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

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.