State Space Models of Lossless Layered Media.

摘要

This paper develops time-domain state space models for lossless layered media which are described by the wave equation and boundary conditions. Our models are for non-equal one-way travel times; hence, they are more general than existing models of layered media which are usually for layers of equal one-way travel times. Full state models, which involve 2K states for a K-layer media system, as well as half-state models, which involve only K states are developed and related. Certain transfer functions, which appear in the geophysics literature in connection with models of layered media with equal travel times, are generalized to the situation of non equal travel times. Our state space models represent a new class of equations, causal functional equations, some of whose properties and approaches to simulation are discussed.