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Simplified signal models of the bottom reverberation are widely used in the sonar literature, but the simplifications themselves are seldom discussed. In this paper, the formulation of the joint modeling of signal propagation, bottom scattering, and reception is reviewed, and an emphasis is placed on the assumptions which lead to model simplification. The interest extends to modeling for sensor motion compensation algorithm development, and it is in this context that an in-depth understanding of the assumptions and simplifications becomes essential. The formulations help pave the way for the derivation of motion compensation algorithms. One such algorithm is presented in the companion paper.