Accounting for uncertain fault geometry in earthquake source inversions – I: theory and simplified application

Abstract

The ill-posed nature of earthquake source estimation derives from several factors including the quality and quantity of available observations and the fidelity of our forward theory. Observational errors are usually accounted for in the inversion process. Epistemic errors, which stem from our simplified description of the forward problem, are rarely dealt with despite their potential to bias the estimate of a source model. In this study, we explore the impact of uncertainties related to the choice of a fault geometry in source inversion problems. The geometry of a fault structure is generally reduced to a set of parameters, such as position, strike and dip, for one or a few planar fault segments. While some of these parameters can be solved for, more often they are fixed to an uncertain value. We propose a practical framework to address this limitation by following a previously implemented method exploring the impact of uncertainties on the elastic properties of our models. We develop a sensitivity analysis to small perturbations of fault dip and position. The uncertainties of our fixed fault geometry are included in the inverse problem under the formulation of the misfit covariance matrix that combines both prediction and observation uncertainties. We validate this approach with the simplified case of a fault that extends infinitely along strike, using both Bayesian and optimization formulations of a static slip inversion. If epistemic errors are ignored, predictions are overconfident in the data and slip parameters are not reliably estimated. In contrast, inclusion of uncertainties in fault geometry allows us to infer a robust posterior slip model. Epistemic uncertainties can be many orders of magnitude larger than observational errors for great earthquakes (M w > 8). Not accounting for uncertainties in fault geometry may partly explain observed shallow slip deficits for continental earthquakes. Similarly, ignoring the impact of epistemic errors can also bias estimates of near-surface slip and predictions of tsunamis induced by megathrust earthquakes.

Joint Inversion of Coseismic and Early Postseismic Slip to Optimize the Information Content in Geodetic Data: Application to the 2009 Mw6.3 L'Aquila Earthquake, Central Italy

“…This impact could mean the assumed fault and Earth properties are not realistic enough to capture the real seismic rupture and/or that small variations of the fault geometry (slight curvature and roughness) or of the Earth model (3‐D heterogeneities) largely affect our slip models. The influence of epistemic uncertainties is greater on the coseismic model, as expected from the fact that these uncertainties scale with the amount of slip (Duputel et al., ; Ragon et al., ). Accounting for uncertainties of the forward model allowed us to exclude the possibility of deep slip for the coseismic models, but not totally for the postseismic models probably because of the much lower slip amplitudes.…”

“…For instance, this structure is frequently approximated as a homogenous elastic half‐space and the causative fault geometry is usually reduced to a flat rectangular plane. The uncertainties related to our approximations of the physics of the Earth affect the inferred source models (Ragon et al., ). As the early postseismic slip is of limited amplitude, it may be particularly impacted by uncertainties of the forward model.…”

“…() for the Earth elastic properties and Ragon et al. () for the fault geometry. The epistemic uncertainties are calculated from the sensitivity of the Green's functions and are included in a covariance matrix C p .…”

“…The fault is divided into 154 subfaults of 1.8‐km length and 1.6‐km width. As our fault geometry does not reflect the reality and is poorly constrained, we account for its uncertainties (Ragon et al., , ) and assume a standard deviation on the fault dip of 5° and on the fault position (the fault position varying perpendicularly from the fault trace) of 1.5 km, regarding the discrepancies between published fault models (e.g., Lavecchia et al., ). We do not account for uncertainties in the fault strike for simplicity, and because its influence might be small when uncertainty in the fault position is already acknowledged (Ragon et al., ).…”

Distribution of interseismic coupling along the North and East Anatolian Faults inferred from InSAR and GPS data

“…C χ is the covariance matrix, which translates data and epistemic uncertainties into uncertainties on the inverted model m (Duputel et al, 2014;Bletery et al, 2016;Ragon et al, 2018;Ragon, Sladen, & Simons, 2019;Ragon, Sladen, Bletery, et al, 2019). Here, we only account for data uncertainties.…”