Eric Andreas Hetland

Coseismic deformation of the 9 August 2020 Mw 5.1 Sparta, North Carolina, earthquake was captured by an Advanced Land Observing Satellite 2 interferogram, a Sentinel 1A/B interferogram, and differential light detection and ranging (lidar). Owing to the moderate surface deformation compared to the inherent uncertainties of interferometric data, the interferograms suffered from low signal-to-noise ratios, exacerbated by spurious signals arising from the discrepancy in resolution between the interferograms and digital elevation model used during processing. Nevertheless, coseismic slip can be imaged using graph-guided fused LASSO, where LASSO is the least-absolute shrinkage and selection operator—an inverse method that combines sparsity constraints and smoothness regularization—to infer signal from noisy and/or incomplete data. We develop five coseismic slip models, one determined only from the Sentinel 1A/B interferogram, one determined from both interferograms, one determined from all the Interferometric Synthetic Aperture Radar (InSAR) data masking potentially spurious data corresponding to industrial parks, one from lidar 3D displacements only, and one constrained by the masked InSAR and the lidar data. All five models are coseismic slip on a single fault plane, trending northwest–southeast with dips ranging from 41° to 60° to the southwest. Coseismic slip is imaged to be shallow, with predominantly oblique reverse slip extending to about 2 km depth. We find that masking the interferometric data corresponding to the industrial parks yields a coseismic slip model in better concordance with ancillary information about the Sparta earthquake and that the lidar data yield additional constraints on near-surface coseismic slip. We show that our preferred coseismic slip model is consistent with a stress regime that does not depart from an Andersonian thrust regime to a large degree, constraining that the background stress is larger than 20–30 MPa.

We use a Bayesian Markov chain Monte Carlo estimation strategy to estimate the state of pre-earthquake stress from eight published coseismic slip models (CSMs) of the 2016 Mw 7.8 Kaikōura, New Zealand, earthquake. Our estimation relies on the Wallace–Bott assumption, which equates the direction of slip and the orientation of maximum shear stress along a fault plane, and is analogous to methods that infer stress from focal mechanisms. We infer the orientations and relative magnitudes of the principal components of tensorial stress preceding the 2016 Mw 7.8 Kaikōura, New Zealand, earthquake as stress posterior probability density functions (PDFs). We find that the orientations of the principal stresses are well resolved, with weaker to no resolution of the relative magnitudes of the principal stresses. We form a nonmutually exclusive composite posterior PDF as an aggregate of the individual posterior PDFs estimated from each CSM, which allows for the true coseismic slip to be included in any or all of the CSMs. We find that the Kaikōura earthquake can be described by a homogeneous pre-earthquake tensorial stress, despite the complex pattern of slip on multiple fault segments. This state of crustal stress is best represented by an Andersonian thrust regime with a west-northwest–east-southeast trending, horizontal most compressive stress. In addition to describing the state of pre-earthquake stress, the nonmutually exclusive composite posterior PDF allows for the evaluation of the mechanical consistency of the features within CSMs, both individually and as an ensemble. The estimated stress posteriors allow for testing of the CSMs for consistency with known slip mechanisms on the Hope fault, as well as arbitration between differences in inferred slip presented by the CSMs.