In the geophysical and related sciences, experiments are usually performed under controlled conditions (i.e., in a systematic manner), and the outcome may be numerical values that represent our observations at fixed (or predetermined) intervals, say. These observations of some properties of the physical world are commonly referred to as the EXPERIMENTAL or OBSERVATIONAL DATA. Since such a set of data is systematically collected there must be some way of explaining or coordinating them. To draw any inferences from these data, we need to understand the relationship between the distribution of the properties of the physical system under study (e.g, the Earth) and the observable geophysical responses. The system of equation that describe this relationship constitute the FORWARD THEORY. Inferece of the properties of the physical system from observational data is the opposite procedure and we need to apply some quantitative tools collectively referred to as the INVERSE THEORY.
Inverse theory is au organised set of mathematicaa and statistical techniques (calculus, matrix algebra, statistical estimation and inference, etc) for retrieving useful information about a physical system (or the physical world) from controlled observations on the system. It is directly concerned with the analysis of experimental data, the fitting of mathematical models to these data by estimating the unknown parameters of the models, and optimal experimental design. Inverse theory is practiced by every scientist that analyses data relating to the physical world which in the case of geoscientists is the Earth. As a matter of fact, anyone that has fitted a line
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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.”