Spectral Expansion Inversion for the 2015 Mw 7.8 Gorkha Earthquake: Investigation on the Boundaries of Rupture

The current standard approach for static or quasi-static slip inversion with geodetic data is by discretizing a fault into a number of patches whose size is mostly smaller than their depth, thus a straightforward inversion usually leads to wild oscillations in slip. This is because forward elastic models that relate slip at depth to surface deformation contain an exponential upward continuation term [Steketee 1958], which makes this problem inherently non-unique [Parker 1994]. To stabilize the inversion, a smoothness regularization is usually applied along with a non-negative slip constraint (e.g. left lateral slip only) [Jonsson et al 2002]. Sometimes a checkerboard test is performed in order to understand the resolving power of the data [Tong et al 2010]. While this approach can provide us with one reasonable model, we would also like to establish the complete set of models that is equally consistent with the data and assumptions. Here we investigate the possibility of applying linear inverse theory [Parker 1977] to slip inversion, in particular, the spectral expansion approach. This approach inverts for slip as a linear combination of orthonormal functions that span the model space. More important the spectral expansion approach isolates the parts of the model that are well determined by the data from those that are not. Based on the upward continuation nature of this problem, it is almost certain the part with lowest order or largest wavelength (i.e. seismic moment) is well determined. We plan to apply this approach to the recent Mw 7.8 Gorkha earthquake with ScanSAR acquisitions from ALOS-2 [Lindsey et al 2015] to investigate the distribution of the slip. The results will be reported at the meeting.