In the past, most seismic surveys were along surface lines, which yield 2D subsurface images. Because of great strides in computer technology and seismic instrumentation, exploration geophysics has made the transition from 2D to 3D processing.
The wave equation behaves nicely in one dimension and in three dimensions but not in two dimensions. In one dimension, waves on a uniform string propagate without distortion. In three dimensions, waves in a homogeneous isotropic medium propagate in an undistorted way except for a spherical correction factor. However, in two dimensions, wave propagation is complicated and distorted. By its very nature, 2D processing never can account for events originating outside of the plane. As a result, 2D processing is broken up into a large number of approximate partial steps in a sequence of operations. These steps are ingenious, but they never can give a true image.
On the other hand, 3D processing accounts for all of the events. It is now cost-effective to lay out seismic surveys over a surface area and to do 3D processing. No longer is the third dimension missing, so consequently, the need for a large number of piecemeal 2D approximations is gone. Prestack depth migration is a 3D imaging process that is computationally extensive but mathematically simple. The resulting 3D images of the interior of the earth surpass all expectations in utility and beauty.
Reflection seismology is a remote-imaging method used in petroleum exploration. The seismic reflection method was developed in the 1920s. From then until about 1965,
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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.