Fast Bayesian optimal experimental design for seismic source inversion

Fast Bayesian optimal experimental design for seismic source inversion

Q. Long, M. Motamed, R. Tempone, Fast Bayesian optimal experimental design for seismic source inversion, Computer Methods in Applied Mechanics and Engineering, vol. 291, pp. 123-145, 2015.​​
Q. Long, M. Motamed, R. Tempone
Bayesian experimental design, Information gain, Laplace approximation, Monte Carlo sampling, Seismic source inversion, Sparse quadrature, Uncertainty quantification
2015
We 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 de fined as the square of the weighted L  2 norm of the di fference 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 conditional number of the original Hessian matrix. We use a second-order accurate fi nite diff erence 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.
doi:10.1016/j.cma.2015.03.021