Betti designature and elastic demultiple of multi-component seismic data

Abstract

In this work I show that Bettis's theorem provides the theoretical basis for eliminating the physical response of the medium above the receiver surface (overburden) in the multi-component source, multi-component receiver seismic experiment. Other than the position of the orthogonally oriented source elements, no source characteristics are required to eliminate all seismic waves scattered from the overburden. The physical radiation characteristics (signatures) of the multi-component sources are transformed into any desired radiation characerisitic. A fundamental assumption of the elimination scheme is that the data recordings can be properly decomposed into upgoing and downgoing wave consitituents. The wave-equation method to eliminate source radiation characteristics and waves scattered from the overburden is denoted by Betti designature/elastic demultiple.

The Betti designature/elastic demultiple method has the following additional characteristics: it preserves primary amplitudes; it requires no knowledge of the medium below the receiver level; it requires information only of the local density and elastic wave propagation velocities at the receiver level.

Following the Betti designature/elastic demultible step I introduce an elastic wavefield decomposition step that decomposes the multi-component source, multi-component receiver Betti designatured/elastic demultipled data into primary PP,PS,SP and SS wave responses that would be recorded from pressure wave and shear wave sources and receivers. The combined elastic wavefield decomposition on the source and receiver side gives data equivalent to data from a hypothetical survey with overburden absent, with single component pressure and shear wave sources, and single component pressure and shear wave receivers.

In the case when the medium is horizontally layered, I show that the Betti designature/elastic demultiple scheme greatly simplifies, and is conveniently implemented as determinisitic multidemensional deconvolution and elastic source-receiver wavefield decomposition of common shot gathers.