Fast Bayesian optimal experimental design for seismic source inversion
KAUST DepartmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Stochastic Numerics Research Group
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AbstractWe develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem. © 2015 Elsevier B.V.
SponsorsThe authors are grateful for support from the Academic Excellency Alliance UT Austin-KAUST project-Uncertainty quantification for predictive modeling of the dissolution of porous and fractured media. Quan Long and Raul Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.