Deconvolution of Exploration Seismic Data

Abstract

A layered-earth seismic model is subdivided into two subsystems. The upper subsystem can have any sequence of reflection coefficients but the lower subsystem has a sequence of reflection coefficients which are small in magnitude and have the characteristics of random white noise. It is shown that if an arbitrary wavelet is the input to the lower lithologic section, the same wavelet convolved with the white sequence of reflection coefficients will be the reflected output. That is, a white sedimentary system passes a wavelet in reflection as a linear time-invariant filter with impulse response given by the reflection coefficients. Thus, the small white lithologic section acts as an ideal reflecting window, producing perfect primary reflections with no multiple reflections and no transmission losses. The upper subsystem produces a minimum-delay multiple-reflection waveform, called the multiple wave train or the multiple wavelet. Therefore, the received seismic signal within the time gate corresponding to the lower subsystem is given by the convolution of the multiple wavelet with the white reflection coefficients of the lower subsystem. This is the linear time-invariant seismic model used in predictive deconvolution. This model explains why time-invariant deconvolution filters can be used within various time gates on a received seismic signal, which at first appearance might look like a continually time-varying phenomenon.