Observations noise and stability of geodetic variable slip fault models

Abstract

SUMMARY Variable slip models of seismic faults represent ill-posed (or underdetermined) problems with infinity of solutions; a single solution is typically obtained using constraints imposed by the L-curve theory, through an experimentally derived coefficient which optimizes the trade-off between fault roughness (smoothness, mean slip gradient) and mean misfit of observations to the fault model. However, in some cases, diverse variable slip fault models (VSFM) have been presented, even using the same data sets. In this paper, we investigate the problem of stability (sensitivity) of VSFM to input geodetic (GNSS/GPS, INSAR) ground slip measurements, based on statistics of synthetic data: statistically similar sets of synthetic ground displacements were the only degree of freedom in an analysis leading to comparable VSFM, regarded as images of slip amplitude and of rake. Differences of synthetic models from the reference fault model for different levels of noise, both for filtered and for PCA-filtered were examined, and results were summarized in images depicting the differences and the variability (standard deviation) of each fault slip patch, both for slip and rake. From this ‘truth’-based approach, it was found that an increase in observations noise is reflected in increase of variability (instability) of fault models, especially away from the fault centre, higher for slip than in rake. Analysis with a different virtual observations system indicates that stations above the fault tend to show spurious stress concentration areas on the fault surface, in agreement with previous studies. Analysis with synthetic data appears as a promising strategy to validate a VSFM based on geodetic data.