ALBERT

Description: Finite-fault earthquake source inversion is an ill-posed inverse problem leading to non-unique solutions. In addition, various fault parametrizations and input data may have been used by different researchers for the same earthquake. Such variability leads to large intra-event variability in the inferred rupture models. One way to understand this problem is to develop robust metrics to quantify model variability. We propose a Multi Dimensional Scaling (MDS) approach to compare rupture models quantitatively. We consider normalized squared and grey-scale metrics that reflect the variability in the location, intensity and geometry of the source parameters. We test the approach on two-dimensional random fields generated using a von Kármán autocorrelation function and varying its spectral parameters. The spread of points in the MDS solution indicates different levels of model variability. We observe that the normalized squared metric is insensitive to variability of spectral parameters, whereas the grey-scale metric is sensitive to small-scale changes in geometry. From this benchmark, we formulate a similarity scale to rank the rupture models. As case studies, we examine inverted models from the Source Inversion Validation (SIV) exercise and published models of the 2011 Mw 9.0 Tohoku earthquake, allowing us to test our approach for a case with a known reference model and one with an unknown true solution. The normalized squared and grey-scale metrics are respectively sensitive to the overall intensity and the extension of the three classes of slip (very large, large, and low). Additionally, we observe that a three-dimensional MDS configuration is preferable for models with large variability. We also find that the models for the Tohoku earthquake derived from tsunami data and their corresponding predictions cluster with a systematic deviation from other models. We demonstrate the stability of the MDS point-cloud using a number of realizations and jackknife tests, for both the random field and the case studies.

Description: Earthquake rupture models inferred from inversions of geophysical and/or geodetic data exhibit remarkable variability due to uncertainties in modelling assumptions, the use of different inversion algorithms, or variations in data selection and data processing. A robust statistical comparison of different rupture models obtained for a single earthquake is needed to quantify the intra-event variability, both for benchmark exercises and for real earthquakes. The same approach may be useful to characterize (dis-)similarities in events that are typically grouped into a common class of events (e.g. moderate-size crustal strike-slip earthquakes or tsunamigenic large subduction earthquakes). For this purpose, we examine the performance of the spatial prediction comparison test (SPCT), a statistical test developed to compare spatial (random) fields by means of a chosen loss function that describes an error relation between a 2-D field (‘model’) and a reference model. We implement and calibrate the SPCT approach for a suite of synthetic 2-D slip distributions, generated as spatial random fields with various characteristics, and then apply the method to results of a benchmark inversion exercise with known solution. We find the SPCT to be sensitive to different spatial correlations lengths, and different heterogeneity levels of the slip distributions. The SPCT approach proves to be a simple and effective tool for ranking the slip models with respect to a reference model.