Affiliation:
1. Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093, USA
Abstract
Summary
In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about the correct earth model x E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals.
We compare two forms of prior information: a ‘soft’ bound on x E is a probability distribution px on the model space X which describes the observer's opinion about where x E is likely to be in X; a ‘hard’ bound on x E is an inequality QX (x E , x E ) 1, where Qx is a positive definite quadratic form on X. A hard bound Qx can be ‘softened’ to many different probability distributions px , but all these px 's carry much new information about x E which is absent from Qx , and some information which contradicts Qx. For example, all the px 's give very accurate estimates of several other functions of x E besides Qx (x E , x E ). And all the px 's which preserve the rotational symmetry of Qx assign probability 1 to the event Qx (x E , x E ) =∞. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound px. If that probability distribution was obtained by softening a hard prior bound Qx , rather than by objective statistical inference independent of y, then px contains so much unsupported new ‘information’ absent from Qx that conclusions about z obtained with SI or BI would seem to be suspect.
Publisher
Oxford University Press (OUP)
Subject
Geochemistry and Petrology,Geophysics
Cited by
53 articles.
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