A TRANSFORMATIONAL APPROACH TO GEOPHYSICAL INVERSE PROBLEMS

A set of coordinate transformations is used to linearize a general geo physical inverse problem. Statistical and analytic techniques are empl oyed to estimate the parameters of such linearization transformations. In the transformed space, techniques from linear inverse theory may b e utilized. Consequently, important concepts, such as model parameter covariance, model parameter resolution and averaging kernels, may be c arried over to non-linear inverse problems. I apply the approach to a set of seismic cross-borehole traveltimes gathered at the Conoco Boreh ole Test Facility. The seismic survey was conducted within the Fort Ri ley formation, a limestone with thin interbedded shales. Between the b oreholes, the velocity structure of the Fort Riley formation consists of a high-velocity region overlying a section of lower velocity. It is found that model parameter resolution is poorest and spatial averagin g lengths are greatest in the underlying low-velocity region.