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Acoust amplitude angle applied approximation array arrivals assume attenuation average becomes bottom boundary calculated caustic coherent complete components consider constant continuous coordinates correlation corresponding curves defined depends depth direction discussed distance distribution effect energy equation example experimental experiments expressed field Figure filter fluctuations follows frequency function given gives half-space harmonic homogeneous horizontal incident increases infinite integral irregular layer limit matched mean measured medium method modes noise normal observed obtained ocean particular path phase plane position pressure problem propagation pulse radiation range reflection region relative response result rough scattered shows signal similar simple solution sound sound velocity source and receiver space spectrum stratified studies substitution surface tends theoretical theory tion total reflection transformation transmission turning point values vertical wave waveguide York zero