Reconditioning fault slip inversions via InSAR data discretization

A major difficulty in inverting geodetic data for fault slip distribution is that measurement errors are mapped from the data space onto the solution space. The amplitude of this mapping is sensitive to the condition number of the inverse problem, i.e., the ratio between the largest and smallest singular value of the forward matrix. Thus, unless the problem is well-conditioned, slip inversions cannot reveal the actual fault slip distribution. In this study, we describe a new iterative algorithm that optimizes the condition of the slip inversion through discretization of InSAR data. We present a numerical example that demonstrates the effectiveness of our approach. We show that the condition number of the reconditioned data sets are not only much smaller than those of uniformly spaced data sets with the same dimension but are also much smaller than non-uniformly spaced data sets, with data density that increases towards the model fault.