Accounting for prediction error when inferring subsurface fault slip

Zacharie Duputel, Piyush S. Agram, Mark Simons, Sarah E. Minson, & James L. Beck

Published 2014, SCEC Contribution #1791

This study lays the groundwork for a new generation of earthquake source models based on a general formalism that rigorously quantifies the impact of uncertainties in fault slip problems. We distinguish two sources of uncertainty when considering the discrepancy between data and forward model predictions. The first class of error is induced by imperfect measurements and is often referred to as observational error. The second source of uncertainty is generally neglected and corresponds to the prediction error, that is the uncertainty due to imperfect forward modeling. Yet the prediction error can be shown to scale approximately with the size of earthquakes and thus can dwarf the observational error particularly for large events. In the Gaussian assumption, both sources of uncertainty can be formulated using the misfit covariance, Cχ, which combines covariances in observations, Cd, and covariances associated with inaccurate model predictions, Cp. We develop a physically-based statistical model for the prediction error and show how Cp can be calculated to account for inaccuracies in the Earth model. We demonstrate the importance of including Cp using the simple example of an infinite strike­slip fault in the quasi­static approximation. The advances proposed here are the foundation for a generation of subsurface fault slip models that leads to more reliable images of the earthquake rupture, are more resistant to over­fitting of data and include more realistic estimates of uncertainty on inferred model parameters.

Duputel, Z., Agram, P. S., Simons, M., Minson, S. E., & Beck, J. L. (2014). Accounting for prediction error when inferring subsurface fault slip. Geophysical Journal International, 197, 464-482. doi: 10.1093/gji/ggt517.