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

Tuesday, October 18, 2005 - 3:50pm - 4:40pm

EE/CS 3-180

Partha Routh (Boise State University)

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.

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.

MSC Code:

34A55

Keywords: