1:45 PM - 2:00 PM
[STT39-01] Application of massively parallel computing for advanced inverse analysis of crustal
deformation
★Invited Papers
Keywords:Inverse analysis, Crustal deformation, Bayesian estimation, Parallel computing
Estimating fault geometry (e.g. location, angle, and size) and slip distribution on the fault plane through inverse analysis of observation data such as crustal deformation is crucial for understanding earthquake mechanisms. Particularly for intraplate earthquakes, the fault plane is often unknown beforehand, and it is necessary to estimate both fault geometry and slip distribution. The typical approach involves initially determining the fault geometry with a uniform slip distribution and then refining the slip distribution on the obtained fault plane. However, this stepwise method does not guarantee a proper solution considering nonuniform slip distribution. “Simultaneous Bayesian estimation”, which incorporates nonuniform slip distribution into the process of estimating fault geometry based on Bayesian statistics, has been attempted.
In practical slip distribution estimation, constraints are often applied to the slip direction and maximum amount of slip to avoid unrealistic results. It is expected that employing these constraints in simultaneous Bayesian estimation could avoid unnatural slip distribution and stabilize the estimation, but it has been difficult to achieve because the computational cost increases with this extension. In this study, we have addressed this challenge using massively parallel computing, enabling simultaneous Bayesian estimation of fault geometry and slip distribution within realistic time while incorporating appropriate slip constraints.
The goal of this estimation is to determine the posterior probability distribution of fault geometry parameters. As settings for probability distribution, we assume a uniform prior probability distribution for objectivity. Considering nonuniform slip distribution, the likelihood for fault geometry is defined by the marginal likelihood: integrating the likelihood for a pair of fault geometry and slip distribution over all possible slip distribution. When slip constraints are imposed, the marginal likelihood cannot be calculated analytically and requires Monte Carlo sampling of slip distributions to approximate the integral by summation over finite number of samples. Since the likelihood function of fault geometry parameters can only be obtained numerically, the posterior probability distribution of them is also intractable and approximated by numerous samples.
This estimation process presents a hierarchical sampling problem: sampling of fault geometry is performed, and sampling of slip distribution is performed for each fault plane to compute its marginal likelihood. We implemented this with Sequential Monte Carlo, an algorithm suitable for parallelization. In the sampling process, the samples of fault geometry are distributed across many MPI processes, each of which performs sampling of slip distribution independently. Estimation using up to 8,000 compute nodes of the Fugaku supercomputer was performed, resulting in convergent solutions for both fault geometry and slip distribution without significant loss of parallel efficiency.
Using this method, simultaneous Bayesian estimation was conducted with constraints on slip direction and maximum slip amount. This method was validated through synthetic tests, and inverse analysis of crustal deformation in the 2018 Hokkaido Eastern Iburi earthquake showed consistent results with a previous study. It was confirmed that these constraints helped eliminate unrealistic slip distributions and prevent excessively small fault planes and large slip estimates. Additionally, it was observed that the posterior distribution of fault geometry remained invariant to parameterization, indicating the robustness of this method.
In summary, we present a method for objective inverse analysis of crustal deformation based on simultaneous Bayesian estimation. By introducing massively parallel computing, we can further enhance the stability and robustness of estimation.
In practical slip distribution estimation, constraints are often applied to the slip direction and maximum amount of slip to avoid unrealistic results. It is expected that employing these constraints in simultaneous Bayesian estimation could avoid unnatural slip distribution and stabilize the estimation, but it has been difficult to achieve because the computational cost increases with this extension. In this study, we have addressed this challenge using massively parallel computing, enabling simultaneous Bayesian estimation of fault geometry and slip distribution within realistic time while incorporating appropriate slip constraints.
The goal of this estimation is to determine the posterior probability distribution of fault geometry parameters. As settings for probability distribution, we assume a uniform prior probability distribution for objectivity. Considering nonuniform slip distribution, the likelihood for fault geometry is defined by the marginal likelihood: integrating the likelihood for a pair of fault geometry and slip distribution over all possible slip distribution. When slip constraints are imposed, the marginal likelihood cannot be calculated analytically and requires Monte Carlo sampling of slip distributions to approximate the integral by summation over finite number of samples. Since the likelihood function of fault geometry parameters can only be obtained numerically, the posterior probability distribution of them is also intractable and approximated by numerous samples.
This estimation process presents a hierarchical sampling problem: sampling of fault geometry is performed, and sampling of slip distribution is performed for each fault plane to compute its marginal likelihood. We implemented this with Sequential Monte Carlo, an algorithm suitable for parallelization. In the sampling process, the samples of fault geometry are distributed across many MPI processes, each of which performs sampling of slip distribution independently. Estimation using up to 8,000 compute nodes of the Fugaku supercomputer was performed, resulting in convergent solutions for both fault geometry and slip distribution without significant loss of parallel efficiency.
Using this method, simultaneous Bayesian estimation was conducted with constraints on slip direction and maximum slip amount. This method was validated through synthetic tests, and inverse analysis of crustal deformation in the 2018 Hokkaido Eastern Iburi earthquake showed consistent results with a previous study. It was confirmed that these constraints helped eliminate unrealistic slip distributions and prevent excessively small fault planes and large slip estimates. Additionally, it was observed that the posterior distribution of fault geometry remained invariant to parameterization, indicating the robustness of this method.
In summary, we present a method for objective inverse analysis of crustal deformation based on simultaneous Bayesian estimation. By introducing massively parallel computing, we can further enhance the stability and robustness of estimation.