Toward the next generation of earthquake source models by accounting for model prediction error

The last decade has seen considerable improvements in the numerical fidelity of forward models aimed at understanding the distribution of subsurface fault slip. In addition, we have experienced a dramatic expansion of geophysical observations including broadband seismic data, continuously recording GPS positioning data and spatially synoptic geodetic imaging data from orbiting radar and optical satellites. Despite these developments, perhaps the biggest obstacle to significant progress in observational earthquake source modeling arises from imperfect predictions of geodetic and seismic data due to uncertainties in the material parameters and fault geometries used in our forward models - the impact of which are generally overlooked. Indeed, for large earthquakes, our ability to measure ground motions exceeds our ability to robustly model them. In this study, we develop physically based statistics for the model prediction error and show how to account for inaccuracies in the Earth model elastic parameters. Of particular importance is the recognition that modeling errors can induce strong spatial and temporal correlations in our observations and that these (co)variances depend the on the amplitude and spatial distribution of fault slip. The advances proposed here will enable production of the next generation of source models that are more resistant to over-fitting of data, provide a physical basis for the relative weighting between disparate data sets, and include more realistic estimates of uncertainty on the inferred model parameters. Avoiding overly simplistic assumptions for the prediction error by capturing the relevant physics of the geodetic and seismic forward problem leads to more reliable images of earthquake rupture phenomena. While this project is motivated by specific goals related to the study of large earthquakes, the developed techniques can be applied to a broad range of problems in geophysics and earthquake engineering such as volcano monitoring and earthquake early warning.