96

Sensitivity

Sanj1National Ins

2Department of Ocea

Abstract— Sensitivitycoherence in a shalloschemes based on mparameters are comparmodel parameter selecsensitivity for the acoua layered environmenparameter the cost funparameter values withfunction values should

Index Terms— Ambie

1. Introduction

Traditionally natural or mconsidered as unwanted nuisadetecting signals harder. contains information about thewhich it propagates and this uled to a new interest in extraabout the ocean or seabed frsources of interest include noise, biological noise and ship noise. Random noise ocean and received by two resome coherence. Under certaproperty provides an oppambient noise for the infeproperties [1]. The noise corris an active area of researcocean acoustics and meInversion techniques, whictheoretical model for noise c

PROCEEDINGS O

y Analysis of Model Parameters Geoacoustic Inversion

jana M. C.1, Latha G1 and Gopu R. Potty2

stitute of Ocean Technology, Chennai 600 100, India. an Engineering, University of Rhode Island, RI 02882

y of model parameters to the cost function defined w water environment is discussed here. Since, in i

matched field processing, the values of model ared to arrive at the best estimate, a sensitivity study ction and also ensures the quality of the inversion.ustic properties of sediment layer and basement is chent in this study.In order to investigate the sensitivnction is evaluated and plotted for all possible valuehin it’s search bound. . In this way, the distributiond provide an indication of the parameter sensitivity.

ent noise, geoacoustic inversion, Cost function

man-made noise is ance which makes But noise also

e medium through understanding has acting information from it. The noise surface generated distant or nearby produced in the

eceivers will have ain conditions this portunity to use erence of seabed relation processing ch in seismology, edical acoustics. ch incorporate a coherence, for the

inference of seabed properties body of research. As a prelude tit is essential that we explore ththe model parameters of interfunction that we employ in the ensures that the model parameteadopt is optimal which in turefficient inversion strategy bycomputational resources to separameters. This study summarto investigate the sensitivity parameters to the cost function iinversion scheme.

Model based acoustic inverare popular in determining the psea bed. Matched Field procesuch an inversion technique applied successfully in charactbed and the layers underneath. passive techniques are em

OF SYMPOL 2013

in

2, USA.

by noise inversion and field

helps in Model

ecked for vity of a es of the n of cost

belong to this to any inversion, he sensitivity of rest to the cost algorithm. This

erization that we rn results in an y adapting the nsitivity of the rizes our efforts of the seabed

in a noise based

rsion techniques properties of the ssing (MFP) is that has been

terizing the sea Both active and

mployed using

Sanjana et al.: Vertical Coherence of Ambient Noise in Shallow Water 97

vertical/horizontal arrays as receiver with or without a sound source. The simplest configuration is a vertical linear array of receivers spanning a small portion of the water column[2]. In MFP, the model and field parameters are combined, and the error estimate is quantified in the least squares sense based on a cost function.

In this paper, the site is modeled using the geoacoustic model OASES[3] and the cost function is evaluated against the field solution as each seabed parameter takes on all possible values.

2. Ocean Acoustic Model

The principles of wavenumber integration for horizontally stratified media was introduced into underwater acoustics by Pekeris [4]. In underwater acoustics, wave number integration approaches are often called FFPs (Fast Field Programs) because of the use of FFT's for evaluation of the spectral integrals in early implementations. The technique is to apply a series of integral transforms to the Helmholtz equation to reduce the original four dimensional partial differential equation to a series of ordinary differential equation in the depth coordinate.

There are basically two steps, the first is the computation of the depth dependent green's function and the second is the numerical evaluation of the wave number integral yielding the field versus range and depth.

The Helmholtz equation is

)()(2

22

sxxpxc

p −−=+∇ δω where p is pressure,

ω is radial frequency, c(x) is speed of sound.

Applying Fourier-Bessel transform to the Helmholtz equation yields the Green’s function as shown below:

, ,

⇒

0 0; 0

where k is the medium wave number, z is depth, r is range, J0 is Bessel function of the first kind of order zero.

The pressure field is reconstructed using the inverse transform;

kdkkrJzkgzrp )(),(),(0

0∫∞

=

which can be efficiently evaluated using an FFT [5];

dkekzkgr

ezrp ikrKi

∫≈max

0

4/

),(2

),(π

π

The general purpose computer code

'OASES', which is widely use in the ocean acoustic community for modeling seismo-acoustic propagation in horizontally stratified waveguides using wave number integration in combination with the Direct Global Matrix solution technique, is adopted here[5]. The model output is the horizontal wave number and the complex Green’s function representing the field at the two receivers.

Deane et al. [6] has derived a theoretical model for computing vertical coherence of wind generated noise in shallow waters using the complex Green’s function.

2/1

0 0

2

2

2

1

0

*21

12

⎥⎦

⎤⎢⎣

⎡=Γ

∫ ∫

∫∞ ∞

∞

dpGpdpGp

dpGpG

pp

pp

To evaluate the integrals it is necessary to know the functions pG1 and pG2 representing the field at the two receivers and the horizontal wave number p. These functions are given by the OASES output.

98 PROCEEDINGS OF SYMPOL 2013

3. Model Environment

The environment is described by a one layer geoacoustic model (sediment overlying an infinite half space). OASES is capable of incorporating shear components also in the model. Hence, in the basement shear speed and shear attenuation is also considered.

Fig.1: Schematic of the model environment showing the sediment layers.

Physical model is represented by water

column of 30 m depth. The wind noise generators are modeled as a plane of omnidirectional point sources just below the pressure release surface. The water column consists of sound speed cw and density ρ. The sediment layer consists of compressional sound speed cp1, compressional attenuation αp1 and density ρ1. An acoustic bottom half space characterized by compressional wave speed and attenuation cp2 and αp2; shear wave speed and attenuation cs2 and αs2; and density ρ2 is considered. Two receivers are placed at water depths of 15.0 m and 15.6 m respectively.

4. Results and Discussion

The inversion is based on simple curve fit between theoretical and measured coherence. Since coherence is a function of the sea bed parameters, the best fit will occur when the parameters used in the model is match the parameters existing at the experimental site. Inversion algorithms iteratively comapre

measured acoustic field data withmodeled acoustic data from an acoustic propagation model using a cost function that is a measure of the mismatch between measured and modeled data. An algorithm minimizes the cost function by efficiently searching the model parameter space. A priori information about the values of the model parameters helps to provide bounds for this search. The objective of the inversion algorithm is to search the model parameter space until a low cost function value is found. If a low cost function value is obtained the resulting model parameter values are assumed to represent the true geo-acoustic parameters. The cost function [7] used in the inversion algorithm is

2

))Im()(Im())Re()(Re()(

2/12

mod

2/12

mod ⎥⎦

⎤⎢⎣

⎡ Γ−Γ+⎥⎦

⎤⎢⎣

⎡ Γ−Γ=

∑∑i

eldatai

eldata

mE

where dataΓ is coherence from data and

elmodΓ is coherence from model. Model sensitivity is checked for

• half-space density

• half-space compressional attenuation

• half space shear sound speed

• half-space shear attenuation

• half space compressional speed

• sediment layer depth

• sediment layer density

• sediment layer compressional speed

• sediment layer compressional attenuation

The averaged field coherence for sensor separation of 0.6 m (for a frequency of 1.25 kHz corresponding to λ/2) is given in Figure.2. The sensitivity of model parameters to the cost function is checked by comparing the field and model values. For a specific parameter, the acoustic field is computed for all possible values in its search space. Meanwhile, the other

Water Column

h=30m, cw, ρ

Sediment layer cp1; ρ1; αp1 h1

Bottom half space cp2; ρ2; αp2; cs2; αs2

Sanjana et al.: Vertical Coherence of Ambient Noise in Shallow Water 99

parameters are held fixed at its reference values. The nine parameters considered and their reference values are: cp1=1570 m/s, αp1=0.2 dB/λ, ρ1=1.4 g/cm3, h1=0.5 m, cp2=1750 m/s, αp2=0.45 dB/λ, cs2=50 m/s, αs2=2.5 dB/λ and ρ2=1.9 g/cm3.

Fig. 2: Averaged real and imaginary coherence for the site for sensors spaced 0.6 m apart vertically (the dashed line shows the standard deviation in coherence.

The results of the sensitivity study are presented in Figure 3. From the sensitivity analysis shown in Figure 3, it is clear that the parameters that are most sensitive in the sediment layer are layer depth, density, and compressional speed. For the basement the most sensitive parameter is the compressional sound speed. The cost function is seen to remain constant for shear attenuation as the parameters takes on a range of values.

It can be seen from Figure that the parameters which are most sensitive are the sediment layer depth, basement compressional wave speed and sediment density. On the other hand the shear properties of the basement are least sensitive. Hence, the sensitivity curves suggest that the shear components in the basement may be omitted and the sound speed may be limited to compressional components. The number of inversion parameters may be reduced to seven.

Fig. 3: Cost function evaluated against all possible sediment layer and basement parameters indicating their sensitivity.

5. Conclusion

The shallow continental shelf site is modeled using the geoacoustic model OASES

1000 2000 3000 4000 5000 6000 7000-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

frequency (Hz)

cohe

renc

e

real coherence

std. dev. in real coherence

imag. coherence

std. dev. in imag. coherence

1550 1600 1650 17000.8

0.9

1

1.1

1.2

1.3

1.4

sed. comp. speed(m/s)

cost

func

tion

1 1.2 1.4 1.6 1.8 20.8

0.9

1

1.1

1.2

1.3

sed. density(g/cm3)0 0.05 0.1 0.15 0.2 0.25

0.8

0.9

1

1.1

1.2

1.3

sed. comp. attn.(dB/lambda)

0 2 4 6 8 100.8

0.9

1

1.1

1.2

1.3

1.4

sed. layer depth (m)

cost

func

tion

16001700180019000.8

0.9

1

1.1

1.2

1.3

1.4

basement comp. speed(m/s)100 200 300 400 500

0.8

0.9

1

1.1

1.2

1.3

1.4

basement shear speed(m/s)

1 1.2 1.4 1.6 1.8 20.8

0.9

1

1.1

1.2

1.3

1.4

basement density (g/cm3)

cost

func

tion

0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

1.4

basement comp. atten.(dB/lambda)

0 1 2 30.8

0.9

1

1.1

1.2

1.3

1.4

basement shear atten. (dB/lambda)

100 PROCEEDINGS OF SYMPOL 2013

and vertical coherence is estimated for varying bottom conditions. The model coherence is compared with the averaged field coherence at the site, and error estimate is quantified using a cost function. A Sensitivity Analysis was carried out to understand the significance of parameters in the sediment layer and basement. The parameters that least influence the model can be kept constant and thus the number of inversion parameters can be reduced which will help in better convergence.

ACKNOWLEDGMENTS The authors thank Director, NIOT for

encouraging this research work. The authors acknowledge the support of the team members of the Ocean Acoustics group during the course of this work.

References

[1]. W. A. Kuperman. Ocean Noise: Lose it or use it, Proceedings of Meetings on Acoustics, Vol. 19, 040115, 2013.

[2]. Carbone N M, Deane G B and Buckingham M J (1997). Estimating the compressional and shear wave speeds of a shallow water seabed from the vertical coherence of ambient noise in the water column. J. Acoust. Soc. Am., 103(2), 801-813.

[3]. H. Schmidt and F.B. Jensen (1985). A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid-solid interfaces. J Acoust. Soc. Am., 77, 813-82585.

[4]. C L Pekeris, (1948). Theory of propagation

of explosive sound in shallow water, Geol. Soc. Am. Mem., 27.

[5]. H. Schmidt (2004). OASES Version 3.1,

User Guide and Reference Manual, Massachussetts Institute of Technology.

[6]. Deane G B, Buckingham M J and Tindle C

T (1997). Vertical coherence of ambient noise in shallow water overlying a fluid sea bed. J. Acoust. Soc. Am., 102(6), 3413-3424.

[7]. Desharnais F, Drover M L and Gillard C A (2002). Inversion of a layered sea bed using noise coherence and simulated annealing, Acoustics 2002- Innovations in Acoustics and Vibration, Annual Conference of the Australian Acoustical Society, 13-15 November, Adelaide, Australia.