INTRODUCTION 



This report describes the bottom loss models that comprise part of our effort in 

 the Bottom Interaction Program for 1974-1977. Although some of these models were 

 developed earlier, they continue to be modified and updated for current uses. 



Our linear gradient multilayer model and our sohd multilayer model were designed 

 to study reflection of low frequency sound from the ocean bottom. Considerable depths 

 (up to a kilometer) of ocean sediments are insonified at low frequencies. Consequently, 

 sediment parameters can undergo considerable variation in the insonified region. This 

 variation of sediment properties with depth must be taken into account if an accurate 

 representation of bottom loss is to be attained. The hquid multilayer model can account 

 for many layers of sediment in which the sound speeds are complex to account for ab- 

 sorption. The linear gradient model assumes complex sound speeds, also, but the sound 

 speeds vary in a linear fashion in a particular sediment layer. 



Our solid multilayer model is a general purpose plane wave reflection model that 

 can account for both liquid and/or sohd layers. We know that sediments have rigidity and, 

 therefore, for more accurate model calculations we must take rigidity into account. Im- 

 portant parameters to the solid model are the speed and attenuation of both the com- 

 pressional and shear waves that travel in the sediment. In our most recent programs we 

 have chosen to model the variable sediment properties with many layers (up to 1000 

 layers or more, if necessary), and maintain the needed accuracy by use of Knopoff's 

 formulation. We have taken the concept of many constant layers as in the liquid model 

 (but for solid layers, i.e., sediments with rigidity) and made it possible to have the many 

 constant layers approximate the results of a linear gradient concept. 



The distinguishing features of the solid multilayer model are the following: 

 All sediment layers can be reahstically represented to have rigidity 

 Both solid and liquid layers can be taken into account if required 

 The Knopoff formulation provides fast and accurate computations 

 Continuous density variations are accounted for 



The various outputs include bottom loss and/or R versus grazing angle 

 The graphical forms include 3-dimensional representation 

 A so-called equivalent bottom concept has been developed for the Parabohc Equa- 

 tion (P.E.) propagation program. The Gibb's oscillations caused by a density discontinuity 

 at the interface can be handled by calculating an equivalent reflection coefficient by 

 assuming different sediment parameters. An example of the technique is included. This 

 technique should enable the P.E. propagation program to be used for bottom limited areas. 



FORMULATION OF THE SOUND FIELD USING THE PLANE WAVE 

 REFLECTION COEFFICIENT R 



There are two types of solution to the wave equation which are of particular 

 importance in sound transmission. One is the transformation of the wave equation to the 

 eikonal equation and a solution in terms of wave surfaces and rays. The other is a develop- 

 ment through specific boundary conditions into a solution in terms of normal modes. In 



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