Toward understanding slip inversion uncertainty and artifacts: 2. Singular value analysis

Seismic slip inversion is studied by means of singular value decomposition (SVD), with emphasis on the role of singular vectors and regularization of the solution. Because the stable part of the slip inversion result is given in terms of a linear combination of the leading singular vectors (representing directions in the model space most sensitive to data), the performance of the inversion depends simply on how well the real slip model can be expanded into these vectors. The analysis is demonstrated using a synthetic model of a symmetric bilateral rupture with two asperities. Inverting the data yields a persisting false asperity in the middle of the fault, regardless of the inversion scheme used, because such a model cannot be well represented by only the leading singular vectors. The parallel study of the singular vectors from the individual stations and the whole network is suggested in order to understand how to achieve balance between overregularized solutions (with possible slip inversion artifacts) and underregularized solutions (vulnerable to data errors). The ideas are applied to the Mw 6.3 Movri Mountain earthquake, 2008, Greece, showing a weak indication of an asymmetric bilateral rupture. We suggest that inversion methods, not working explicitly with singular vectors, may yield artifacts, the origin of which can be also often explained by the SVD technique. Therefore, practical earthquake studies should be broadly complemented by the analysis of the leading singular vectors, a simple tool to evaluate the efficiency and potential drawbacks of the slip inversion.