Describing and Formulating Inverse Problems
Published:January 01, 1995
A detailed description or formulation of an inverse problem will address the following nine golden questions:
What is the applicable parameterization- discrete or continuous?
What is the nature of the geophysical data; what are the errors in the observations?
Can we pose the problem mathematically and if so how well posed is it?
Are there any physical constraints on the problem?
5.What types of solution to the problem are desirable; and to what accuracy?
Are we looking for an approximate solution, bounds of the solution or the exact solution?
Is the problem linear or non-linear?
Is it an overdetennined, underdetermined or even-determined problem?
What is the best method of solving the problem?
What are the confidence limits of the solution?
Can it be appraised by other means?
All the above issues will be addressed in this course.
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Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice
“This publication is designed to provide a practical understanding of leastsquares methods of parameter estimation and uncertainty analysis. The practical problems covered range from simple processing of time- and space-series data to inversion of potential field, seismic, electrical, and electromagnetic data. The various formulations are reconciled with field data in the numerous examples provided in the book; well-documented computer programs are also given to show how easy it is to implement inversion algorithms.”