Constrained Linear Least Squares Inversion
In many geophysical problems it is possible to generate a set of completely different solutions that adequately explains the experimental data, especially where measurement errors are present. Ultimately, one solution has to be selected as the ‘best’ or most feasible answer to the problem. To do this we have to add to the problem some information not contained in the original equation d=Gm. This extra information is referred to as a priori information and serves to constrain our solutions so as to satisfy any of our quantified expectations of the model parameters. A priori information can take several forms. It may represent previously obtained geophysical, borehole or geological data or may simply be dictated by the physics of the probem. Consequently, constrained inversion takes many forms.
Figures & Tables
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.”