Generalized linear inversion of reflection seismic data

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Abstract
Generalized linear inversion, sometimes known as model perturbation, nonlinear regression, or inverse modeling, is applied to synthetic and real seismic data sets with the objective of obtaining an impedance profile as a function of time. The impedances solved for are parameterized in a manner that describes the unknown earth using fewer variables than previous seismic generalized linear inversion techniques. In this application only single traces of common‐midpoint (CMP) processed data will be inverted. The method of generalized linear inversion (GLI) presented here is designed to improve on the shortcomings of recursive inversion with respect to relative and absolute scale of the impedance results, resolution of impedance boundaries, and distortion from residual wavelet effects. In obtaining these goals other advantageous aspects of GLI were discovered. For example, it is insensitive to noise in many cases, and it will allow an interpreter to fix the impedance of any number of known lithologies in an interval being inverted. This last property is extremely useful when evaluating a prospect on an otherwise well‐understood seismic line. The GLI method is illustrated on a number of synthetic examples and one field data set from the Powder River basin of Wyoming.

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