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.
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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Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing (SEG Geophysical References Series No. 15), covers the basic ideas and methods used in seismic processing, concentrating on the fundamentals of seismic imaging and deconvolution. Most chapters are followed by problem sets. Some exercises supplement textual material; others are meant to stimulate classroom discussions. Text and exercises deal mostly with simple examples that can be solved with nothing more than pencil and paper. The book covers wave motion; digital imaging; digital filtering; various visualization aspects of the seismic reflection method; sampling theory; the frequency spectrum; synthetic seismograms; wavelets and wavelet processing; deconvolution; the need for continuing interaction between the seismic interpreter and the computer; seismic attributes; phase rotation; and seismic attenuation. The last of the 15 chapters gives a detailed mathematical overview. Digital Imaging and Deconvolution, nominated for the Association of Earth Science Editors award for best geoscience publication of 2008–2009, will interest professional geophysicists, graduate students, and upper-level undergraduates in geophysics. The book also will be helpful to scientists and engineers in other disciplines who use digital signal processing to analyze and image wave-motion data in remote-detection applications. The methods described are important in optical imaging, video imaging, medical and biological imaging, acoustical analysis, radar, and sonar.