrections. These

errors are called residual statics.

This correction is applied to the N MO-corrected CMP gathers.

I t is done in a consistent manner on shot-receiver locations (Yilmaz

1987). Tlie estimated residual statics are then applied to tlie original

CMP gathers. It is done in a consistent manner in wliich time shifts

are dependent only on shot-received locations (Yilmaz 1987). Tlie

final stacking is done using improved velocity field.

4.3.9 Migration

Migratiotl is data positioning ad-justment. It moves energy from

it's CMP position to it's proper spatial location. The aim is to make

the stacked section appear similar to tlie geologic cross-section along

seismic line. 111 migration a depth section sliould be obtained from a

stacked section, however in accuracy of velocity estimates makes

stacked sections to be displayed in time. Migration collapses

diffi-actions to focii, increases visual spatial resolution, corrects

amplitude for geometric focusing effects, spatial smearing and moves

dipping events to their true (supposedly) subsurface location,. I t is

regarded as imaging process. The three main types of migration are

kirclioff

summation, finite difference method and Fourier transformation

method. Kirchoff summation combines data found along curves on

the section. Finite difference migrates data layer by layer, while

Fourier transform migrates data which is expressed in terms of

frequency and wave number. Time section migration is appropriate

since lateral velocity variations ;rre moderate.

Migrated seismic sections are used for geologic interpretation.

4.4 Tnterpretation of seismic reflection 'data.

4.4.1 Introduction

The objective of seismic survey and interpretation is to locate

structures which prove excellent hydrocarbon traps. The lithology

and geologic history of the area is derived to form an opinion on the

probability of encountering petroleum in the structures mapped.

Icterpretation of seismic data is the translation of the

information obtained by the reflected acoustic energy into the geology

of the subsurface. It is important to understand the geologic factors

that generate reflection. The orgmic materials which form crude oil

are buried to a depth where temperature and pressure are high enough

for conversion to petroleum .

Petroleum is found in a rock layer. The porosity of the rock

influences the quantity of oil contained in the total volume. Petroleum

is found in a porous rock layer but there must be sealing rock layers

below and above the porous layer which traps the oil. The oil is

prevented by the seal from migrating to the surface.

The information to be extracted for interpretation of the

geology of an area are structural traps, lithology and stratigraphy of

the subsurface (Brown and fisher 1982). These are obtained using

seismic method and are used for evaluation of the subsurface.

Interpretation starts with assembling of the data as tools for

interpretation. These include seismic sections, well log data, velocity-

depth profiles, vertical seismic profiles, synthetic seismogram, other

geophysical data and paleontology studies. The knowledge of

regional geology of the area is vital to obtain a consistent

interpretation.

According to sheriff and Geldart(1983), the interpretation of

seismic reflection data is based on these geophysical assumptions.

The coherent events seen on the seismic records are reflections

from acoustic impedance contrast in the earth.

The acoustic impedance contrasts are associated with bedding which

represent geologic structures.

Mapping the arrival times of coherent events gives the map

showing the geologic structure. The seismic-wave shape ax!

amplitude are related to geologic detail hence reveal the stratigraphy

and nature of the interstitial fluids.

4.4.2 Ch:~ractc?rktics of seismic e-ients.

T ~ P characteristics of seismic events hzlps us to select events

which represent primary reflections. To interpret seismic section, we

pick the strong reflections then obtained arrival time for mapping of

the reflecting horizoas. The following features distinguish events in

the seismic section.

Coherence. This refers to the similarity in appearance fiom trace to

trace of peaks and troughs. The wave produces the same effect on

each geophone hence the wave shape looks more or less alike for

strong events during the interval it arrives at the geophone.

Amplitude standout refers to the increase of amplitude that

results from arrival of coherent events. Coherence and amplitude

standout tells us if the event present is strong or weak. In a seismic

section, the alignment of peaks and troughs represents a layer where

there is strong seismic event resulting from contrast in acoustic

impedance. Character refers to the distinct appearance of the wave

form. It is used in identifying a particular event, for instance event

may be a diffraction or a reflection.

Moveout is the systematic difference in arrival time from trace

to trace of an event. It is the most distinctive criterion for identifying

events. Character and normal moveout are used in identifying the

type of event. Diffractions and refractions have higher normal

moveout than primary reflections. There is a range of normal

moveout for which an event is acceptable as primary reflection.

The presence of oil may cause significant change in reflection

character. Interference may occur also phase reversals take place at

the edges of reservoirs,. There is a spiit of wavelets at the fault

termination. Also gas reservoirs cause high absorption of seismic

znergy. The .howledge of characteristics of seismic events is

important in interpretation of seismic data. It is also important to

know the structural styles and stratigraphic patterns which produce

special characters on seisnic sent' ions.

4.4.3 Hydrocarbon habitats and trap pin^.

Hydrocarbons are trapped due to different tectonic setting and

stratigraphic patterns. In this section we examine various structures

that trap hydrocarbons.

Faults and rock deformation.

Faults are produced by unbalanced stresses which exceed the

strength of rocks. The type of fault depnds mainly on which

component of the stress is greater. Normal faults result when the

maximum compressive stress is vertical and the minimum

compressive stress is horizontal. The dip is of the order 50 to 60

degrees. Reverse faults or thrusts occur when the maximum

compressive stress is horizontal with a fau!t plane dip of order 30 to

40 degrees. When the maximum and minimum stresses are

horizontal, wrench faults occur with angle of about 30" to the

minimum stress direction.

Anticlines, synclines and domes may result when the rock

folds under stress. Anticlines are produced whzn the fold is upwards.

Syncline are produced when the fold is downwards. Domes result

when solid structures of various shapes p ro~ube upwards.

Deformation which creates structures capable of trapping

petroleum is relatively cold defoim~tion. i t tzkes place under

temperature and presswe condit ic ns which are mild. "Cold"

deformation implies that associated fractures propagate in generally

elastically deforming media. According to Bally (1975) this follows

shear failure.

Faults are good oil and gas traps. In most cases the permeable

beds overlain by impermeable bed is faulted against the impermeable

bed. A trip exists if there is a closure in a direction parallel to h e

fault as when there is folding. Hydrocarbons are mainly trapped

upthrown to normal faults. Downthrown faults exist mainly when the

normal fault is associated with rollover anticlines and are listric faults

(Tearpock and Biscke 1991).

The extensional tectonic habitat is one of the principal

petroleum related settings for normal faults. It is a major large scale

gravity slide structure. The normal faults in this category decrease in

dip with depth to low angle fault. The often become bedding plane.

The major listric fault is refereed0 to as master fault. These listric

growth faults are syndepositional. The exhibit significant increase in

stratigraphic thickening in the down thrown block or hanging wall.

This type of stratigraphic thickning indicate movement along the

surface of the fault during deposition. These faults are

contemporaneous because it was occurring when adjacent sediments

were being deposited.

According to supper et a1 (1984) growth faults are often

associated with anticlines called rollovers. There develop as a result

of bedding on the handing wall fault block. The rollover anticlines

are important hydrocarbon traps associated with listric growth faults.

Hydrocarbo accumul~tion is expected to occur at the crest. The

structural style of Niger delta is dominated by growth faults with

associated rollover anticlines.

Wrench faults are high angle vertical strike-slip faults. They

from under horizontal compression. The primary hydrocarbon traps

associated with wrench faults are anticlines that saddle the wrench

system. The faulting may be normal or reverse. Wrench faults are

good hydrocarbon traps because they form early and coininonly

develop large closures.

The compressional tectonic settings are good hydrocarbon

traps. The hydrocarbon is mainly trapped by hanging wall anticlines.

It might be a fault propagated fold, fault bend fold or duplex

structures. Synelines are not good traps as the hydrocarbon migrates

from the sides (Hindle 199 1). Intrusive salt structures have extremely

varied and complex geometry resulting in numerous types of

hydrocarbon traps. They include simple domal anticlines, graben

fault traps over the dome, porous cap rock (limestone or dolomite),

flanks or pinchouts, traps beneath on overhang, traps against the salt,

unconformities, fault traps down thrown away from the dome and

traps towards the dome.

Unconformities alone or in combination with faults or

stratigatpliic anomalies such as sand pinchouts series as excellent

hydrocarbon traps. An unconformity is a surface of erosion or non

deposition that separates strata of different ages. It's development

involves several stages of activity. The initial sediment is deposited,

then subaerial erosion or non deposition takes place hence there will

be a deposition of younger sediments above the unconformity. They

exist in many geologic setting but occur mainly in steeply dipping

structures. The nature of sediments above and below the

irnconformity are not parallel to one another. The rocks below dip at a

steeper angle than those above. Impedance contrasts occur hence

unconforrnities are good reflection.

Stratigraphic traps.

Stratigraphic concepts are important in the study of seismic data

(Brown and fisher 1982). A classification of stratigraphic traps is

given by sheriff and Geldart (1983) as modification of the table of

stratigraphic traps from Rettehouse (1972). The classification is used

below to show various types of stratigraphic traps.

Classification of strntigrnvhic

Not adjacent to unconformities.

facies-change traps involving current transported reservoir rock.

Folian (dunes and sheets)

Alluvial fan

Alluvial valley (braided stream, channel fill, paint bar)

Deltaic (distributary mouth or finger bar, spit, tidal delta or flat)

Non-deltaic coastnl (Seach, barrier b:u; spit, tidal delta or flat)

Shallow marine (tidal bar, sand belt, washover, shelf edge,

shallow turbiditc or wimowing).

Deep marine (marine fan, deep turbidite or winnowing)

Non current transported reservoir rock

Gravity (slump)

Biogenic carbonate (shelf-margin reef, patch reec algal build-

up or blanket)

Diagenetic traps

Change from Non reservoir to reservoir.

Replacement and leached (dolomitized

Leached

(Brecciated)

fractured

Change from reservoir to non-reservoir

Compaction (physical or chemical)

Cementation

Adjacent to unconfomities.

Traps below unconformities

seals above uncornformities

subcrop at unconformities

Topography (valley flank or shoulder, dip-slopes escarpment,

valley, beveled).

Seal below unconformity

mineral cement

Tar seal

Weathering product

Traps above unconformity

Reservoir location controlled by unconformity topography

on two sides (valleys, canyon, fill)

on one side ( M e or coastal cliff, va!ley side).

Transgressive.

4.4.4 Evidence of fmd:'nz on seismic sec~on .

The fallowing are evidences of faulting on a seismic section (sheriff

1952).

(1) The abrupt ternination of reflections especially on migated

data.

(2) Sharp change in amplitude caused by diffraction to a fault

termination.

(3) Changes in actual dip associated with the fault which may

flatten or deepen depending on the nature of the fault. Changes

in dip rate occur near the fault and sometimes at appreciable

distance away from the fault. The changes include drag and

rollover.

(4) Distorted dips seen through the fault may be an evidence of

faulting. A fault juxtaposes different parts of the earth.

Velocities differ along the fault line. The raypaths passing

through the fault plane are bent due to change of velocity to

different directions. This distorts the apparent dip for events

below the fault plane in an irregular manner.

( 5 ) Cut out of coherent events bsneath the fault plane takes place.

We normally recognise reflections by seeing same phase on a

xdjacent seismic traces, it adjacent ray paths encounter dif'crent

velocity contracts at the fault and are bent by different amounts,

the distortions become so rapid. This destroys coherency of

reflections.

(6) Shift of horizon along the fault pim. There is a shift of the

overall reflection pattern dong the fault plane.

These are used in interpreting faults on seismic sections. Along

the fault plane reflections with distiact character are offset on

opposite sides of the fault. In some situations distinctive

reflections cannot be correlated across the fault p ix : except

when the package of reflectioas is used. Fault plane reflections

occur and may not be reco,or,ised especialiy reflection from

steeply dipping fault planes. This is because the their evidence

is far from fault plane and the character may not be constant.

Faults cause misties of seismic lines. When we follow an event

around a loop of a seismic grid, misties may result due to faults. The

faults. The faults crossed may have different throws at different

locations or the throw may change laterally resulting in misties.

4.5 Sesimic stratigraphy.

According to Brown and fisher (1982), the integration of

seismic data with stratigraphic concepts is an advancement in basin

analysis. Seismic facie analysis is carried out using three dimensional

data and computer. The basic assumption is that seismic reflection is

inferred to represent an isochronous surface except where there is an

unconformity. Isochronous reflections may pass through many facies

identified by change in amplitude and frequency.

There are two approaches to seismic stratigaphy.

(1) A physical modeling of lithic and fluid composition utilizing

computer analysis of velocity, ampiitude, frequency and other

wave parameters.

(2) Stratigrapiiiclfacie approach using reflection szctions and

geophysical well logs. This is used in the interpetation of

lithohcies and subsequently depositional sequence.

Recognition of depositional systems on seismic proiiles permit

mapping of potentizl reservoirs, source and seal deposits. This

provides a basis far reconstructing the structural, depositional

and erssional history of the basin.

Prirnary reflections are in response to significant impedance

changes except for fluid contacts such as oil-water contact and

gas-water contact.

Unconformities are diachronous, though strata between them

constitute time-stratigraphic units. Stratal surfaces represent

conformable changes in depositional regime. The seismic response

to them is chronostratigraphic reflections. Reflections confonn with

collective configurations, continuities, velocity-density contrasts and

other physical properties.

Seismic stratigraphy is a direct detection technique. It is based

on the effect of porosity and fluid content on density and velocity.

The diagnostics used in interpretation of hydrocarbon reservoirs are

bright spots, phase reversals and variance of reflection dips fiom

structural dips in gas-oil, oil-water and gas-water contacts. This

technique is amplitude dependent hence amplitude conservation

processing is used during processing of the 3-D data.

4.6 Data wed in seismic Interpretatinn

It is pertinent to describe briefly some vital geophysical and

geological data used in seismic interpretation. There are other types

of data used for detailed geologic interpretation of seismic data. The

fallowing data are required, vertical seismic sections acquired from

the area of s w e y , well log data fiom a well within or close to the area

of survey, vertical seismic profile, synthetic seismogram, base map of

area of survey, and depth-velocity profile.

4.6.1 Seismic sections

Vertical seismic sections are obtained fiom the 2-D or 3-D

seismic data acquired fiom an area of survey. The acquired field data

is taken to the processing centre where the seismic sections used for

interpretation are obtained. Each seismic section gives the data for a

line of profiling. There are lines were shot along the strike while the

other lines shot along the dip to the horizon. This forms a grid of lines

covering the area where data was acquired. Migrated seismic sections

are used for interpretation as it presents a better image of the

subsurface.

4.6.2 Vertical seismic profile (V.S.P)

This is a seismic section made with shot on the surface while

the geophone positions were lowered down the hole usually a well.

A V3.P can be used to identi& an event on a seismic section. A

depth in the well can be located on the first break curve and reflection

at that point on the VSP can be matched with the one at the same

reflection time on the seismic section (coeffeen 1936). Where

available the VSP may be correlated with the seismic section to pick a

horizon at formation top.

4.6.3 Synthetic Seismo :ram

It is a seismic a, like trace produced fiom velocity infomation

in a sonic log. It partly bridges the gap between well data and seismic

data. Synthetic seismogram is made at the time scale of the section

but the depths can be plotted on the other side of the seismogram.

The formation tops from the well c m be plotted on the depth scale.

T.le reflection on the seismogram is expected to be strong at the

interface that produces it or gt a lag of about 30 to 60ms if tile

synthetic seismogram is of minimum phase. The reflection is similar

to the reflections of the seismic section hence on correlation, the

reflection character looks alike. When the reflections do not match

each other at the depth of correlation, the synthetic is slid up or down

within possible lag to find best point of ovcrall similarity of

reflections. The synthetic seismograms is used by an interpreter to

select the top of sand which will be mapped on the seismic section.

4.6.4 Base Man.

A base map of the survey area prepared by surveyors is

important to the interpreter. Base maps are prepared on transparent

material for easy reproduction. It contains information showing all

the seismic lines of profiling, the shotpoints, existing well locations,

political boundaries, company's lease and geographical location.

Contour map is produced using the base map. The reflection time will

be posted to the seismic line on the base map. Contouring makes

numerical data visual for recognition if low and high grdient areas.

The contour m:?ps hence gives a 3-D view of the survey area.

4.6.5 Wsll IOE 4 s

The geophysical well log d:cta is very important in seismic data

inteqrztation. It is used in producing cross sections. The well log is

useful in selecting the depth of top sand which when converted to time

can be located on the seismic section. In this way seismic - log

correlation is carried out to select strong reflections on the seismic

section which correspond to top of formaxion sand. In the absenca of

V.S.P. and synthetic seismogram the well to seismic ccrrelation is

used in selecting the strong reflection for picking on the seismic

section.

Geophysical well logging provides various types of data. These

include.

Self potential log data (SP). This is used for locating the boundary

between shale and porous bed (Telford et a1 1988). It utilizes

electrochemical effect which gives rise to voltage drop. Shale has

higher SP value than sandstone. The shape of the curve characterises

depositional sequence.

The grammar ray log is used in measuring the shale content.

This is because there is greater quantity of radioactive element in clay

and shale than in sandstone. It is used mainly where SP log is not

diagnostic especially in resistive formations. This is due to little

difference between salinities of mud and formation water or oil based

muds. Delta T or density log. It measures the transit time through the

porous formation hence it is used in determining the porosity of a

formation. The density log is useful in predicting over pressured

zones. The log value increases in the order of shale, sandstone and

pore filled with brine. The Neutron log is used in locating porous

zones and in determining the amount of liquid filled porous zone. It

utilizes the amount of hydrogen per unit volume or hydrogen index. It

measures porosity better than the density log.

Resistivity log measures resistivity at various depths. It is used

for marking out the boundaries between shale and sandstone. It is

useful when selecting the top of formation sand to avoid mapping

shale horizon on seismic section.

4.7 Seismic data interpretation sequence.

The general routine sequence of interpreting seismic data is

here outlined, however this is not exhaustive depending on the

interpreter and the detail of interpretation required.

4.7.1 Selection o f mapaing horizons.

The horizon to be mapped on the seismic section is important.

,This is because a horizon which represents the top of shale will not be

prospective for oil. Also a good horizon must have lateral continuity

across the survey area. The best horizon to be selected is that of the

top of an oil sand. The selection of mapping horizon involves mainly

three things.

Assembling geological data. Well logs are used to obtain the

boundary between shale and sands tone as could be obtained in a

resistivity well log. The porosity and fluid content of the selected

sand in order to map an oil sand horizon is determixed using other

well log data such as neutron log and spontaneous as potential log.

Therefore prospective reservoirs are identified and fluid contacts are

deterinined using geological data.

The geophysical data required include the fo\!owing the base

map of the sslwey area showing shot point location, velocity surveys

or velocity - depth profile of a well located within c- close to i:i< ile'd

and u~unarked seismic sections. It is pertinent to asce:xir! that all line

ties are defined at the top of each seismic scction. The pertinent

formation tops and total depth of the wells l o c ~ t d on or near the

seismic lines are spoted on the seismic sections.

Well to seismic correlation. Using the depth of the selected oil

smd formation and depth velocity profile a two way travel time is

obtained. The formation depth is determined on a wcll located on a

seismic line. The two way travel time obtained for depth of the oil

sand formation is then marked on the seismic section. This is used in

selecting the horizon to be mapped. However a synthetic seismogram

or V.S.P can be used to select the mapping horizon cin a seismic

section. In the absence of a good reflector at the level, a reliable

seismic event believed to be representative of the structure at reservoir

level can be selected. When the mapping horizon has been selected,

then interpretation of the seismic sections follows.

4.7.2 Interpretation of seismic sections.

The seismic interpretation of structures mainly involves fault

interpretation and horizon interpretation.

Fault interpretation is carried out fclrst on the seismic sections of

the dip lines. The dip lines are then tied with the strike lines to mark

the faults on the strike line. Faulting is noticed using seismic

diffractions and break in wavelets, also well controls help in

establishing the throw of faults, other factors due to faulting are

seismic data detoriation later followed by a strong event (reflection),

mistie of seismic reflection correlation and vertical displacement of

seismic reflection bands. The faults in all the dip and strike lines have

to be delineated before correlating reflection on the seismic lines.

Faults which are not identified could cause mistie especially where the

throw is large.

Following reflections on a horizon is another important part of

seismic interpretation. The continuity of reflection on a seismic

section is followed to the point where it ties with another line. The

interpretation is carried onto the line by tying at the point of

intersection. At such point the reflection on the two seismic sections

are similar and continuos. Interpretation across a fault is established

by using a package or band of reflections. The seismic section is

folded or juxtaposed to establish continuity of the reflection across the

fault.

In figure 4.1, the choice of which part of a reflection to pick is

shown. The peak is better and easier for an inexperienced

geophysicist. A 2B black pencil marker is adequate when the peak is

to be picked. When a coloured marker is used the trough is picked as

it shows the colour. Also the part of reflection to be followed depends

on if the processing is zero phase or minimum phase. In zero phase

processing, the use of the trough or peak is adequate while in

minimum phase processing, the use of zero crossing is better

especially where a coloured marker is required. Interpreted horizons

could be used as a check on each other as illustrated in figure 4.2.

When interpretation is completed on all the lines, the loop will tie

with the starting point. All the points of intersection in the grid of

lines will all tie. In figure 4.3, the sequence of loop ties starting fiom

a well is illustrated. When the loop doesn't tie, the error could be fiom

the interpreter or arise fiom a fault. The fault may not have been

identified or the proper throw on a horizon is not established leading

to the interpretation of a different horizon. It is also important to note

that when a loop ties, it doesn't mean that the interpretation is

perfectly in order. When the loop ties and the sections have been

checked, the two way travel time is measured ad posted for contouring

and mapping.

4.7.3 Fault mapping and contouring

The faults interpreted on the seismic sections ax-:: identified with

letters. These are posted to the base map. The throw of the fault is

established fiom the well control if available or a throw could be

established by "jump correlations seismic events across faults. Major

-- Cough -- -- zero crossing -- peak

fig 4.1. Choosing part of reflection to pick.

Fig 4.2. Using interpreted horizons as a c k c k on each other.

Fig 4 .3 . Sequence of loopties starting from a well.

.-..

I Fig 4.1, 4.2 and 4.3 picking and tying of reflect ions ( wilken 1990 ) .

faults are mapped using parallel dip lines. The fault traces of the

major faults are expected to conform with the regional structural

grain. Minor faults could follow the structural grain or trend in an

oblique direction. Where fault alignment options exist, preference

would be given to downthrown "concave" fault trace alignments as

opposed to "convex".

Where the two way travel time has been posted on the base

map, contouring is then carried out dter mapping the faults. The time

could be posted on the shot points r;r at the appropriate position along

the seismic line based on the contour interval (coeffeen 1982). In

most projects, a twenty millisecond contour interval is used in

mapping. Initial structural kame work could be established using

anticlines and synclines or by contouring at a 100 millisecond interval

initially. The subsequent filling in of the twenty millisecond intervals

and reshaping as required is then carried out. Map "smoothing" may

be desirable, and can be accomplished to a certain extent by arbitrarily

changing -two-way time values plus or minus two milliseconds. This

is within the accuracy limitation reading of two-way times fiom

seismic sections at a vertical scale of 2% inches per second.

In contouring, where options exists, highs are emphasized in

preference to lows. Attempts are made to continue structural trends

scross faults although some lateral displacement could occur. It is

important to check contouring adjacent faults, to determine that

throws are properly shown. Where dips are critical adjacent to f ~ l t s ,

values are placed on the map at location between shot points.

A comp1etedcontour map is rechecked for mechanical accuracy.

CHAPTER FIVE

INTERPRETATION OF 2-D SEISMIC REFLECTION DATA FROM

MEREN FIELD

5.1 Location of Meren field.

Meren field is located offshore in the Niger delta basin. The

field lies at the western edge of Niger delta. The depth of water

within the field is less than 200m. Tlie location map of the field is

shown in figure 5.1. The field lies between longitudes 4" 40'E and 6"

40'E and latitudes 5 20'N and 6 ' OO'N. Tlie total land area.. of the

field is about ten thousand square kiloinetres. Meren field lies close

to the mouth of Benin river into the Atlantic ocean. It is covered

under Oil mining lease (OML)95.

Tlie geology of Meren field was discussed in section 1.4. It is

however pertinent to know that the structural style of the western edge

of Niger delta offshore differs from the structural style in the southern

offshore depobelt. The delta edge is dominated by growth faults. The

presence of hanging wall and rollover anticlinal structures dominate

this part of the delta. This is unlike the southern offshore depobelt

where complex structures dominate the structural style. The faulted

anticlhes are found within Mere11 field with few complex structures.

The location of this field influenced method of data acquisition.

---1.-

-- - - . , -c-Y.- C. y , d--* -- . .C . , , ,.,: .,.:,.I -Shooting direction -+ bJ E%,Ci.. , . . . , . . . , ,

Fig 5.1 locatih map of Meren field.

5.2 Data acquisition

The 2-D seismic reflection data were acquired by carrying out a

marine survey.

A total of eighty two seismic lines were shot . These consist of

fifty four dip lines and thirty two strike lines. The dip lines were shot

in north east direction while the strike lines were shot in south east

direction. Thirteen seismic lines made up four strike lines and nine

dip lines were used for this project. The data was acquired by

compagnie general de geophysique (C.G.G) for chevron. In this

survey the energy source was vaporhoc, whose capacity is one octojet.

The depth of the energy source in water is 4.9.m. A shot point

interval of 25m or 2x50m was used for data acquisition

A floating or drag cable steamer at a depth of 4.2m in water was

used. A total of forty eight hydrophone groups were carried by the

streamer. The group interval is 25m while the number of

hydrophones per group is twenty four. The type of hydrophone used

is HC 202. The streamer has a total length of 1200m.

The data was recorded with SN338B instrument and the tape

format used is SEG B. A frequency of 125HZ,72dB/oct was used for

filtering. The recorded data was sampled at a rate of 2ms while the

recording length is six seconds. The recorded data on field tapes

were then taken to the processing centre.

5.3 Data Processing

The data used for this study were processed by (C.G.G), The

summery of the steps followed in processing is described here.

The SEGB recorded field data was demultipexed to sort out the

information into appropriate geophone channel outputs. The data was

94

subsequently resampled from rate of 2ms to 4ms in order to reduce the

volume of data that will be processed. The data was edited to

normalise and balance traces before gain recovery was applied to even

up and enhance weak reflections. Tlie data was sorted into CDP

gather and signature stabilization was carried out to minimum phase

using recorded vaporclioe signature. At the CDP stage of processing

line merging where necessary was done since a floating streamer was

used in shooting tlie lines.

Spiking deconvolution was carried out to compress the

effective source wavelet contained in tlie seismic trace to a spike. At

a window gap of 0.3 to 1.75 the operators length is l6OMS and pre-

whitening is 5%. At a window gap of 1.4-3.0s the operators length is

l6OOMs and pre-whitening of 5%. Tlie initial velocity analysis was

carried out using one velocity spectra at every Ikm. Using the

velocity analysis Nmo correction was then applied.

The traces were muted to eliminate shallow parts of the longer

traces and deeper parts of the short traces. The data was then stacked

using 2400% or 24 fold stack. Predictive deconvolution was carried

out after stacking at a gap of 24MS. A total operator length of 16OMS

and pre-whitening of 5% was used for both window gaps of 0.35 - 1.7s and 1.4s - 3.0,s.

The data was mib~ated so that events were taken to their true

locations. This is to enable the estimation of depths of the reflecting

interfaces to be made within tolerable error. Wave equation migration

was used on this data.

To restrict the time to the given set of frequencies the data was

again filtered using time variant filter. At a time interval of 0.0 to

0.65s, the frequency window is 10,15-70,90 Hz. At a time interval of

1.2-1.8s, the frequency window is 10,150 60, 80Hz. While at a time

interval of 3.0-5.0s fiequency window is 8, 12-40, 50Hz. The

dynamic equalization was then carried out with a single data and

design window of 0.3-3.0s.

The data was displayed with a polarity in which a compression

wave at hydrophone was recorded as negative number. The negative

number was displayed as trough (white), while the positive number

was displayed as peak (black). Horizontal scale of the seismic section

is 1:12,500 while the vertical scale is Sincheslsecond. The seismic

sections were used for geologic interpretation.

The data used for the present study was a subset of the data

acquired by chevron Nig. Ltd. in the Meren field. To be specific, the

sections used in this project consists of four strike lines and nine dip

lines.

5.4 Interpretation Of Data

5.4.1 Examination Of The Data

The geological data used for the interpretation was the well log

of M-73 well. This well is underviated. The well logs were those of

resistivity, gamma ray and interval transit time. The well log shows

that the depth interval of logging from 2100ft to about 4000ft gives

very low resistivity, high delta-T value and low gamma ray value.

This represents the saline fluid in the continental alluvial sand of the

Benin formation. The interval of 5150ft to about 8900ft gives at

certain depths high resistivity value, low interval ,transit time and high

gamma ray value. In this depth interval the shale and sandstone

Fiq 5.2 sectbns of well log of M-73 well (chevron 1982).

boundaries could be demarcated. In this interval the paralic clastics of

Agbada formation was observed. The Agbada formation sand is

pierced by shale, clay and silts in various proportions. The depth

interval from 9000ft to about 9700ft give low resistivity high gamma

ray value and low interval transit time. This shows the top of Akata

formation composed of shales and silts with few streaks of sand. At

such sand depths high resistivity obtained with low gamma ray value.

The sections of M-73 well log are shown in fig. 5.2.

The geophysical data used in the interpretation were vertical

seismic sections, velocity - depth profile of M-73 well (table 5.1) and

the base map of the survey area. The position of the well, M-73 was

located on the seismic line - 14. The positions of intersection of

seismic lines were marked. All the seismic sections were migrated

except the line - 14 which is a strike line. The seismic lines were

marked on the base map. The shot points were located and their

interval on the base map was examined to correspond with interval on

the seismic sections. In a situation where the interval of incorrect

intersection is small, it was neglected. However intersection error

could result from original navigational data.

Based on the quality of 2-D reflection data the quality of

reflections on the seismic sections interpreted was fairly good

generally. However in the interval 0 to 1 looms the reflections were

discontinuous. Most of the faults terminated at the base of this level.

This interval on the seismic section represents the Benin formation as

shown in the well logs.

The data in the interval 1300ms to 240ms is of good quality.

The reflections were found to be continuos and of relatively high

amplitude. Most of the faults lie within this interval. It represents the

LEVEL MEASURE NUMBER DEFIX

FROM KB FI' t

1 143 .O 2 2150.0 3 2790 . 0 4 3242 .0 5 3400 .0 6 3 5 0 0 . 0 7 3924. 0 8 4382. 0 9 4724. 0 10 5154. 0 11 + 5410.0 12 5866.0 13 61 12.0 14 6435.0 15 6608.0 16 7 0 0 0 . 0 17 7415.0 18 7912.0 19 8305.0 20 + 8630.0 21 8750.0 22 9040.0 23 9410.0 24 9800 .0 25 10100.0 26 10640.0 27 11240.0

VERTIC VERTIC OBSERV VERTIC VERTIC AVERAGE DELTA DELTA DEPTH TRAVEL TRAVEL TRAVEL TRAVEL DEPTH TIME TIME FROM FROM TlME TIME TJME SRDIGEO BETWEEN BETWEEN

SRD GL HYDIGEO SRUGEO SRDIGEO SHOTS SHOTS FT FT MS MS MS FT/S FI' MS t t

62.0 0 12.40 12.40 12.40 5000 2069.0 2007.0 341.25 342.71 342.71 6037 2007.0 330.3 1 2709.0 2647 .O 429.48 431.46 431.46 6279 640.0 88.75 3161.0 3099.0 486.33 488.55 488.55 6470 452.0 57.09 3319.0 3257.0 506.41 508.69 508.69 6525 158.0 20.15 34 19.0 3357.0 521.92 524.23 524.23 6522 1 0 0 . 0 15.54 3843.0 3781.0 576.67 579.12 579.12 6636 424.0 54.89

4301.0 4239.0 63 1.62 634.19 634.19 6782 458.0 55.07 4643.0 4581.0 678.53 681.16 681.16 6816 342.0 46.98 5073.0 5011.0 726.74 729.45 729.45 6955 430.0 48.29

+ 5329.0 5267.0 756.48 + 759.23 + 759.23 7019 256.0 29.78 5785.0 5723.0 807.95 810.76 810.76 7135 456.0 51.53 6031.0 5969.0 835.39 838.23 838.23 7195 246.0 27.47 6354.0 6292.0 870.49 873.37 873.37 7275 323.0 35.13 6527.0 6465.0 888.43 891.32 891.32 7323 173.0 17.96 69 19.0 6857.0 927.92 928.85 930.35 7433 392.0 39.53 7334.0 7272.0 %4.62 965.58 967.58 7580 415.0 36.74 783 1.0 7769.0 1015.04 1016.04 1018.04 7692 497.0 50.45 8224.0 8 162.0 1058.73 1059.75 1061.75 7746 393.0 43.71

+ 8549.0 + 8487.0 1090.31 1091.35 +1093.35 7819 325.0 3 1 .GO 8669.0 8607.0 1100.43 1101.47 1103.47 7856 120.0 10.13 8959.0 8897.0 1126.69 1127.75 1129.75 7930 290.0 26.27 9329.0 9267.0 1161.26 1162.34 1164.34 8012 370.0 34.59 9719.0 9657.0 1197.57 1198.66 1200.66 8095 390.0 36.33 10019.0 9957.0 1223.89 1224.99 1226.99 8165 3 0 0 . 0 26.33 10559.0 10497.0 1281.61 1282.73 1284.73 8219 540.0 57.74 1 1 159.0 11097.0 1346.78 1347.92 1349.92 8266 6 0 0 . 0 65.19

INTER' VELOC BETWEEN

SHOTS FT/S

TABLE 5.1 DEPTH - VELOCITY PROFILE OF M- 73 WELL (CHEVRON 1982).

Agbada formation as obtained in the well logs. The quality of

reflections in the interval 2500ms to 4000ms was found to be poor.

The reflections were distorted and discontinuous. The data was

dominated by low frequency reflection packages. The interval

represents t$e Akata formation hence the processing of data at such

level may not be of much importance. The faults terminated at the top

of this interval.

Two strong seismic events were observed at the time interval of

100 to 150ms. These events had a strong amplitude and represent the

direct waves arriving at the receiver from shallow depth. A section of

line 14 is shown in fig. 5.3. The quality of reflection at various time

intervals were shown. The depth - velocity profile of M-73 well is

shown in table 5.1. The profile was combined with the well log to

select horizons mapped on the seismic section.

5.4.2 Well Log -To-Seismic Correlation

he well-to-seismic correlation method was used in selecting

the horizons mapped on the seismic sections. The resistivity log was

mainly used to obtain the boundary between shale and oil sand. The

gamma ray log and the interval transit time log were used to pick a

good sand-stone formation. A combination of the three log values was

used in deciding the depth of top sand selected for mapping.

The depth of top sand for horizon I was selected at 5410ft

(1623m). When the kelly bushing (KB) height of 81ft (24.3m) was

removed, the sea reference depth (SRD) of j329ft (1598.7m) was

obtained. The selection of this top sand was based on the following

values. The resistivity log of 20 ohm-m, gamma ray value of 36

GAP1 and interval transit time (AT) log value of 75psIft. These are

shown in sections of M-73 well log in fig 5.3. The depth-velocity

profile shown in table 5.1 was used to obtain the one way travel time.

At a vertical depth from SRD of 5329A, the one way travel time

(vertical) is 759.23 ms. This value was doubled to give 15 l8.46ms

which is the two way travel time on the seismic section. The top sand

depth of the second horizon was taken at 8630ft (2589.0m).. When

the kelly bushing (KB) height was removed, the vertical height from

SRD gave 8549ft 2565.7m). The two way travel time obtained for

this depth is 2186.70 ms. The log values at the top of this is and level

are as follows; A resistivity value of 9 ohm-m, gamma ray value of

60GAPI and interval transit time (AT) of 80psIft. Using the two way

travel time the second horizon was selected on the seismic section.

At the position of M-73 well on seismic section of line-14 a

vertical line was drawn to the level of the two horizons. The positions

corresponding to the time for horizon I and the time for horizon I1

respectively were annotated along the well position. This was

illustrated in fig 5.3. The use of this method may not locate

accurately the formation top on the seismic section hence the strongest

reflection close to the position annotated for each of the horizons was

mapped. The method was used because vertical seismic profile or

synthetic seismogram were not available. When the horizons to be

mapped were selected, fault and horizon interpretation on the seismic

sections were then carried out.

5.4.3 Interpretation of faults

The dip lines were used for interpretation of the faults. The

evidence of faults on seismic sections has been discussed in section

4.4.4. These were used as a guide in picking the faults on each

Fig 5.4 faults and horizons interpreted on seismic section.

seismic section. The faults interpreted were labelled as B, C, D, Dl,

D2, E and X as showdin fig. 5.4 . The faults X, Dl and D2 are the

minor faults while B,C and D are the major faults. The major faults

cut through the two horizons mapped. The faults interpreted are

normal growth faults. The faults interpreted on the dip lines were

used in locating the faults on the strike lines. To do this, strike lines

were tied to the dip lines at the point of intersection and the fault

positions were marked.

To identify each fault and label them on subsequent parallel dip

lines, two closest parallel dip lines were used. One of the seismic

sections is folded horizontally and laid on top of the other such that

the faults on both seismic sections are found to match each other at

their respective positions. The faults were then identified and

labelled. The termination of reflection packages on each fault may

look similar on parallel dip lines where such fault cuts across. In

many situations the position of the faults shift from one seismic

section to the other. The blocks of sediment deposition and

subsequent faulting was shown by the termination of reflections. The

&ow of the faults and continuity of reflection across the fault is

obtained by folding the seismic section across the fault and correlating

packages of reflection and nature of wavelets.

When all the faults on the seismic sections have been

interpreted and tied properly, the horizon interpretation was then

carried out.

5.4.4 Picking reflection on horizons

The events on each of the two horizons selected were found to

have good lateral continuity across the seismic sections. The

reflections on each of the two horizons were picked after

interpretation of faults. Picking of reflection started from the well

position on line -14. The part of reflection followed is the peak using

a 2B pencil. The horizon interpretation moved from well position to

the intersection of L-14 with seismic line 42 which is a dip line. The

interpretation was carried to the dip line by tying the two sections at

the point of intersection. The reflection was then followed to the next

point of intersection. In this way interpretation of the horizon was

carried round the entire grid of lines forming the loop.

At fault positions, the reflections terminated and wavelets were

found to split. The continuity of reflection along the horizon was

determined by folding the seismic section across the fault and

correlating packages of reflection above and below the horizon. The

dsplacement and character of reflection package were used in

determining the throws of the faults. Also where reflections were

weak and not clearly visible; the seismic section was folded and the

reflection package was used to determine continuity of reflection.

The two horizons interpreted were carried along together. This

acted as a guide in following reflections. The relative separation was

found to be nearly equal along the seismic lines. The change in

separation where it occurred was gradual and consistent.

When interpretation was completed on all the lines, the loop

was checked at various points of intersection for proper tying of lines.

The positions of mistie were interpreted again until all the lines were

found to have tied. It would be noted that misties which occurred

could have resulted from inaccuracies in the original data, difference

in wavelet at intersection, unequal throw of faults, adjustment made

during processing and wrong interpretation.

5.4.5 Horizon and fault mappinz

A time contour and fault map was produced for each of the two -+

horizons interpreted . The faults and time contours were mapped

together on the same base map.

In these maps shown in figures 5.5 and 5.6 the two way travel

times were posted to the shot point locations. The disadvantage of

using this in contouring is that the spacing of contours can not be

accurate. This is because contour values which lie between two shot

points will be fixed by approximation while drawing the contours.

The other method is to post time values at their exact positions along

the seismic lines on the base map. The time values posted here are

those whose values fall within the contour interval being used. The

contcur interval used in this work is 20 ms. The time was therefore

posted on all the shot point locations and at the positions of the &act

contour value along the seismic line on the base map. The faults were

also posted on each seismic line on tlie base map. The down throw

and up throw of the faults were indicated. The space between the

down throw and up-throw of each fault depends on the throw of that

particdar fault. Each fault posted was identified with it's labelled

letter. The major faults had a bigger throw than the minor faults.

The faults were fxst mapped. In this the up-thrown sides of a

particular fault were joined from one seismic line to th:: other. Also

the downthrown sides were joined in a similar way. The fault

curvature of each fault was smoothened on the base map. The faults

were found to have a concave curvature towards the downthrown side.

In the map of horizon I fig. 5.5, the faults x and Dl terminated on the

major fault D. The minor faults were only found in horizon I. They

died out before the deeper horizon 11. The throws of the faults were

highlighted in mapping. The major faults had a bigger throw than the

minor faults.

Faults are important not only as structural traps but also in tying

contours. Therefore the faults were properly mapped before

contouring.

The contour interval used in the map is 20ms. The structural

pattern was worked out using anticlines and synclines before

contouring. The contour was drawn by joining equal values fiom one

seismic line to another based on the contour interval. A contour

rounded where it joined itself. Some of the contours terminated on a

fault while those at the extreme were drawn to terminate outwards.

The highest contours were drawn first and contouring conticued

outwards to lower areas. The high gradient areas were worked out to

locate closures correctly. Also closures against faults were carefully

drawn especially the faulted closures. The highs were made rounded

while lows were made angular.

To contour across a fault, the throw of the fault was considered

as the contours were not continuous on the same position across the

faults successive contours were made to run approximately parallel to

each other from one position to the other in an area, the relative

spacing of the contours depends on the position of the contour value

along the seismic line.

A time contour map was produced for each horizon interpreted.

The map gives a 3-D view of the subsurface mapped hence closures

can be located. This was used by enables the interpreter to make

recommendations and draw conclusion.

5.5 Comments, recommendations and conclusions.

5.5.1 Comments

The seismic sections interpreted revealed the tripartite

stratigraphic sequence of the Niger delta. The interval 0-1 100ms on

the seismic section was dominated by high frequency and

discontinuous reflections. The section represents the Benin formation

composed mainly of continental alluvial sand containing saline water

as shown in well log (fig 5.2). The interval from about 1300ms to

2400ms consists of continuous strong reflection events of high

amplitude. The faults in this interval were identified. The section

represent the Agbada formation based on well log interpretation in

secticn 5.4.1.. This is the hydrocarbon bearing sequence of the Niger

delta. The two horizons interpreted were selected from this interval.

The deepest part of the seismic section from 2500ms to 4000ms

consists of poor data. The reflections were discontinuous and consists

of low frequency package. The interval represents the top of Akata

formation. This consists mainly of shale and few streaks of sand. The

faults terminated mainly at the base of Benin formation. They passed

through the interval of Agbada formation to terminate at the top of

Akata formation.

The interpretation shows four major faults (B,C,D and E) and three

minor faults (X,Dl, and D2 ). These are shown in figure 5.3. The

faults are normal growth faults.

The two horizons interpreted also revealed existence of simple

rollover anticlinal structures. The rollover structures terminated

against the downthrown side of the normal growth faults. There were

faulted anticlinal structures on both horizons interpreted.

The contour map of horizon I shown in figure 5.5 revealed that

the horizon dips in a direction from northeast to southwest. The time

value for the shallow part northeast is 1380111s while the time value for

the deepest part on the horizon is 1740ms at the southwest. The

major faults identified on horizon I are C,D and E which are the major

faults. The minor faults on the horizon are X, Dl and D2 . These

faults gave rise to the faulted closures identified on horizon I.

All the faults on horizon I are found to be concave towards the

downthrown side. This agrees with the regional structural geology of

Northwestern part of Niger delta offshore. The faults were; oriented in

a direction northwest to southeast.

The closures identified on the contour map of horizon I (fig. 5.5

were numbered. Seven closures were located on this horizon.

Closures (1) and (4) are located at the southeastern part of the survey

area. The closure (1) is below the downthrown side of fault D. The

contours round it move outwards to low gradient area. The closure

cut across three seismic lines which on examination does not show

high amplitude anomaly. The value of the closing contour is 1460111s.

Most closures at the downthrown side of normal faults contain high

gas to oil sand ratio. Closure (1) may not contain a high volume of oil

sand. Closure (4) is against the upthrown of fault C. It lies between

the faults C and E. The value of the closing contour is 1400 ms. The

amplitude anomaly on the seismic section shows the closure as a

good hydrocarbon trap. Closure (2) is located at the southwestern part

of the surrey area. The contour values of this closure is 1480ms. The

amplitude anomaly on seismic section shows that it is a good

hydrocarbon trap. Closures (3) is located at the central part of the

survey area. The contour value is 1480ms. It is located between

faults Dl and D. The seismic sections shows that the closure is a good

hydrocarbon trap. Closure (5) is a faulted closure. It lies at the

northeastern part of survey area. Three faults X, C and E cut across

the closure. The seismic sections shows high amplitude anomaly

hence the trapping of hydrocarbon will be by combination of the fault

and the anticlinal closure. Closures (6) and (7) lie on the northwestern

part of the survey area. These closures are unfaulted. Closure (6) has

a contour value of 1460ms, while closure (7) has a contour value of

1540ms. The amplitude anomaly on seismic section shows that the

closure (6) is a good trap. Closure (7) lies between the faults D and C.

The closure cc vers a large lateral area. The closure is a good

hydrocarbon trap, however the low areas further northwest shows that

dry well could be encountered in that side of the closure.

The interpretation of horizon I1 shows that only the major faults

By E, C and D cut across this horizon. The horizon is deeper hence

the minor faults died out before reaching the horizon. The faults gave

rise to faulted closures observed on the horizon.

The contour map of horizon I1 (fig 5.6) revealed that the

subsurface layer dips in a direction from northeast towards southwest.

The shallow part of the northeast had a minimum time value of

1920ms while the deepest part southwest had a time of 24OOms.

The faults on the horizon were found to be concave towards the

downthrown side. The orientation of the faults is from nonvest to

southeast.

Five closures were identified on this horizon. Closures (1) is

located at the southwestern part of the survey area. The contour

value is 2140ms. The contour closed against the downthrown side of

fault D. The closure against the downthrown side of a fault does not

prove to be a good oil trap hence gas well may be obtained if drilled.

Closures (2) and (4) are located in the eastern part of the survey area.

Closure (2) is faulted by the faults C and E. The seismic sections

shows there is high amplitude anomaly. The contour values ranges

from 2000ms at the downthrown of fault C then 1980 mg at the

downthrown side of fault E to 1960ms at the upthrown side of fault C.

The hydrocarbon trapping will be by combined effect of the fault and

the anticlinal structure. Closure (4) is against the upthrown side of

fault B. This upthrown closure is a good hydrocarbon trap. It shows a

strong reflection on the seismic section. Closure (3) lies between two

faults (C and D), it covers a large lateral area. The closure has

rounded contours around it. The contour value is 2020ms and it

shows strong reflection on the seismic section. The closure proves to

be a good hydrocarbon trap. Closure (5) is located at the northern part

of the survey area. It lies between two faults (E and B). The contours

around this closure are rounded. Also there was a high amplitwk

contrast on the seismic sections examined for this closure. The

closure was taken as a good hydrocarbon trap.

5.5.2 Recommendations.

The recommendations made here are ba eductions made

from the available data and the need for further studies.

The closures identified on the contour map of horizon I shows

that positions (3), (4), (5) and (6) are highly prospective for

hydrocarbon and are recommended for drilling. The closures (I), (2)

and (7) in horizon I would require further studies to determine where

wells could be positioned to avoid drilling dry gas wells.

Closures (2), (4) and (5) in the contour map of horizon I1 are

considered highly prospective hydrocarbon traps hence recommended

for drilling. Closures (1) and (3) will require a detailed study using

cross sections to properly position wells in order to drill wet wells.

It is also recommended, that a 3-D survey or an improved

seismic reflection survey should be carried out in the area. This is to

obtain a data of higher quality. The data obtained will be used in

carrying out lithostratigraphic sequence analysis and to determine the

hydrocarbon content in the identified closures.

Cross sections and geologists isopach map need to be produced in

order to properly position wells and determine the oil sand volume.

5.5.3 Conclusion

The structural interpretation carried out using 2-D seismic

reflection data from Meren field has revealed that the structural style

of the area consists mainly of normal growth faults. The orientation

of the faults is from northwest to southeast. The structural traps found

were mainly simple rollover anticlinal' closures, faulted anticlines and

closures against faults.

The well log data and reflections on seismic sections shows that

most of the closures are good hydrocarbon traps. Drilling of wells

was therefore recommended at the locations of these closures. The

hydrocarbon structural traps found shows that Meren field is a good

prospective area for oil and gas.

REFERENCES

Anstey, NA; 1977 Seismic interpretation- The p l~~s ica l aspects. I.H.R.D. (1.4) Boston USA.

Avbovbo, A.A, and Ogbe F.A; 1978 Geology and hydrocarbod productive trends of southern Nigeria basin. Oil and Gas Journal V. 76 no.48 P.90-93.

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