Nonlinear seismic tomography and model uncertainty estimation with the Markov chain Monte Carlo method
Conventional linear seismic tomography methods have limitations in solving nonlinear problems, such as overcoming the local minimum problem and objective estimation of derived model uncertainties. In this research, an adaptive heating Markov Chain Monte Carlo (MCMC) method is proposed, tested and applied to real data. The standard MCMC method is first compared with the pure Monte Carlo approach using a simple model to demonstrate its accuracy, efficiency and the ability to converge from a location far away from the true model. The low mixing rate problem (local minima) of the standard MCMC method in solving more complex seismic tomography problems is then illustrated and an adaptive heating algorithm to solve this problem is proposed and tested with synthetic models. A two step seismic tomography approach with the MCMC method is described to obtain an optimal model solution and provide objective estimation of model uncertainty. In the first step, various sized blocks are used in the MCMC process to obtain geologically realistic models. In the second step, a uniform block size is used to objectively estimate model uncertainty. A procedure for determining the uniform block size used in the second step is described. Model studies using forward calculations are used to demonstrate that the estimated uncertainties using this procedure and the MCMC method are reasonably accurate. Synthetic testing also shows the ability of the MCMC method to do simultaneous inversion with refraction data and zero-offset reflection data. The proposed adaptive heating MCMC method is applied to two real data sets: the SAGE 2002 high resolution seismic data and the JTEX seismic refraction and gravity data. The upper crustal velocity structure beneath the Valles caldera and its vicinity (San Juan Basin and Rio Grande rift) above approximately 6 km depth is obtained from inversion of the JTEX seismic data using the adaptive heating MCMC method. Modeling of the gravity data is also used to interpret deeper density structure. These synthetic tests and real data applications show that the adaptive heating MCMC method is an effective technique for seismic tomography which can avoid the problems of local minima, be used for efficient inversion of optimal models, and that can provide reasonably reliable estimates of derived model uncertainty.
Braile, Purdue University.
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