Out of Plane effects in seafloor sound-speed characterization

Sensitivity analysis of the image source method (ISM) to

out-of-plane eects

S. Pinson

1& C.W. Holland

2

1Laboratrio de Vibrao e Acstica

Universidade Federal de Santa Catarina (Brazil)

[email protected]

2Applied Research Laboratory

Penn State University

[email protected]

Indianapolis, October 2014

Introduction

Introduction

Context: measure sediment sound-speed prole in arbitrary range

dependent environment by the image source method.

Objective: analyze out-of-plane eects (interface slopes and roughnesses).

Pinson & Holland (LVA) ISM: out-of-plane eects Oct 2014 2 / 47

Introduction

Outline

1

Models

2

Image source method

3

Results

4

Conclusion


Models

Outline

1

Models

Measurement system

Out of plane interface slopes

3D roughness scattering

2

Image source method

3

Results

4

Conclusion


Models Measurement system

Outline

1

Models

Measurement system



2

Image source method

3

Results

4

Conclusion


Models Measurement system

Conguration of the measurement system

AUV towing an horizontal array:

Water

Basement

Source

AUV

25

hydrophones

Array

20m

9, 6m 30m

z

x

Layers


Models Out of plane interface slopes

Outline

1

Models

Measurement system



2

Image source method

3

Results

4

Conclusion



Simulated seaoor

Interfaces are parametrized by:

the dip angle,

the strike angle,

the depth at x = 0, y = 0.



Simulated seaoor

Layer parameters:

Layer thickness Sound speed (m/s) Density (kg/m

3)

Water 1500 1000

3 m 1490 1100

7 m 1550 1300

10 m 1600 1500

Basement 1700 1700



Simulated signals

The reected signal from the seaoor is modeled using the Born and the

ray approximation:

pn(t) =l

A(l)n s(t (l)n

),

The ray method for arbitrarily orientated interfaces is described by

Langston in:

Charles A. Langston, "The eect of planar structure on source and receiver

responses for constant ray parameter", BSSA, 67, pp 1029-1050, 1977.



Simulated seaoor

For each interface reection,

Langston method steps are:

1

send a ray from the source,

2

calculate intersection coordinate

on next interface,

3

calculate transmission coecient

and ray refraction,

4

iterate 2 and 3 to the last

interface,

5

calculate reection coecient,

6

iterate 2 and 3 to the receiver

plane.



Simulated seaoor



1


2


on next interface,

3


and ray refraction,

4


interface,

5


6


plane.



Simulated seaoor

Geometric divergence is calculated by

sending 2 other rays with a small

change in incidence (0) and azimut(0). Then the geometricdivergence is calculated with:

D =

J(1)J(s)1/2 ,with:

J =

xs

x0

x0

ys

y0

y0

zs

z0

z0



Simulated seaoor

The correct arrival point is found

using the Newton-Raphson method

(one or two iterations needed to reach

the receiver within a 1 cm radius).



Simulated signals

Simulated signals (emitted signal

centered on 1 kHz with 300 Hz

Bandpass):



Simulated signals

Simulations performed with a xed dip angle (5

) of interface n

4 and

various strike angle:



Simulated signals

For each strike angle, simulations are performed every 5 m over a 60 m

total range:


Models 3D roughness scattering

Outline

1

Models

Measurement system



2

Image source method

3

Results

4

Conclusion



Simulated seaoor with rough interfaces

Interface roughnesses (Von Karman

spectrums):

W2(kx, ky) =w2

(k2x + k2y + 1/L

2)2/2

with L = 10m and 2 = 3.




Approximations:

Born,

transmission through at interfaces,

ray for transmitted waves through interfaces,

small roughness,

roughness curvature radius such that 2kR sin 1




Recorded signal modeled by:

P (rn, ) =l

P (l)s (rn, ) ,

using the Kirchho (tangent plane) approximation:

P (l)s (rn, ) =1

4pi

S(l)

RPi(r, )

G(r, rn, ) +G(r, rn, )R

Pi(r, )dr

with:

Pi(r, ) = S()A(r0, r) exp [i(r0, r)] , G(r, rn, ) = A(r, rn) exp [i(r, rn)] .




Kirchho approximation can also be

written by:

P (l)s (rn, ) =S()

4pi

S(l)dr

R(.ui)A(r0, r)A(r, rn) exp [i ((r0, r) + (r, rn))] ik (.ui + .us)

Ray paths, transmission coecients

and geometric divergence are calcu-

lated using Langston's method:

Source Receiver





written by:

P (l)s (rn, ) =S()

4pi

S(l)dr





Source Receiver

Geometric divergence value on the 4

th

interface obtained from ray tracing:





written by:

P (l)s (rn, ) =S()

4pi

S(l)dr





Source Receiver

The values to be interpolated are:

amplitudes A (Geometricdivergences + transmission

coecients),

travel times to the atinterface,

incidence vectors u on the at

interface.




P (l)s (rn, ) =S()

4pi

S(l)dr

R(.ui) A(r0, r)A(r, rn) exp [i ((r0, r) + (r, rn))] ik (.ui + .us)

Roughness neglected

Roughness considered

Assuming that u u,

huz

h(r)

u

u

travel times are corrected by:

= huzc(l)




Simulations are performed every 5 m over a 60 m total range:




Simulated signals:




Simulated signal (1

sthydrophone):


Image source method

Outline

1

Models

Measurement system



2

Image source method

3

Results

4

Conclusion


Image source method

Idea of the method

1

Consider the geological interfaces as acoustical mirrors on which

images of the real source appear

2

Locate image sources in a water sound-speed medium

3

Deduce travel time and angle of arrival on the array

4

Calculate sound-speed prole


Image source method

Array processing

Image sources located by array processing:

Migration of the recorded signals:

Im(r) = 1N

Nn=1

sHn (tn(r))

2

Semblance function:

Isemb(r) =

1N Nn=1 sHn (tn(r))21N

Nn=1 |sHn (tn(r))|2


Image source method

Geometry of the problem

Ray diagram in the equivalent

sound-speed medium:

h(l)

rs

source

rc

receiver

r

(l)simage

source l

i

n

t

e

r

f

a

c

e l

(l)

(l)

(l)eq

(l)eq

h(l

)+

si

n

(l)

t (l)c c (l)eq

z

x

Given triangle geometric rela-

tion, for small (l) and ,sin((l) + ) 2h(l)/ rc rs, = 0, using the Snell-Descartes law

and assuming that c(l)eq varies much

more slowly than t(l)c , it is possible to

write c(l)eq as a function of measurable

parameters:

(c(l)eq )2 =

c(0) |xc xs|t(l)c sin

(l)0 c

(0)

4d(t

(l)c )2

d

h(l), z(l), (l)eq and (l) are then de-duced from geometric relation.


Image source method

Layer sound-speed

Ray diagram in the equivalent

sound-speed medium:

h(l)

rs

source

rc

receiver

r

(l)simage

source l

i

n

t

e

r

f

a

c

e l

(l)

(l)

(l)eq

(l)eq

h(l

)+

si

n

(l)

t (l)c c (l)eq

z

xFinally, layer sound-speeds are ob-

tained by the Dix formula:

c(l) =

c(l)rmsz(l) c(l1)rms z(l1)z(l)/c

(l)rms z(l1)/c(l1)rms

More details on ISM with dipped interfaces in "Pinson & Holland, JASA

136 2014".


Results

Outline

1

Models

Measurement system



2

Image source method

3

Results

4

Conclusion


Results

Results with out-of-plane interface slope

Simulation done using Langston's method (4

thinterface dip angle of 5):


Results

Results with rough interfaces

Rough interface simulation (no dip angle):


Conclusion

Outline

1

Models

Measurement system



2

Image source method

3

Results

4

Conclusion


Conclusion

Conclusion

Out-of-plane eects on the image source method:

out-of-plane interface slopes weak inuence (?)

out-of-plane backscattering from roughness strong inuence

Perspectives:

Find theoretical sound-speed uncertainty from roughness parameters


Conclusion

Conclusion

Out-of-plane eects on the image source method:

out-of-plane interface slopes weak inuence (?)out-of-plane backscattering from roughness strong inuence

Perspectives:

Find theoretical sound-speed uncertainty from roughness parameters


Conclusion

Acknowledgments

This work is supported by the CAPES (Coordenao de Aperfeioamento

de Pessoal de Nvel Superior from Brazil) through the young talent funding

and partially funded by Wavetech company.


Conclusion

Thanks for attention\


Conclusion

Validation of the models

To validate Langston's model, a

simulation is performed with null

slopes and is compared with the

result obtain by a numerical

evaluation of the Sommerfeld integral

(reection of a spherical wave using

plane wave decomposition).

.


Conclusion

Validation of the models

To validate Kirchho-Langston's

model (KLM), a simulation is

performed with null roughnesses and

is compared with the result obtain by

a numerical evaluation of the

Sommerfeld integral (reection of a

spherical wave using plane wave

decomposition).

.


Conclusion

Squared travel time variation measurement

Picture of image source squared

travel times:

Parameter of interest:

dt2cd

= tan( pi/2)Radon Transform:

t2c

d

Ip(, t2c)


Conclusion



travel times:


dt2cd

= tan( pi/2)

Radon Transform:

t2c

d

Ip(, t2c)


Conclusion



travel times:


dt2cd

= tan( pi/2)Radon Transform:

t2c

d

Ip(, t2c)


Conclusion



travel times:

Radon transform:


ModelsMeasurement systemOut of plane interface slopes3D roughness scattering

Image source methodResultsConclusion

0.0: 0.1: 0.2: 0.3: 0.4: 0.5: 0.6: 0.7: 0.8: 0.9: 0.10: 0.11: 0.12: 0.13: 0.14: 0.15: 0.16: 0.17: 0.18: anm0: 1.0: 1.1: 1.2: 1.3: 1.4: 1.5: 1.6: 1.7: 1.8: 1.9: anm1: 2.0: 2.1: 2.2: 2.3: 2.4: 2.5: 2.6: 2.7: 2.8: 2.9: 2.10: anm2: 3.0: 3.1: 3.2: 3.3: 3.4: 3.5: 3.6: 3.7: 3.8: 3.9: 3.10: anm3: 4.0: 4.1: 4.2: 4.3: 4.4: 4.5: 4.6: 4.7: 4.8: 4.9: anm4: 4.EndLeft: 4.StepLeft: 4.PauseLeft: 4.PlayLeft: 4.PlayPauseLeft: 4.PauseRight: 4.PlayRight: 4.PlayPauseRight: 4.StepRight: 4.EndRight: 4.Minus: 4.Reset: 4.Plus: 5.0: 5.1: 5.2: 5.3: 5.4: 5.5: 5.6: 5.7: 5.8: anm5: 5.EndLeft: 5.StepLeft: 5.PauseLeft: 5.PlayLeft: 5.PlayPauseLeft: 5.PauseRight: 5.PlayRight: 5.PlayPauseRight: 5.StepRight: 5.EndRight: 5.Minus: 5.Reset: 5.Plus:

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Out of Plane effects in seafloor sound-speed characterization