A sum autoregressive formula for the reflection response

Abstract

The normal incidence unit impulse reflection response of a perfectly stratified medium is expressible as an autoregressive‐moving average (ARMA) model. In this representation, the autoregressive (AR) component describes the multiple patterns generated within the medium. The moving average (MA) component, on the other hand, bears a simple relation to the sequence of reflection coefficients (i.e., primaries only) of the layered structure. An alternate representation of the reflection response can be formulated in terms of a superposition of purely AR time‐varying minimum‐delay wavelets. Each successive addition of a deeper interface to the layered system gives rise to an AR wavelet whose leading term is equal to the magnitude of the primary reflection originating at this interface. We accordingly call these wavelets “generalized primaries.” The AR component of every generalized primary contains only those multiple reflections that arise from the addition of its particular interface to the layered medium.