Extended fault inversion through Popperian falsification: rupture directivity resolution and spatial comparison tests

Abstract:

Non-uniqueness for extended fault slip inversions is well-known and current efforts are focused on assessing and understanding the uncertainties. These ambiguities can be explored through Popperian falsification, where trial models either become members of the solution ensemble or are falsified resulting due to a large data misfit. Classification of slip-maps according to different measures of similarity can help to interpret the inversion results and test different hypotheses for the source process. As a feasibility study, we selected two moderate sized earthquakes with observed source directivities, the 2011 Mw 5.2 Lorca (Spain) mainshock and Mw 4.6 foreshock. We first obtained the Apparent Source Time Functions (ASTF) from a deconvolution using the largest aftershock (Mw 3.9) as an empirical Green's function. We then used a global inversion scheme for random slip-maps with a von Karman autocorrelation function in order to fit the ASTFs. The resolution of rupture directivity is assessed with two quantitative parameters, the direction and amount of asymmetry of the solution slip-maps. This is performed using the moment centroids of the solutions and displayed as directivity rose plots. The individual solutions of the ensembles for the mainshock and foreshock show a similar directivity distribution but have a variable fine structure of slip. We therefore applied a spatial comparison test to find slip-map families with similar rupture patterns. This can be used to identify sub-groups of slip models within the overall solution ensemble according to specified similarity criteria, and evaluate the resolution and ambiguities of the Popperian solution set.