Analysis of the Spectral Characteristics of a Thin-Bedded Sequence

Abstract

As a result of the development of spectral methods for interpreting seismic data in recent years [1–6], many methods for computing the spectral characteristics for various representations of layered media have been developed for waves of different types. Analyses have also been made of the properties of the spectral characteristics computed for several representations of the medium. Spectral characteristics have been established for the case of the wave incident on a planar layer consisting of sinusoids. Primarily, the methods which have been developed are valid for determining the spectral characteristic for normal incidence and longitudinal reflection of waves [7–12]. In some of the previous work, methods have been presented for computing the spectral characteristics of a layered medium for the case of inclined wave incidence either using the principle of geometric optics [12, 13] or expressions for wave propagation in a continuous, ponderable medium [14–16]. The method described in references [14, 16] allows the determination of the spectral characteristic for reflected and transmitted waves: longitudinal, volume, and transverse. Here, we will consider only the case of normal incidence of waves on a layer or sequence of layers.