Appraisal Analysis in Geophysical Inverse Problem: Tool for Image Interpretation and Survey Design

October 18, 2005
  • Inverse problems
  • 34A55
Joint work with Doug Oldenburg. Image appraisal in geophysical inverse problem can provide insight into the resolving capability and uncertainty of estimates. Although a rigorous approach to solve nonlinear appraisal analysis is still lacking but several methods have been proposed in the past such as linearized Backus-Gilbert analysis, funnel function method and nonlinear Backus-Gilbert formulation where forward problem can be expressed as scattering series. In this talk I will discuss appraisal analysis and how it can be used for image interpretation and survey design. In image interpretation the goal is to quantify what part of model can be resolved by the data and what parts are consequence of regularization operator? In survey design the objective is to determine optimal survey parameters, such as the position of sources/receivers and possibly frequencies in EM experiments, that would provide better' model resolution in a region of interest. For both of these problems we examine the resolution measure called point spread function. The point spread function quantifies how an impulse in the true model is observed in the inversion result and, hence, the goal is to adjust the survey parameters so that the point spread function is as delta-like as possible. This problem is solved as a nonlinear optimization problem with constraints on the parameters. Examples from ray-based tomography and controlled source electromagnetics will be presented.