Linear inverse theory with a priori data
Methods of solution of linear inverse problems are reviewed, with emphasis on the relationship between algebraic and probabilistic approaches. Numerical methods for stabilizing the solution of ill-conditioned equations and interpretive methods for calculating the resolving power of experimental data require implicit assumptions about the solution. In many cases this information may be provided explicitly in the form of a ‘a priori data’. This results in considerable simplification of the numerical procedures required both for estimating the solution and for calculating resolving power.
The method is illustrated with a geophysical example. The earths' upper mantle beneath oceanic regions is characterized by a “lid” of high seismic velocity overlying a low velocity “channel”. Gravity and seismic surface wave data are inverted to find the shape of the lid and channel beneath the East Pacific Rise. Without the use of a priori data, the problem is horribly underdetermined, and the resolving kernels do not provide much guidance in identifying physically meaningful “average” structures which can be resolved by the data. However, a great deal is known about the earth's upper mantle from a number of completely independent previous experiments. When these data are incorporated, the gravity and seismic data then lead to a very reasonable solution.
KeywordsInverse Problem Rayleigh Wave Normal Matrix Density Contrast Extremal Model
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