Error Analysis in Linear Inversion
One question that is fundamental to geophysical data analysis is, how representative of the real geophysical system is our reconstructed least squares model or how accurate is our solution to the given problem? Recall that our initial assumption was that the experimental data contain errors (which is why we cannot fit them exactly). One may therefore be interested in how the experimental errors translate into errors in the model estimates. The answers obviously come from statistics. Inverse theory not only provides us with estimate of the relevant parameters but also furnishes a plethora of related information that enable us to gauge the "goodness" of the least squares solution to the inverse problem. Some of such “auxiliary parameters” are described following a discussion of how to incorporate available observational errors directly in the inversion process.
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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.”