Weighing Geophysical Data With Trans-Dimensional Algorithms: An Earthquake Location Case Study

In geophysical inverse problems, the distribution of physical properties in an Earth model is inferred from a set of measured data. A necessary step is to select data that are best suited to the problem at hand. This step is performed ahead of solving the inverse problem, generally on the basis of expert knowledge. However, expert-opinion can introduce bias based on pre-conceptions. Here we apply a trans-dimensional algorithm to automatically weigh data on the basis of how consistent they are with the fundamental hypotheses made to solve the inverse problem. We demonstrate this approach by inverting arrival times for the location of a seismic source in an elastic half-space, assuming a point-source and uniform weights in concentric shells. The key advantage is that the data do no longer need to be selected by an expert, but they are assigned varying weights during the inversion procedure.