Pulse Propagation In A Random Ocean-a Linear Systems Theory Approach

Abstract

A general, modular, pulse-propagation model for underwater acoustics that i s based on linear systems theory for sound-speed profi les a function of depth is presented. Results from two prelfminarycomputer simulation studies involving the transmission of CW and LFM pulses i n the ocean are reported. The f i r s t study examined a shallow water problem and used the transfer function of a Pekeris waveguide. The ocean surface and bottom were treated as smooth, plane boundaries between two f lu id media and were characterized by general Rayleigh reflection coefficients. The second study examined a free-space propagation problem(i.e., no boundaries) and used a transfer function of the ocean medium based on the WKB approximation. INTRODUCTION Since the wave equation i s linear fo r small-amplitude acoustic signals, the ocean medium can be treated, i n general, as a linear, time-variant, space-variant, random f i l ter or communlcation channel(e.g., see [ l1-[31). Although the linear systems theory approach to ocean acoustics has been in the research l iterature since the middle 1960's(e.g., see [4]-[61), most of the results have been very formal and abstract, that is, not amenable to computer simulation. Based on recent successes i n the derivation of ocean medium transfer functions[71,[81, it is now possible(with the use of "coupling equations" [91) t o derive analytical expressions for the complex acoustlc f ie ld and the output electrical signal(pu1se) a t each element in a hydrophone array in terms of the frequency spectrum of the transmitted pulse, the far-field direct iv i ty functions of the transmit and receive arrays, and the ocean medium transfer function[71,[ 101. These same analytical expressions are also amenable to computer simulation studies[ 1 1 ],[ 121. In th is paper, we shall present a general, modular, pulsepropagation model for underwater acoustics that i s based on linear systems theory and the coupling equations for sound-speed profi les a function of depth. The resulting model i s analogous t o the fast-f ield-wogram(FFP) technrque[l31. The maln premlse i s that since the coupling equations are, in fact, the formal solution of the pulsepropagatlon problem, and since the coupling equations depend on the transfer function of the ocean medium, the only thing that changes from problem to problem, from an ocean acoustics point of view, i s the transfer function. In this paper, we shall present a general, modular, pulsepropagation model for underwater acoustics that i s based on linear systems theory and the coupling equations for sound-speed profi les a function of depth. The resulting model i s analogous t o the fast-field-program(FFP1 technique[l3]. The main premise i s that since the coupling equations are, i n fact, the formal solution of the pulsepropagation problem, and since the coupling equations depend on the transfer function of the ocean medium, the only thing that changes from problem t o problem, from an ocean acoustics point of view, i s the transfer function. Therefore, regardless of the problem under consideration, the coupling equations only need t o be programmed once. We shall present pre/iminacv results from two computer simulation studies that involved the transmission of CW and LFII pulses. The f i r s t study examined a shallow water prGblem and used the transfer function o f a Pekeris waveguide. The ocean surface and bottom were treated as smooth, plane boundaries between two f lu id media and were characterized by general Rayleigh reflectlon coefficients. A plot of the output pulse at the receive array illustrates the ef fects of dispersion. The second study examined a free-space propagation problem(i.e., no boundaries) and used a transfer function of the ocean medium based on the WKB approximation.