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Book Chapter

Inverse Problems in Geophysics

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Published:
January 01, 1995

Abstract

In order to fully understand the meaning of the term ‘inverse problem’, it is instructive to consider, first, the opposite situation dubbed the ‘forward problem’. Traditionally, the interpretation of some geophysical data (e.g., resistivity depth sounding data) involves comparison with theoretical Master curves (or nomograms). These curves are computed using certain relationships (mathematical model) assuming a particular distribution of the physical properties of the subsurface, i.e., the curves are the theoretical responses for idealised Earth-type structures. The procedure is simple:

‘Given some information on the values of the set of parameters (e.g., number of layers, their resistivities and thicknesses) far a hypothetical Earth-model, a theoretical relationship (mathematical model) is used to derive the values of same measurable quantities {cgn apparent resistivities and phases)’.

This procedure constitutes the FORWARD APPROACH and solves our forward problem (see Fig 2.1). Note that what is generally known to many geophysicists as ‘Forward modelling by interactive computing’ is nothing but a more versatile extension of the original curve-matching technique. In interactive forward modelling the theoretical curves generated for an input model are displayed together with the field curves, say, on a interactive terminal, The model parameters are adjusted and the operations repeated until an acceptable visual fit is obtained between the field and theoretical curves.

In the inverse approach, the Earth's structure (or other useful information) is directly retrieved from the.field data (Fig. 2.2). The inverse procedure is described as: ‘Given same information on the values of some measured quantities (field or experimental data), we’

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Society of Exploration Geophysicists Course Notes

Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice

Max A. Meju
Max A. Meju
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Society of Exploration Geophysicists
Volume
6
ISBN electronic:
9781560802570
Publication date:
January 01, 1995

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