ALBERT

Description: One way to improve the accuracy and reliability of kinematic earthquake source imaging is to investigate the origin of uncertainty and to minimize their effects. The difficulties in kinematic source inversion arise from the nonlinearity of the problem, nonunique choices in the parameterization, and observational errors. We analyze particularly the uncertainty related to the choice of the source time function (STF) and the variability in Earth structure. We consider a synthetic data set generated from a spontaneous dynamic rupture calculation. Using Bayesian inference, we map the solution space of peak slip rate, rupture time, and rise time to characterize the kinematic rupture in terms of posterior density functions. Our test to investigate the effect of the choice of STF reveals that all three tested STFs (isosceles triangle, regularized Yoffe with acceleration time of 0.1 and 0.3 s) retrieve the patch of high slip and slip rate around the hypocenter. However, the use of an isosceles triangle as STF artificially accelerates the rupture to propagate faster than the target solution. It additionally generates an artificial linear correlation between rupture onset time and rise time. These appear to compensate for the dynamic source effects that are not included in the symmetric triangular STF. The exact rise time for the tested STFs is difficult to resolve due to the small amount of radiated seismic moment in the tail of STF. To highlight the effect of Earth structure variability, we perform inversions including the uncertainty in the wavespeed only, and variability in both wavespeed and layer depth. We find that little difference is noticeable between the resulting rupture model uncertainties from these two parameterizations. Both significantly broaden the posterior densities and cause faster rupture propagation particularly near the hypocenter due to the major velocity change at the depth where the fault is located. Online Material: Figures of inverted rupture models, trade-off curve, and posterior probability density function.

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.

Description: One way to improve the accuracy and reliability of kinematic earthquake source imaging is to investigate the origin of uncertainty and to minimize their effects. The difficulties in kinematic source inversion arise from the nonlinearity of the problem, nonunique choices in the parameterization, and observational errors. We analyze particularly the uncertainty related to the choice of the source time function (STF) and the variability in Earth structure. We consider a synthetic data set generated from a spontaneous dynamic rupture calculation. Using Bayesian inference, we map the solution space of peak slip rate, rupture time, and rise time to characterize the kinematic rupture in terms of posterior density functions. Our test to investigate the effect of the choice of STF reveals that all three tested STFs (isosceles triangle, regularized Yoffe with acceleration time of 0.1 and 0.3 s) retrieve the patch of high slip and slip rate around the hypocenter. However, the use of an isosceles triangle as STF artificially accelerates the rupture to propagate faster than the target solution. It additionally generates an artificial linear correlation between rupture onset time and rise time. These appear to compensate for the dynamic source effects that are not included in the symmetric triangular STF. The exact rise time for the tested STFs is difficult to resolve due to the small amount of radiated seismic moment in the tail of STF. To highlight the effect of Earth structure variability, we perform inversions including the uncertainty in the wavespeed only, and variability in both wavespeed and layer depth. We find that little difference is noticeable between the resulting rupture model uncertainties from these two parameterizations. Both significantly broaden the posterior densities and cause faster rupture propagation particularly near the hypocenter due to the major velocity change at the depth where the fault is located. Online Material: Figures of inverted rupture models, trade-off curve, and posterior probability density function.