Abstract

The two-dimensional (2-D) reflection path from a dipping plane between an offset source-receiver combination in a constant velocity medium can be described with several parameters (coordinates, offsets, angles, and lengths). Although there are many parameters, only four independent ones are needed to locally determine the reflection geometry. Given four determining parameters, the evaluations of other ones present problems that range from trivial to formidable.The circumscribed circle about the source, receiver, and specular point turns out to have a number of remarkable properties that are useful for the solution of these problems. The radius of the circle is a useful new auxiliary parameter. Triangles constructed in the circle provide nonintuitive mathematical relationships between angles and lengths. The use of mathematical relations derived from the circle has allowed the creation of formulas to fully recover the reflection geometry in a vast majority of valid sets of four known parameters. This circle provides a powerful tool for the calculation of nondetermining parameters as well as new insight into the geometry of reflection with straight raypaths.

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