Time-Domain Extraction of Broad-Band Sources by Tikhonov-Phillips Regularization of Triangular Toeplitz Kernels*

Abstract

Single receiver source deconvolution in a shallow water environment is an ill-posed problem whose difficulty is compounded by the multipath nature of the propagation operator. If only sources that are quiescent prior to some initial time to are considered, the result of discretizatizing the problem in the time domain is an ill-conditioned triangular Toeplitz system. In this paper we show how an algorithm of Elden can be used to implement Tikhonov-Phillips regularization for this system. Unlike the multichannel deconvolution techniques used in underwater acoustics, this method can extract source signatures using the outputs of a single sensor. In addition, when the propagation is multipath and source signature extraction is performed as part of an optimization procedure for environmental inversion, we can work with shorter time windows so that the process becomes computationally more efficient than frequency domain deconvolution. A number of examples of the use of the Tikhonov-Philips regularization method for source series extraction are provided. (Also cross-referenced as UMIACS-TR-95-87)