A form of Kirchhoff’s wave equation is presented which is useful to the geophysicist doing an amplitudeinterpretation of seismic reflection data. A simple rearrangement of Kirchhoff’s retarded potential equation allowsthe reflection process to be evaluated as a convolution of the derivative of the source wavelet with a term called the“wavefront sweep velocity”. The wavefront sweep velocity is a measure of the rate at which the incidentwavefront covers the reflecting boundary.
By comparing wavefront sweep velocities for geologic models with different curvature, one obtains an intuitive feeling forthe relation of diffraction and reflection amplitudes to boundary curvature. Also, from this convolutional form of the waveequation, the geometrical optics solution for reflection amplitude is easily obtained. But more important, from thewave-front sweep velocity approach, a graphical method evolves which allows the geophysicist to use compass and ruler toestimate the effects of curvature and diffraction on seismic amplitude.
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The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years. “Seismic Diffraction” covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.