Coupling ratio of Coupling ratio of geophone in the sea bedgeophone in the sea bed

X.Roset , M.Carbonell & A.ManuelX.Roset , M.Carbonell & A.ManuelUniversitat Politècnica de CatalunyaUniversitat Politècnica de Catalunya

International Summer Course of International Summer Course of Non-homogeneous Turbulence’08Non-homogeneous Turbulence’08

Objectives of the workObjectives of the work• Get the performance of the geophone in the sediment in order to know its

coupling in the bottom sea

• Obtain the transfer function of coupling between the geophone and the sediment sea by shaker table without using a detailed model of interaction OBS/seabed.

Automatic CalibrationAutomatic Calibration• The LabVIEW program obtain first the frequency response to the sensitivity of sensor in

acceleration units, and in a second seep we can detailed the parameters of sensor for her characterization completely. We show one of the pages of the process program of LabVIEW in the figure 3, when the second sweep is beginning.

(1)

Fig.3 One of the visual program panel

• An acceleration model can characterize the geophone sensitivity with the expression (1). We can express the transfer function of the magnetic accelerometer according to the voltage output in function to the acceleration input in one axis

Coupling ratioCoupling ratio• The response to forced oscillations of OBS with the seabed is the coupling

ratio > r

• The coupling ratio between bottomed and suspended velocities follows Osler and Chapman equation :

bot

sus

bot

sus

sus

bot

mm

mm

Zmmj

mmj

v

vr

)(

)(

Rj

kZ

hydrodynamic added mass

bottomed added massinteraction impedance between an OBS and the seabed

bottomed velocity

seabed stiffnessdamping

Transfer function for horizontal Transfer function for horizontal seabed motionseabed motion of geophone of geophone

mbotv

vo

vT

r

r

mm

k

mm

Rss

R

ks

mm

R

v

vT

botbot

bot

oh 1

2

boto mm

k

R

mmkQ bot )(

resonance frequency

quality factor

m

MEASURES IN THE LABMEASURES IN THE LAB

Material of the bottom seabed

1955,0.918,35

shear stress in Pa

rate of shear strain in s-1

Laboratory studies have been carried out using co-axial cylindrical reometer Haakewhich indicate this material performs reologically as a non-Newtonian substance

Rotary-oscillatory reometer Rotary-oscillatory reometer HaakeHaake

1

10

100

1000

10000

0,01 0,1 1 10 100 oscilatory shear strees ( Pa )

G' ,

G"

( P

a )

G'

G''

1

10

100

1000

10000

100000

0,01 0,1 1 10Frecuency ( Hz )

G' ,

G"

( P

a )

G' G''

G' G''

elastic module component G’ is always higher than the viscous module G’’

frequency 1Hz varying the shear stress. 1 Pascal stress varying the frecuency

Shake table measurementsShake table measurements

T

o

oG

T

SGBERAN v

v

v

vH

v

VoltageSens .

The measures in the shaker table with transducer vibration calibrator BERAN

Measured

Deduced Th Transfer function

About 1

Geophonesensibility

In the table Sediment Geofoneon top

mbotv

vo

vT

Shake table measurementsShake table measurements

Sweep frequency of 1 to 100Hz for the sensibility (amplitude 3mm/s)

1

10

100

1000

1 10 100frequency

Transfer function geophone versus sediment

-30-25-20-15-10-505

1015

1 10 100

frecuency

dB

Sweep frequency of 1 to 100Hz for measure the sensibility (amplitude 3mm/s)

Transfer function [Th]geophone versus sediment

fo= 11 Hz ; Q=4 ;zero frequency = 44 Hzmsus = 0,588 kg ; mbo t= 0,78 kg

SensBeran

HG

Deduced parametersDeduced parameters

boto mm

k

shear wave velocity of sediment Cs= 2,97m/s

Considering the Poisson coefficient σ = 0,49,geophone radius = 0,1 mdensity of the material of geophone 2830kg/m3

seabed stiffness k = 19380 kg/s2

damping R = 69,2 kg/s

fo = 11 Hz Q = 4 zero frequency = 44 Hz, m, msus, mbot

2

1

4sc

ak

R

mmkQ bot )(

ConclusionsConclusions

• We have inferred valuable parameters related to the coupling in the geophone-sediment interaction and the shear wave velocity of sediment.

• They have been obtained from a reology and vibration laboratory test.

• These parameters allows to perfectly characterize the coupling between the sensor and the sediment, and how the geophone performs when recording the ground and seabed vibrations data, what the expected dynamic range is and its accuracy level.