scholarly journals Bayesian inference of earthquake rupture models using polynomial chaos expansion

2018 ◽  
Vol 11 (7) ◽  
pp. 3071-3088 ◽  
Author(s):  
Hugo Cruz-Jiménez ◽  
Guotu Li ◽  
Paul Martin Mai ◽  
Ibrahim Hoteit ◽  
Omar M. Knio
Keyword(s):  
Bayesian Inference ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Fault Plane ◽  
Dominant Role ◽  
Prediction Equation ◽  
Peak Ground Velocity ◽  
Earthquake Rupture ◽  
Physical Constraints ◽  
Rupture Model

Abstract. In this paper, we employed polynomial chaos (PC) expansions to understand earthquake rupture model responses to random fault plane properties. A sensitivity analysis based on our PC surrogate model suggests that the hypocenter location plays a dominant role in peak ground velocity (PGV) responses, while elliptical patch properties only show secondary impact. In addition, the PC surrogate model is utilized for Bayesian inference of the most likely underlying fault plane configuration in light of a set of PGV observations from a ground-motion prediction equation (GMPE). A restricted sampling approach is also developed to incorporate additional physical constraints on the fault plane configuration and to increase the sampling efficiency.

scholarly journals Bayesian inference of earthquake rupture models using polynomial chaos expansion

2018 ◽  
Author(s):  
Hugo Cruz-Jiménez ◽  
Guotu Li ◽  
Paul Martin Mai ◽  
Ibrahim Hoteit ◽  
Omar M. Knio
Keyword(s):  
Bayesian Inference ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Fault Plane ◽  
Dominant Role ◽  
Prediction Equation ◽  
Peak Ground Velocity ◽  
Earthquake Rupture ◽  
Physical Constraints ◽  
Rupture Model

Abstract. In this paper we employed polynomial chaos (PC) expansions to understand earthquake rupture model responses to random fault plane properties. A sensitivity analysis based on our PC surrogate model suggests that the hypocenter location plays a dominant role in peak ground velocity (PGV) responses, while elliptical patch properties only show secondary impact. In addition, the PC surrogate model is utilized for Bayesian inference of the most likely underlying fault plane configuration in light of a set of PGV observations from a ground motion prediction equation (GMPE). A restricted sampling approach is also developed to incorporate additional physical constraints on the fault plane configuration, and to increase the sampling efficiency.

scholarly journals Polynomial Chaos–Based Bayesian Inference of K-Profile Parameterization in a General Circulation Model of the Tropical Pacific

2016 ◽  
Vol 144 (12) ◽  
pp. 4621-4640 ◽  
Author(s):  
Ihab Sraj ◽  
Sarah E. Zedler ◽  
Omar M. Knio ◽  
Charles S. Jackson ◽  
Ibrahim Hoteit
Keyword(s):  
Bayesian Inference ◽  
General Circulation Model ◽  
Surrogate Model ◽  
General Circulation ◽  
Polynomial Chaos ◽  
Circulation Model ◽  
Tropical Pacific ◽  
Uncertain Parameters ◽  
Test Statistic ◽  
The Tropical Pacific

Abstract The authors present a polynomial chaos (PC)–based Bayesian inference method for quantifying the uncertainties of the K-profile parameterization (KPP) within the MIT general circulation model (MITgcm) of the tropical Pacific. The inference of the uncertain parameters is based on a Markov chain Monte Carlo (MCMC) scheme that utilizes a newly formulated test statistic taking into account the different components representing the structures of turbulent mixing on both daily and seasonal time scales in addition to the data quality, and filters for the effects of parameter perturbations over those as a result of changes in the wind. To avoid the prohibitive computational cost of integrating the MITgcm model at each MCMC iteration, a surrogate model for the test statistic using the PC method is built. Because of the noise in the model predictions, a basis-pursuit-denoising (BPDN) compressed sensing approach is employed to determine the PC coefficients of a representative surrogate model. The PC surrogate is then used to evaluate the test statistic in the MCMC step for sampling the posterior of the uncertain parameters. Results of the posteriors indicate good agreement with the default values for two parameters of the KPP model, namely the critical bulk and gradient Richardson numbers; while the posteriors of the remaining parameters were barely informative.

scholarly journals Attenuation relationships of peak ground motions in the Jazan Region

2021 ◽  
Vol 14 (3) ◽  
Author(s):  
Ali K. Abdelfattah ◽  
Abdullah Al-amri ◽  
Kamal Abdelrahman ◽  
Muhamed Fnais ◽  
Saleh Qaysi
Keyword(s):  
Saudi Arabia ◽  
Ground Motions ◽  
Prediction Equation ◽  
Peak Ground Velocity ◽  
Local Magnitude ◽  
Ground Acceleration ◽  
Data Set ◽  
Hypocentral Distance ◽  
Distance Range ◽  
Attenuation Relationships

AbstractIn this study, attenuation relationships are proposed to more accurately predict ground motions in the southernmost part of the Arabian Shield in the Jazan Region of Saudi Arabia. A data set composed of 72 earthquakes, with normal to strike-slip focal mechanisms over a local magnitude range of 2.0–5.1 and a distance range of 5–200 km, was used to investigate the predictive attenuation relationship of the peak ground motion as a function of the hypocentral distance and local magnitude. To obtain the space parameters of the empirical relationships, non-linear regression was performed over a hypocentral distance range of 4–200 km. The means of 638 peak ground acceleration (PGA) and peak ground velocity (PGV) values calculated from the records of the horizontal components were used to derive the predictive relationships of the earthquake ground motions. The relationships accounted for the site-correlation coefficient but not for the earthquake source implications. The derived predictive attenuation relationships for PGV and PGA are$$ {\log}_{10}(PGV)=-1.05+0.65\cdotp {M}_L-0.66\cdotp {\log}_{10}(r)-0.04\cdotp r, $$ log 10 PGV = − 1.05 + 0.65 · M L − 0.66 · log 10 r − 0.04 · r , $$ {\log}_{10}(PGA)=-1.36+0.85\cdotp {M}_L-0.85\cdotp {\log}_{10}(r)-0.005\cdotp r, $$ log 10 PGA = − 1.36 + 0.85 · M L − 0.85 · log 10 r − 0.005 · r , respectively. These new relationships were compared to the grand-motion prediction equation published for western Saudi Arabia and indicate good agreement with the only data set of observed ground motions available for an ML 4.9 earthquake that occurred in 2014 in southwestern Saudi Arabia, implying that the developed relationship can be used to generate earthquake shaking maps within a few minutes of the event based on prior information on magnitudes and hypocentral distances taking into considerations the local site characteristics.

scholarly journals Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems

2016 ◽  
Vol 46 ◽  
pp. 107-119 ◽  
Author(s):  
Andres A. Contreras ◽  
Olivier P. Le Maître ◽  
Wilkins Aquino ◽  
Omar M. Knio
Keyword(s):  
Bayesian Inference ◽  
Polynomial Chaos ◽  
Elasticity Problems

scholarly journals A stochastic rupture earthquake code based on the fiber bundle model (TREMOL v0.1): application to Mexican subduction earthquakes

2019 ◽  
Vol 12 (5) ◽  
pp. 1809-1831 ◽  
Author(s):  
Marisol Monterrubio-Velasco ◽  
Quetzalcóatl Rodríguez-Pérez ◽  
Ramón Zúñiga ◽  
Doreen Scholz ◽  
Armando Aguilar-Meléndez ◽  
...  
Keyword(s):  
Fiber Bundle ◽  
Fault Plane ◽  
Heterogeneous Material ◽  
Computer Code ◽  
Rupture Process ◽  
Maximum Magnitude ◽  
Earthquake Rupture ◽  
General Terms ◽  
Fiber Bundle Model ◽  
Earthquake Rupture Processes

Abstract. In general terms, earthquakes are the result of brittle failure within the heterogeneous crust of the Earth. However, the rupture process of a heterogeneous material is a complex physical problem that is difficult to model deterministically due to numerous parameters and physical conditions, which are largely unknown. Considering the variability within the parameterization, it is necessary to analyze earthquakes by means of different approaches. Computational physics may offer alternative ways to study brittle rock failure by generating synthetic seismic data based on physical and statistical models and through the use of only few free parameters. The fiber bundle model (FBM) is a stochastic discrete model of material failure, which is able to describe complex rupture processes in heterogeneous materials. In this article, we present a computer code called the stochasTic Rupture Earthquake MOdeL, TREMOL. This code is based on the principle of the FBM to investigate the rupture process of asperities on the earthquake rupture surface. In order to validate TREMOL, we carried out a parametric study to identify the best parameter configuration while minimizing computational efforts. As test cases, we applied the final configuration to 10 Mexican subduction zone earthquakes in order to compare the synthetic results by TREMOL with seismological observations. According to our results, TREMOL is able to model the rupture of an asperity that is essentially defined by two basic dimensions: (1) the size of the fault plane and (2) the size of the maximum asperity within the fault plane. Based on these data and few additional parameters, TREMOL is able to generate numerous earthquakes as well as a maximum magnitude for different scenarios within a reasonable error range. The simulated earthquake magnitudes are of the same order as the real earthquakes. Thus, TREMOL can be used to analyze the behavior of a single asperity or a group of asperities since TREMOL considers the maximum magnitude occurring on a fault plane as a function of the size of the asperity. TREMOL is a simple and flexible model that allows its users to investigate the role of the initial stress configuration and the dimensions and material properties of seismic asperities. Although various assumptions and simplifications are included in the model, we show that TREMOL can be a powerful tool to deliver promising new insights into earthquake rupture processes.

Polynomial Chaos Based Solution to Inverse Problems in Petroleum Reservoir Engineering

2019 ◽  
Author(s):  
Sufia Khatoon ◽  
Jyoti Phirani ◽  
Supreet Singh Bahga
Keyword(s):  
Bayesian Inference ◽  
History Matching ◽  
Polynomial Chaos ◽  
Reservoir Engineering ◽  
Model Parameters ◽  
Petroleum Reservoir ◽  
Model Predictions ◽  
Production History ◽  
Porosity And Permeability ◽  
Computationally Expensive

Abstract In reservoir simulations, model parameters such as porosity and permeability are often uncertain and therefore better estimates of these parameters are obtained by matching the simulation predictions with the production history. Bayesian inference provides a convenient way of estimating parameters of a mathematical model, starting from a probable range of parameter values and knowing the production history. Bayesian inference techniques for history matching require computationally expensive Monte Carlo simulations, which limit their use in petroleum reservoir engineering. To overcome this limitation, we perform accelerated Bayesian inference based history matching by employing polynomial chaos (PC) expansions to represent random variables and stochastic processes. As a substitute to computationally expensive Monte Carlo simulations, we use a stochastic technique based on PC expansions for propagation of uncertainty from model parameters to model predictions. The PC expansions of the stochastic variables are obtained using relatively few deterministic simulations, which are then used to calculate the probability density of the model predictions. These results are used along with the measured data to obtain a better estimate (posterior distribution) of the model parameters using the Bayes rule. We demonstrate this method for history matching using an example case of SPE1CASE2 problem of SPEs Comparative Solution Projects. We estimate the porosity and permeability of the reservoir from limited and noisy production data.

scholarly journals TREMOL: A stochastic rupture earthquake code based on the fiber bundle model. Application to Mexican subduction earthquakes

2019 ◽  
Author(s):  
Marisol Monterrubio-Velasco ◽  
Quetzalcóatl Rodríguez-Pérez ◽  
Ramón Zúñiga ◽  
Doreen Scholz ◽  
Armando Aguilar-Meléndez ◽  
...  
Keyword(s):  
Fiber Bundle ◽  
Fault Plane ◽  
Heterogeneous Material ◽  
Real Data ◽  
Element Model ◽  
Rupture Process ◽  
Maximum Magnitude ◽  
Earthquake Rupture ◽  
General Terms ◽  
Fiber Bundle Model

Abstract. In general terms, earthquakes are the result of brittle failure within the heterogeneous crust of the Earth. However, the rupture process of a heterogeneous material is a complex physical problem which is difficult to model deterministically due to the numerous parameters and physical conditions, which are largely unknown. Considering the variability within the parametrization, it is necessary to analyze earthquakes by means of different approaches. Computational physics may offer alternative ways to study brittle rock failure by generating synthetic seismic data based on physical and statistical models, and by the use of only few free parameters. The Fiber Bundle model (FBM) is a discrete element model, which is able to describe complex rupture processes in heterogeneous materials. In this article, we present a computer code called stochasTic Rupture Earthquake MOdeL, TREMOL. This code is based on the principle of the FBM to investigate the rupture process of asperities on the earthquake rupture surface. In order to validate TREMOL, we carried out a parametric study at first to identify the best parameter configuration while minimizing computational efforts. As test cases, we applied the final configuration to 10 Mexican subduction zone earthquakes in order to compare the synthetic results by TREMOL with real data. According to our results, TREMOL is able to model the rupture of an asperity that is defined essentially by two basic dimensions: (1) the size of the fault plane, and (2) the size of the maximum asperity within the fault plane. Based on this data, and few additional parameters, TREMOL is able to generate numerous earthquakes as well as a maximum magnitude for different scenarios within a reasonable error range. The simulated earthquakes magnitudes are of the same order as the real earthquakes. Thus, TREMOL can be used to analyze the behavior of a single asperity or a group of asperities since TREMOL considers the maximum magnitude occurring on a fault plane as a function of the size of the asperity. TREMOL is a simple, and flexible model which allows its users to investigate the role of the initial stress configuration, and the dimensions and material properties of seismic asperities. Although various assumptions and simplifications are included in the model, we show that TREMOL can be a powerful tool which can deliver promising new insights into earthquake rupture processes.

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