Bayesian Inversion of Wrapped Satellite Interferometric Phase to Estimate Fault and Volcano Surface Ground Deformation Models

Abstract

Bayesian inference and an improved downsampling method is used to determine earthquake and volcano source parameters using a popular geodetic observation method, satellite radar interferometry. The main novelty of the proposed approach is that the interferometric wrapped phase can be directly inverted, circumventing the ill‐posed phase unwrapping processing step. Phase unwrapping errors severely affect the estimation of earthquake and volcano source parameters using interferometric observations. Therefore, it is desirable to avoid phase unwrapping completely. To overcome the need for phase unwrapping, we propose a downsampling algorithm and a method to estimate the covariance function of the wrapped phase and establish an appropriate misfit function between the observed and simulated wrapped phase. Uncertainties in source parameters are assessed with a Bayesian approach, and finally, the robustness of the inversion methodology is tested in multiple simulations including variable decorrelation and atmospheric noise simulations. The method is shown to be robust in challenging noise scenarios. It features an improvement in performance with the Bayesian approach, compared to similar previous methods, avoiding any influence of seed starting models and escaping local minima. The impact of a small percentage of incorrectly unwrapped phase observations in current state‐of‐the‐art methods is shown to strongly affect the estimation process. We conclude that in the cases where phase unwrapping is difficult or even impossible, the proposed inversion methodology with wrapped phase will provide an alternative approach to assess earthquake and volcano source model parameters.

Aseismic Fault Slip During a Shallow Normal‐Faulting Seismic Swarm Constrained Using a Physically Informed Geodetic Inversion Method

“…To develop the kinematic fault model, we first constructed the fault geometry derived from a nonlinear fault inversion of InSAR wrapped phase observations, solving for uniform distribution on rectangular faults (Jiang & González, 2020). A geodetic inversion directly using the interferometric wrapped phase avoids any potential phase unwrapping error (Figure S6 in Supporting Information S1).…”

“…A geodetic inversion directly using the interferometric wrapped phase avoids any potential phase unwrapping error (Figure S6 in Supporting Information S1). The data variance-covariances describing the noise level are calculated based on the covariograms (Figure S7 in Supporting Information S1) and are used to weight the wrapped phase residuals in the likelihood function as illustrated by Jiang and González (2020). Modeling of a selection of interferograms covering the successive phases confirmed that ground motion could be caused by fault geometry with two distinct planes.…”

“…Then, the fault slip distribution is forward modeled to estimate surface displacement. Following Jiang and González (2020), a misfit function is constructed based on the wrapped phase residuals and the weighting matrix. The misfit function is then regarded as the likelihood function fed into the Bayesian process to retrieve the posterior distribution of crack model parameters.…”

Subduction earthquakes controlled by incoming plate geometry: The 2020 M>7.5 Shumagin, Alaska, earthquake doublet

“…S12) due to the dense gradient of fringes. Instead, our method skips the phase unwrapping step, and directly inverts for fault source parameters by applying the WGBIS method, a Bayesian algorithm that minimizes the weighted wrapped phase residuals (Jiang and González, 2020). Now, using the wrapped InSAR phase and GNSS offsets, we can constrain more tightly the fault geometry parameters (Fig.…”

“…The earthquakes ruptured an area off the Alaska Peninsula covered with scattered islands, and incoherence due to water channels makes it challenging to estimate phase ambiguities during the InSAR phase unwrapping process. Hence, we take advantage of an improved Bayesian inversion of wrapped interferometric phase change observations (Jiang and González, 2020) to estimate the fault geometry and slip distribution. Our coseismic geodetic inversion results reveal that the Alaska megathrust has a complex down-dip segmentation.…”