An Improved Bayesian von Karman Regularization Method for the Joint Inversion of GNSS and InSAR Data

Given the problem that the relative weights of multitype data sets are not considered in the current studies of Bayesian von Karman regularized slip distribution inversion, we propose to add hyperparameters that control the variance-covariance information of different data sets within the Bayesian framework, present a detailed and complete theoretical method, and successfully apply it to the earthquake that occurred in Norcia, Italy, in 2016. Synthetic tests show that compared with the Bayesian von Karman regularization method with equal weights for different data, the improved Bayesian von Karman regularization method can more effectively invert the real slip distribution of this dip-slip earthquake, its inversion results are more stable, and the data fitting accuracy is higher, thus verifying the advantages of the improved method. In the slip inversion of the Norcia earthquake, the hyperparameters of the global navigation satellite system (GNSS) and interferometric synthetic aperture radar (InSAR) data sets converged to different values, which shows it is indeed necessary to determine different relative weights of different data sets. Moreover, the inversion results show that this earthquake ruptured to the surface, the fault slip region was mainly concentrated in a depth range of 0–6 km, the maximum slip was 3.87 m, and the released coseismic seismic moment was $8.95\times {10}^{18}\mathrm{Nm}$, corresponding to a moment magnitude of $M_{\mathrm{W}}=6.60$. These results are consistent with the existing research, thus verifying the practicability of the improved method.