A maximum likelihood approach to nonlinear inversion under constraints

Details A maximum likelihood approach to nonlinear inversion under constraints A maximum likelihood approach to nonlinear inversion under constraints

Aug 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987pepi...47..179m&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 47, p. 179-187.

Physics

16

Scientific paper

Nonuniqueness in geophysical inverse problems is naturally resolved by incorporating prior information about unknown models into observed data. In practical estimation procedures, the prior information must be quantitatively expressed. We represent the prior information in the same form as observational equations, nonlinear equations with random errors in general, and treat as data. Then we may define a posterior probability density function of model parameters for given observed data and prior data, and use the maximum likelihood criterion to solve the problem. Supposing Gaussian errors both in observed data and prior data, we obtain a simple algorithm for iterative search to find the maximum likelihood estimates. We also obtain an asymptotic expression of covariance for estimation errors, which gives a good approximation to exact covariance when the estimated model is linearly close to a true model. We demonstrate that our approach is a general extension of various inverse methods dealing with Gaussian data. By way of example, we apply the new approach to a problem of inferring the final rupture state of the 1943 Tottori earthquake (M = 7.4) from coseismic geodetic data. The example shows that the use of sufficient prior information effectively suppresses both the nonuniqueness and the nonlinearity of the problem.

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