Recursive Bayesian synthetic aperture geoacoustic inversion in the presence of motion dynamics

Abstract

A low signal to noise ratio (SNR), single source/receiver, broadband, frequency-coherent matched-field inversion procedure recently has been proposed. It exploits coherently repeated transmissions to improve estimation of the geoacoustic parameters. The long observation time improves the SNR and creates a synthetic aperture due to relative source-receiver motion. To model constant velocity source/receiver horizontal motion, waveguide Doppler theory for normal modes is necessary. However, the inversion performance degrades when source/receiver acceleration exists. Furthermore processing a train of pulses all at once does not take advantage of the natural incremental acquisition of data along with the ability to assess the temporal evolution of parameter uncertainty. Here a recursive Bayesian estimation approach is developed that coherently processes the data pulse by pulse and incrementally updates estimates of parameter uncertainty. It also approximates source/receiver acceleration by assuming piecewise constant but linearly changing source/receiver velocities. When the source/receiver acceleration exists, it is shown that modeling acceleration can reduce further the parameter estimation biases and uncertainties. The method is demonstrated in simulation and in the analysis of low SNR, 100-900 Hz linear frequency modulated (LFM) pulses from the Shallow Water 2006 experiment.

Change-point detection for recursive Bayesian geoacoustic inversions

“…8 Then, a single-change-point model is introduced where retrospective change-point detection is applied using Bayesian inference from the importance samples and weights from Sec. II B (see Sec.…”

“…The posterior density, pðmjy 1:l Þ, can be represented by importance samples, fm q ; q ¼ 1; …; Qg, that are drawn from the Gaussian mixture, xðm; lÞ, in an adaptive importance sampling procedure described in detail in Ref. 8. From these importance samples, m q , the corresponding uncorrected and unnormalized weights,ŵ q l , were computed recursively usingŵ q l ¼ pðy 1:l jm q Þpðm q Þ ¼ pðy l jm q Þŵ q lÀ1 :…”

“…The range-independent geoacoustic parameters were based on previous SW06 inversion results. 8,9,[23][24][25][26] The source emits 100-900 Hz LFM pulses with 1 s pulse width and 5 s pulse repetition interval. Hence, for l ¼ 128, the source and receiver would have traversed 5 Â 128 Â 2 ¼ 1280 m. The frequency sampling is 5 Hz starting from 100 Hz to 700 Hz.…”

“…8 Methods for detecting gradual model parameter change are less developed and often require strong parametric assumption. For example, time-varying source-receiver separation can be reparameterized into initial source-receiver separation, initial source and receiver velocities and constant source and receiver accelerations.…”

“…For example, time-varying source-receiver separation can be reparameterized into initial source-receiver separation, initial source and receiver velocities and constant source and receiver accelerations. 8,9 However, reparameterizing all of the model parameters in the inversion will adversely increase the dimension of the parameter search space. A typical treatment of gradual model parameters change is applying sequential geoacoustic inversion or particle filtering to track the parameter posterior density between relatively short-interval measurements.…”