A New Strategy to Compare Inverted Rupture Models Exploiting the Eigenstructure of the Inverse Problem

Gallovič, František; Ampuero, Jean‐Paul

doi:10.1785/0220150096

Cited by 26 publications

(18 citation statements)

References 27 publications

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“…Since the dynamic inversion also provides kinematic parameters of the rupture, it can be also viewed as a kinematic inversion constrained by the assumed friction law. This is advisable as kinematic inversions are highly non-unique (Mai et al, 2016;Gallovič and Ampuero, 2015;Gallovič and Zahradník, 2011).…”

Section: Discussionmentioning

confidence: 99%

Bayesian Dynamic Finite-Fault Inversion: 2. Application to the 2016 Mw6.2 Amatrice, Italy, Earthquake

Gallovič¹,

Valentová²,

Ampuero³

et al. 2019

Preprint

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In 2016 Central Italy was struck by a sequence of three normal faulting earthquakes with moment magnitude (Mw) larger than 6. The Mw 6.2 Amatrice event (08/24) was the first one, causing building collapse and about 300 casualties. The event was recorded by a uniquely dense network of seismic stations. Here we perform its dynamic source inversion to infer the fault friction parameters and stress conditions that controlled the earthquake rupture. We consider a linear slip-weakening friction law with spatially variable parameters along the fault. The inversion uses a novel Bayesian framework developed in our companion paper, which combines efficient finite-difference dynamic rupture simulations and the Parallel Tempering Monte Carlo algorithm to sample the posterior probability density function. The main advantage of such formulation is that by subsequent analysis of the posterior samples we can infer stable features of the result and their uncertainty. The inversion results in a million of visited models. The preferred model ensemble reveals intriguing dynamic features. The rupture exhibits a slow and irregular nucleation followed by bilateral rupture propagation through two asperities, accelerating towards the heavily damaged city of Amatrice. The stress drop reaches locally 10-15 MPa, with slip-weighted mean of 4-4.5MPa. The friction drop ranges from 0.1 to 0.4. The characteristic slip-weakening distance is the most heterogeneously distributed dynamic parameter, with values of 0.2-0.8m. The radiation efficiency was rather low, 0.2, suggesting that approximately 80% of the total available energy was spent in the fracture process, while just 20% was radiated by seismic waves.

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Section: Discussionmentioning

confidence: 99%

Bayesian Dynamic Finite-Fault Inversion: 2. Application to the 2016 Mw6.2 Amatrice, Italy, Earthquake

Gallovič¹,

Valentová²,

Ampuero³

et al. 2019

Preprint

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“…We can relate our estimate of the GFs variance to an independent finding of Gallovič & Ampuero (2015), who compared results of synthetic slip inversion benchmark test SIV2a (Mai et al 2016) as obtained by several modellers. They concluded that the results were consistent up to approximately 1/10 of the maximum singular value of the forward design matrix, which corresponds to less than 1 per cent mean data error (cov/RMS 2 = 0.01).…”

Section: Stationarized Covariance Functionmentioning

confidence: 99%

Fast and cheap approximation of Green function uncertainty for waveform-based earthquake source inversions

Hallo

Gallovič

2016

Geophysical Journal International

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S U M M A R YGreen functions (GFs) are an essential ingredient in waveform-based earthquake source inversions. Hence, the error due to imprecise knowledge of a crustal velocity model is one of the major sources of uncertainty of the inferred earthquake source parameters. Recent strategies in Bayesian waveform inversions rely on statistical description of the GF uncertainty by means of a Gaussian distribution characterized by a covariance matrix. Here we use Monte-Carlo approach to estimate the GF covariance considering randomly perturbed velocity models. We analyse the dependence of the covariance on various parameters (strength of velocity model perturbations, GF frequency content, source-station distance, etc.). Recognizing that the major source of the GF uncertainty is related to the random time shifts of the signal, we propose a simplified approach to obtain approximate covariances, bypassing the numerically expensive Monte-Carlo simulations. The resulting closed-form formulae for the approximate auto-covariances and cross-covariances between stations and components can be easily implemented in existing inversion techniques. We demonstrate that the approximate covariances exhibit very good agreement with the Monte-Carlo estimates, providing realistic variations of the GF waveforms. Furthermore, we show examples of implementation of the covariance matrix in a Bayesian moment tensor inversion using both synthetic and real data sets. We demonstrate that taking the GF uncertainty into account leads to improved estimates of the moment tensor parameters and their uncertainty.Downloaded from respectively, computed by the discrete wavenumber method for the source-receiver distance of 50 km (σ M = 10 per cent). The black lines are the 'mother' GFs calculated in the mean velocity model. Other colours of waveforms have no meaning and are used only for clearer view. Panel (c) shows cross-covariance matrices for velocity model perturbations (σ M = 10 per cent) as obtained by the Monte-Carlo approach, while matrices in panels (d) and (e) were obtained by the approximate formulae in eqs (11) and (15), respectively. The width of the uniform PDF L 1 = 4σ t used in the approximate formulae is adopted from graph in Fig. 1(d); L 12 is set to zero as the velocity model is the same for the both components. Duration of the dominant part of the earthquake signal was set T = 15 sec. Panel (f) shows comparison of the stationarized Monte-Carlo cross-covariance function (black) and the SAXCF obtained using eq. (15) (red).

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“…Such regularization has to be specified a priori for the whole model, and it has been shown to be capable of producing artifacts (e.g., Zahradník & Gallovič, ). The issue of ill‐posedness of the linear rupture inversions was tackled by exploring the eigenstructure of the inverse problem by Gallovič and Ampuero (). They decomposed the linear forward operator by singular value decomposition, providing a set of singular vectors in the model space.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Self‐Adapting Fault Slip Inversion With Green's Functions Uncertainty and Application on the 2016M_w7.1 Kumamoto Earthquake

Hallo

Gallovič

2020

JGR Solid Earth

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Kinematic finite‐extent models of earthquake sources can be determined by inverse modeling of observed waveforms and/or geodetic data. Such models are subject to significant uncertainty as a result of inaccurate observations and imperfect physical description of the complex properties of the Earth's crust. For slip inversions of large earthquakes, the major source of uncertainty is related to the uncertainty of Green's functions due to the imperfect description of the crustal model and selected parameterization of the source model. To account for both, we introduce an effective nonlinear Bayesian slip inversion with transdimensional source parameterization, including analytical representation of uncertainties of Green's functions. Our nonlinear slip inversion method relies on a self‐adapting spatial parametrization of the slip distribution by means of a varying number of spline control points on the assumed fault. For the temporal parameterization, it utilizes the regularized Yoffe function with spatially varying rise time and rupture velocity. Rake angle is also treated as an unknown spatially dependent parameter. The Green's function uncertainties are included using full covariance matrices. The posterior probability density function is sampled by the transdimensional Markov chain Monte Carlo algorithm with parallel tempering. The performance of our slip inversion method is demonstrated on a synthetic test from the Source Inversion Validation project and real‐data inversion of the 2016 Mw7.1 Kumamoto earthquake. In the latter test, we infer an ensemble of ~7,300,000 possible rupture models, representing samples of the posterior probability density, and inspect which features of these models are reliable and which are rather artifacts.

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A New Strategy to Compare Inverted Rupture Models Exploiting the Eigenstructure of the Inverse Problem

Cited by 26 publications

References 27 publications

Bayesian Dynamic Finite-Fault Inversion: 2. Application to the 2016 Mw6.2 Amatrice, Italy, Earthquake

Bayesian Dynamic Finite-Fault Inversion: 2. Application to the 2016 Mw6.2 Amatrice, Italy, Earthquake

Fast and cheap approximation of Green function uncertainty for waveform-based earthquake source inversions

Bayesian Self‐Adapting Fault Slip Inversion With Green's Functions Uncertainty and Application on the 2016M_w7.1 Kumamoto Earthquake

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A New Strategy to Compare Inverted Rupture Models Exploiting the Eigenstructure of the Inverse Problem

Cited by 26 publications

References 27 publications

Bayesian Dynamic Finite-Fault Inversion: 2. Application to the 2016 Mw6.2 Amatrice, Italy, Earthquake

Bayesian Dynamic Finite-Fault Inversion: 2. Application to the 2016 Mw6.2 Amatrice, Italy, Earthquake

Fast and cheap approximation of Green function uncertainty for waveform-based earthquake source inversions

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

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Product

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Bayesian Self‐Adapting Fault Slip Inversion With Green's Functions Uncertainty and Application on the 2016M_w7.1 Kumamoto Earthquake