Experimental design for fully nonlinear source location problems: which method should I choose?

Abstract

SUMMARY Statistical experimental design (SED) is the field of statistics concerned with designing experiments to obtain as much information as possible about a target of interest. SED algorithms can be divided into two categories: those that assume a linear or linearized relationship between measured data and parameters, and those that account for a fully nonlinear relationship. We compare the most commonly used linear method, Bayesian D-optimization, to two nonlinear methods, maximum entropy design and DN-optimization, in a synthetic seismological source location problem where we define a region of the subsurface in which earthquake sources are likely to occur. Example random sources in this region are sampled with a uniform distribution and their arrival time data across the ground surface are forward modelled; the goal of SED is to define a surface monitoring network that optimally constrains this set of source locations given the data that would be observed. Receiver networks so designed are evaluated on performance—the percentage of earthquake pairs whose arrival time differences are above a threshold of measurement uncertainty at each receiver, the number of prior samples (earthquakes) required to evaluate the statistical performance of each design and the SED compute time for different subsurface velocity models. We find that DN-optimization provides the best results both in terms of performance and compute time. Linear design is more computationally expensive and designs poorer performing networks. Maximum entropy design is shown to be effectively impractical due to the large number of samples and long compute times required.