Uncertainties in Finite-Fault Slip Inversions: To What Extent to Believe? (A Critical Review)

The matrix inversion of seismic data for slip distribution on finite faults is based on the formulation of the representation theorem as a linear inverse problem. The way the problem is posed and parameterized involves substantial, and often subjective, decision making. This introduces several levels of uncertainty, some of them recognized and some not adequately addressed. First, the inverse problem must be numerically stabilized and geologically constrained to obtain meaningful solutions. It is known that geologically irrelevant solutions also exist that may even better fit the data. It is also known that obtaining a stabilized, constrained solution compatible with the data does not guarantee that it is close to the true slip. Second, once the scheme has been set up, there still remains significant uncertainty in seismological parameterization. Synthetic tests have consistently shown that incorrect assumptions about the parameters fixed in the inversions, such as the rupture speed, fault geometry, or crustal structure, generate geologic artifacts, which are also dependent on array geometry. Third, solving the inverse problem involves numerical approximation of a continuous integral, with the generally grid-dependent result. Fourth, maintaining