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Book Chapter

Synthetics

Published:
January 01, 2008

Abstract

We assume that a seismic trace has been corrected for amplitude decay resulting from spherical spreading over the seismic time scale of interest (say, for example, from 0 to 6 s). However, in reality, other effects also must be considered. One such effect is inelastic absorption — the loss of seismic energy to frictionally generated heat. (We will treat inelastic absorption in Chapter 14.) We must consider the effect of the seismic energy's source. In addition, effects result from the instrumentation; source and instrument effects are man-made at or near the surface of the ground. We lump these surface effects together in the form of a source wavelet, which we denote by s.

However, the most important effect is that of the deep earth itself. The deep earth is represented by the sequence ε of reflection coefficients. This sequence is called the reflectivity (Robinson, 1957; Ulrych, 1999). In an ideal seismic experiment, an impulsive source (i.e., a sharp spike of energy imposed at time 0) produces the impulse response of the earth, which we denote by h. In the elastic range, the earth is a linear system, so we can write the synthetic trace (also called the synthetic seismogram) x as the convolution 
formula

Equation 1 is called the dynamic convolutional model (Robinson, 1999). The model is called dynamic because the reflection impulse response h is a highly nonlinear function of the reflection coefficients. To deconvolve

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Contents

Society of Exploration Geophysicists Geophysical References Series

Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing

Enders A. Robinson
Enders A. Robinson
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Sven Treitel
Sven Treitel
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Society of Exploration Geophysicists
Volume
15
ISBN electronic:
9781560801610
Publication date:
January 01, 2008

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