Abstract

Recently Bortfeld (1982) gave a cursory nonmathematical introduction to a procedure for computing the geometrical spreading factor of a primary zero-offset reflection from the common datum point traveltime measurements of the event. To underline the significance and consequences of this method, a derivation and discussion of geometrical spreading factors is now given for two- and three-dimensional earth models with curved reflecting boundaries. The spreading factors can be used easily to transform primary reflections in a zero-offset seismic section to true amplitude reflections. These permit an estimation of interface reflection coefficients, either directly or in connection with a true amplitude migration. A seismic section with true amplitude reflections can be described by one physical experiment: the tuned reflector model. Hence the application of the wave equation (in connection with a migration after stack) is justified on such a seismic section. Also the geometrical spreading factors that are derived can be looked upon as a generalization of a well-known formula (Newman, 1973), which is commonly used in true amplitude processing and trace inversion in the presence of a vertically inhomogeneous earth.

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