A transformational approach to geophysical inverse problems

Abstract

A set of coordinate transformations is used to linearize a general geophysical inverse problem. Statistical and analytic techniques are employed to estimate the parameters of such linearization transformations. In the transformed space, techniques from linear inverse theory may be utilized. Consequently, important concepts, such as model parameter covariance, model parameter resolution and averaging kernels, may be carried over to non-linear inverse problems. I apply the approach to a set of seismic cross-borehole traveltimes gathered at the Conoco Borehole Test Facility. the seismic survey was conducted within the Fort Riley formation, a limestone with thin interbedded shales. Between the boreholes, 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 averaging lengths are greatest in the underlying low-velocity region.