Greedy selection of optimal location of sensors for uncertainty reduction in seismic moment tensor inversion

We address an optimal sensor placement problem through Bayesian experimental design for seismic full waveform inversion for the recovery of the associated moment tensor. The objective is that of optimally choosing the location of the sensors (stations) from which to collect the observed data. The Shannon expected information gain is used as the objective function to search for the optimal network of sensors. A closed form for such objective is available due to the linear structure of the forward problem, as well as the Gaussian modeling of the observational errors and prior distribution. The resulting problem being inherently combinatorial, a greedy algorithm is deployed to sequentially select the sensor locations that form the best network for learning the moment tensor. Numerical results are presented and analyzed under several instances of the problem, including: use of full three-dimensional velocity-models, cases in which the earthquake-source location is unknown, as well as moment tensor inversion under model misspecification