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Travel Time Inversion of Multi-Offset vertical Seismic Profiling
Carl B. Godkin
Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on July 30, 1985 in partial fulfillment of the requirements for the degree of Master of Science.
Abstract
A robust method of determining one-dimensional velocity structure from vertical seismic profile travel times is formulated by the linearized least squares technique known as Gauss’ method. Since this algorithm uses point to point ray tracing and considers headway refractions, it is versatile enough for even wide offset surveys. The technique is tested with synthetic data under a variety of conditions and is found to produce good results in the presence of noise and when the horizontal layering is improperly modeled.
Three sets of field data, from Mounds , Oklahoma, the Gulf Coast, and the Michigan Basin, were studied with this technique. The Michigan Basin data set was especially interesting as it consisted of data from eight source offsets ranging from 110 to 1940 m with sources azimuthally spread about the borehole for the purpose of seismic imaging of potential reservoir. Good agreement was found between the zero-offset VSP inversion results and velocities from well logs. An attempt made to image the reservoir in question, a Silurian pinnacle reef, by means of travel time residuals calculated from an average model of the region was successful at least from a qualitative point of view.
