Computer modeling of a vertical array in a stratified ocean
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The response of vertical arrays at single frequencies (CW) and for homogeneous media is well known. This paper addresses the issues of frequency dependence and sound velocity gradients for the vertical array response in a deep ocean. I have modified the synthetic seismogram code of Neil Frazer, Subhashis Mallick and Dennis Lindwall to address this problem. The code uses a rearrangement of the Kennett reflectivity algorithm (Kennett, 1974, 1983) which computes the geoacoustic response for depth dependent media and pulse sources by the wave number integration method. The generalized Filon method is applied to the slowness integral for an additional increase in speed (Frazer and Gettrust, 1984; Filon, 1928). The original code computes the response of a single source at a specified depth. The new code has several improvements over the previous one. First, it is a much simplified code addressing only acoustic interaction. The total length is about half the length of the original code. Secondly, the code can compute the response of a vertical array of point sources. By changing the phase delay between the sources, we can steer the beam to the places of most interest. Thirdly, the code reduces considerably numerical noise at large offsets. The original work has numerical noise beyond about 30 km offset at 50 Hz which limits the application of reflectivity modeling in long range problems. The improvement comes with the optimization of the program, both in the speed and program structure. The improved algorithm can be used to get the far offset response (up to 150 km) of a vertical array in the deep ocean at frequencies up to at least 250 Hz. The modeling results are compared to analytical and benchmark solutions. The modified reflectivity code can be applied to the study of pulsed-vertical array sources such as were deployed on the ARSRP (Acoustic Reverberation Special Research Program) acoustic cruises.
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