^{1,a)}, Stan E. Dosso

^{2}and N. Ross Chapman

^{2}

### Abstract

This paper presents geoacoustic inversion of a light bulb implosion recorded during the Shallow Water 2006 experiment. The source is low frequency and impulsive, the environment is shallow water, and the acoustic signal is recorded using a single receiver. In this context, propagation is described by modal theory, and inversion is carried out by matching modal dispersion curves in the time-frequency domain. Experimental dispersion curves are estimated using an advanced signal processing method called warping, allowing inversion to be carried out at a relatively short range ( km). Moreover, the inversion itself is performed using Bayesian methodology. This allows inference of the seabed structure from the data, including the number of seabed layers resolved, optimal estimates of the seabed parameters, and quantitative uncertainty estimates. Inversion results of the experimental data are in good agreement with both ground truth and estimates from other experimental data in the same region.

I. INTRODUCTION

II. EXPERIMENT DESCRIPTION

A. The SW06 experiment

B. Data description

III. DISPERSION CURVE ESTIMATION

A. Modal propagation theory

B. Single receiver context

C. High resolution estimation of the dispersion curves

IV. INVERSE THEORY

V. INVERSION RESULTS

A. Model selection and data error estimation

B. Inversion results for the selected model

C. Discussion of the estimated geoacoustic parameters

VI. CONCLUSION

### Key Topics

- Dispersion
- 34.0
- Speed of sound
- 23.0
- Optical dispersion
- 9.0
- Signal processing
- 9.0
- Probability theory
- 8.0

##### H04R1/44

## Figures

Chirp sonar data along the source/receiver track obtained during the experiment (Ref. 26 ).

Sound-speed profile in the water column measured on CTD41 during the SW06 experiment.

Sound-speed profile in the water column measured on CTD41 during the SW06 experiment.

(Color online) Experimental signals. (a) Spectrogram of the received signal and (b) spectrogram of the corresponding warped signal (arbitrary linear scale). Estimated (black) and modeled (white) dispersion curves are superimposed on the received signal spectrogram in (a). On each spectrogram, white numbers indicate the mode numbers.

(Color online) Experimental signals. (a) Spectrogram of the received signal and (b) spectrogram of the corresponding warped signal (arbitrary linear scale). Estimated (black) and modeled (white) dispersion curves are superimposed on the received signal spectrogram in (a). On each spectrogram, white numbers indicate the mode numbers.

Dispersion curves of the received signal. The circles correspond to the estimated dispersion curves using warping while the continuous lines show the curves predicted for the MAP model estimate.

Dispersion curves of the received signal. The circles correspond to the estimated dispersion curves using warping while the continuous lines show the curves predicted for the MAP model estimate.

(Color online) Data error estimation for mode 1. (a) Residual and (b) corresponding data error covariance matrix (arbitrary linear scale). Other modes show similar results.

(Color online) Data error estimation for mode 1. (a) Residual and (b) corresponding data error covariance matrix (arbitrary linear scale). Other modes show similar results.

Parametrization study that takes into account data error statistics. Models are B: basement only; B + 1U: one layer over basement; B + 2U: two layers over basement. For display purposes, misfit and BIC are shifted so that their minimum value is zero.

Parametrization study that takes into account data error statistics. Models are B: basement only; B + 1U: one layer over basement; B + 2U: two layers over basement. For display purposes, misfit and BIC are shifted so that their minimum value is zero.

Marginal probability densities from Bayesian inversion of the SW06 light bulb data.

Marginal probability densities from Bayesian inversion of the SW06 light bulb data.

(Color online) Selected joint marginal probability densities. Each distribution is normalized independently (arbitrary linear scale).

(Color online) Selected joint marginal probability densities. Each distribution is normalized independently (arbitrary linear scale).

(Color online) Marginal probability profiles: (a) Sound speed and (b) density. Each distribution is globally normalized over 0 to 50 m (arbitrary linear scale).

(Color online) Marginal probability profiles: (a) Sound speed and (b) density. Each distribution is globally normalized over 0 to 50 m (arbitrary linear scale).

## Tables

Inversion parameter list. Prior information is uniform over the given search bound. The last two columns give the MAP estimation and the 95% HPD interval for an environment consisting of a single layer over a basement.

Inversion parameter list. Prior information is uniform over the given search bound. The last two columns give the MAP estimation and the 95% HPD interval for an environment consisting of a single layer over a basement.

Data error statistics: Runs test and KS test p-values for the standardized residuals after covariance weighted inversion.

Data error statistics: Runs test and KS test p-values for the standardized residuals after covariance weighted inversion.

Comparison of the parameters estimated here (given in terms of 95% HPD interval) with other studies. When two sound speed values are separated by a dash, the given values constitute the estimation range. When two sound speed values are separated by a single slash, inversion was carried out assuming a sound speed gradient in the layer: The first value is the estimated sound speed at the top of the layer while the second one is the estimated sound speed at the bottom of the layer. When two sound speed values are separated by a double slash, inversion was carried out assuming two iso-speed layers over a basement; the first value is the estimated sound speed in the first layer while the second one is the estimated sound speed in the second layer. For layer width estimation, a dash signifies that this information was required a priori, a cross indicates that it was not properly estimated and HSB means that inversion was carried out assuming a half space bottom model.

Comparison of the parameters estimated here (given in terms of 95% HPD interval) with other studies. When two sound speed values are separated by a dash, the given values constitute the estimation range. When two sound speed values are separated by a single slash, inversion was carried out assuming a sound speed gradient in the layer: The first value is the estimated sound speed at the top of the layer while the second one is the estimated sound speed at the bottom of the layer. When two sound speed values are separated by a double slash, inversion was carried out assuming two iso-speed layers over a basement; the first value is the estimated sound speed in the first layer while the second one is the estimated sound speed in the second layer. For layer width estimation, a dash signifies that this information was required a priori, a cross indicates that it was not properly estimated and HSB means that inversion was carried out assuming a half space bottom model.

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