Bayesian Dynamic Finite‐Fault Inversion: 1. Method and Synthetic Test

Abstract

Dynamic earthquake source inversions aim to determine the spatial distribution of initial stress and friction parameters leading to dynamic rupture models that reproduce observed ground motion data. Such inversions are challenging, particularly due to their high computational burden; thus, so far, only few attempts have been made. Using a highly efficient rupture simulation code, we introduce a novel method to generate a representative sample of acceptable dynamic models from which dynamic source parameters and their uncertainties can be assessed. The method assumes a linear slip-weakening friction law and spatially variable prestress, strength, and characteristic slip-weakening distance along the fault. The inverse problem is formulated in a Bayesian framework, and the posterior probability density function is sampled using the Parallel Tempering Monte Carlo algorithm. The forward solver combines a 3-D finite difference code for dynamic rupture simulation on a simplified geometry to compute slip rates and precalculated Green's functions to compute ground motions. We demonstrate the performance of the proposed method on a community benchmark test for source inversion. We find that the dynamic parameters are resolved well within the uncertainty, especially in areas of large slip. The overall relative uncertainty of the dynamic parameters is rather large, reaching~50% of the averaged values. In contrast, the kinematic rupture parameters (rupture times, rise times, and slip values), also well resolved, have relatively lower uncertainties of~10%. We conclude that incorporating physics-based constraints, such as an adequate friction law, may serve also as an effective constraint on the rupture kinematics in finite-fault inversions.

Bayesian Self‐Adapting Fault Slip Inversion With Green's Functions Uncertainty and Application on the 2016Mw7.1 Kumamoto Earthquake

“…We also show temporal snapshots of the slip rates (Figures c and d, respectively) and SRFs from six selected points (Figure e) depicted by black stars in Figures a and b. The similarity of our MAP slip rate solution to the target SIV model is very satisfactory, especially when we consider that the original SRFs stem from a dynamic rupture simulation (Gallovič et al, ; Mai et al, ).…”

“…The PT sampling algorithm is similar to the simulated annealing method (Kirkpatrick et al, ), modifying the posterior PDF by an additional parameter called temperature γ ≥ 1. The random samples are then drawn following such modified posterior PDF assuming multiple values of temperature γ (multiple parallel trans‐D Markov chains), while at least one chain has γ = 1 (see also Valentová et al, ; Gallovič et al, & Gallovič et al, ). The acceptance probabilities for perturb, birth, and death moves in equations – with canceled homogenous prior PDFs are then modified as follows: …”

Landers 1992 “Reloaded”: Integrative Dynamic Earthquake Rupture Modeling

“…The waveform comparisons show very good agreement between simulations and observations, although not all details of the recordings are reproduced. However, this does not come as a surprise, because our study does not attempt to find an optimized source parameterization to fit waveforms (in distinction to kinematic (e.g., Cotton & Campillo, ) or dynamic source inversions (Gallovic et al, , )). Still, our synthetic waveforms capture the main S wave pulses, amplitudes, and shaking duration, indicating the quality of dynamic rupture model.…”

Earthquake Stress Drops From Dynamic Rupture Simulations Constrained by Observed Ground Motions

“…Here we aim to reconcile the ambiguity of the various stress drop definitions/measures utilizing a synthetic earthquake database based on dynamic rupture modeling. To generate the event database, we employ a framework that is similar to a Bayesian dynamic source inversion (Gallovič et al, 2019a(Gallovič et al, , 2019b, where GMPEs serve as data instead of waveforms of a single event. In particular, Markov chain Monte Carlo technique samples the dynamic source parameters of linear slip-weakening friction law with heterogeneous distribution on a fault.…”