SEISMIC INTERPRETATION TPG4130

Department of Petroleum Technology and Applied Geophysics

NTNU Trondheim

Egil Tjland 2011

Seismic interpretation Principles (Part 3)

For conventional PP stacked data (P-waves impinging on a surface and reflected as P-

waves) a contrast in acoustic impedance is required in order to get reflected data back to

the receiver.

12

12

ZZ

ZZRPP

(1)

Where iiiZ is the acoustic impedance in layer i.

i and i are density and P-wave velocity in layer i respectively.

The remaining seismic energy will be transmitted to the next reflecting layer, being

reflected and transmitted there in the same way. In such a way we get reflected energy

from each interface where there is a contrast in acoustic impedance.

Figure 1. Well logs showing cyclic variations of parameters within each rock layer

(courtesy Lamont-Doherty Earth Observatory).

In general both densities and velocities increase with depth, but inside each rock layer we

find that these properties vary can be seen in Figure 1. When there is an increase in

acoustic impedance we get a positive reflection coefficient, and when there is a decrease

in acoustic impedance the reflection coefficient becomes negative.

How will this be seen on seismic? To understand this we need to describe mathematically

how a seismic section is produced. For stacked data we normally use the convolution

model to describe the mathematical modeling. In the time domain the convolution d(t) of

a pulse p(t) and a reflection series r(t) is given as:

t

dtrprptd0

)()()( (2)

The convolution is seen as a simple multiplication in the frequency domain

)()()( RPD (3)

Here )(D , )(P and )(R are the Fourier transformations of the seismic data trace d(t),

the seismic pulse p(t) and the reflection series r(t) respectively.

In time domain the result of a convolution of a seismic pulse with a number of reflecting

interfaces is seen in figure 2. Note that the pulse on the top of the diagram is folded (or convolved) with each reflection coefficient (seen as spikes in the figure), and then all

scaled and time shifted pulses are subsequently summed to give the resultant waveform

seen in the lower part of the figure. The various ir s denote reflection coefficients

(equation 1) from each interface. Positive reflection coefficients are plotted to the right

and negative reflection coefficients are plotted to the left. The only interface to be

interpreted with confidence is the first ( 1r ), since this is found from the start of the pulse

p(t). The other interfaces are shown as interfering patterns, and can not be interpreted

with certainty.

Seismic resolution

When searching for hydrocarbons we often work in sedimentary basins. The level of

details of the various rock types in such basins can be found by different type of

measurements. A sonic log (measured in the borehole) will show details of centimeter

scale, whereas an ultrasonic measurement of a core plug will show details of millimeter

scale. For seismic data, the level of details is in the tens of meters range. The frequency

of the probing devise (ultrasonic, sonic or seismic) determines the levels of details.

As a rule of thumb the minimum vertical thickness of a layer to be interpreted on seismic

data is given as:

4/min d , (4)

where is the wavelength of the seismic wave. The wavelength is related to the velocity of the wave and the frequency of the wave in the following way:

f (5)

where is the velocity of the wave and f is the frequency of the wave (measured in Hz).

Seismic velocities in seismic exploration vary from 1500 m/s in water to about 6000 m/s

in lithologies such as anhydrite or volcanic intrusions. Frequencies are normally in the

range of 10 Hz to 60 Hz. For a unit of layered shales having velocities of 2500 m/s and

where the dominant frequency is 50 Hz, the minimum thickness from equation (4) and

(5) then gives mind =12.5 m.

Figure 2. Seismic pulse p(t) convolved with various lithology boundaries r(t) to produce

resultant pulse d(t). Dashed wave forms indicate p(t) scaled by negative reflection

coefficients while full lines indicate p(t) scaled by positive reflection coefficients. Note

that it is not obvious from d(t) where the various lithology boundaries are located.

Modified from Dobrin and Savit (1988).

r2

t

p(t)

t

d(t)

r1

r(t)

r3

r4

r5

r1 r2 r3 r4 r5 r2 r2 r2