Bayesian Estimation and Deterministic Optimization of Earthquake and Interseismic Model Parameters from InSAR and GPS Data

Abstract:

Bayesian inference is increasingly being used to constrain model parameters of nonlinear geophysical problems from geodetic data. The main advantage of using Bayesian estimation is that it provides information about the full posterior probability distribution function (PDF) of the model parameters, while deterministic optimization only gives the best-fitting set of model parameters. By using Bayesian inference, however, we commonly face computational challenges of adequately sampling the model parameter posterior PDF.

To estimate model parameter uncertainties in deterministic optimizations, we have used a scheme of repeated estimations with slightly modified input data. The procedure includes producing a large number N of data error realizations, based on the estimated data covariance matrix, and then adding each error realization to the input data to make N modified sets of input data. We then use each of these modified input datasets to find the best-fitting model parameters, resulting in N sets of model parameters. The distribution of the model parameters has then been taken as a proxy for the posterior PDF of the model parameters. This procedure has been called “Randomize-then-optimize” or RTO and has the advantage that it is easy to implement.

In this presentation, we compare Bayesian inference and deterministic optimization with RTO for typical examples of determining fault model parameters for moderately sized earthquakes and for estimating interseismic model parameters from InSAR and GPS data. We show that the model parameter PDFs estimated using the two methods appear to be the same, a result which also seems to hold when data covariance matrices exhibit significant correlations (i.e. significant off-diagonal elements) and/or do not obey Gaussian statistics. Our results demonstrate the equivalence of these two different methods and that they can be used interchangeably in geophysical model parameter estimations.