Attenuation is a reduction in the energy of a traveling wave as it propagates through a medium. Attenuation — the falloff of a wave's energy with distance — has three main causes: (1) transmission loss at interfaces because of reflection, diffraction, mode conversion, and scattering (Bowman, 1955); (2) geometric divergence effects as waves spread out from a source; and (3) absorption, which is the conversion of kinetic energy into heat by friction (note that kinetic energy is the energy of motion). Writers do not always distinguish between the terms attenuation and absorption. Here, we refer to attenuation in the general sense of energy loss to any cause, and we use the term absorption in the special sense of energy loss to heat.
Transmission loss is a wave's energy loss as the wave travels through an interface. In transmission loss, the energy that is lost is diverted from the traveling wave of interest. There is no loss of total kinetic energy because the lost energy merely travels somewhere else. For example, when a wave meets an interface, some energy is reflected back from the interface, and only part of the wave's energy is transmitted though the interface.
Mode conversion is the conversion of P-wave energy into S-wave energy or vice versa. Mode conversion occurs when a wave arrives at an interface at an obliquely incident angle to that interface. Converted waves divert energy away from the given wave.
The energy of a wave in a homogeneous material is proportional
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Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
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.