2:45 PM - 3:00 PM
[SSS05-05] Applicability of the Hamiltonian Monte Carlo method for single rectangular fault estimation
The rapid estimation of the coseismic fault model and its uncertainty are extremely important to predict the possible hazard such as tsunami. Based on such motivation, Ohno et al. (in revision) developed the estimation method of single rectangular fault model deduced from Markov Chain Monte Carlo (MCMC) method in real-time. They adopted conventional Metropolis-Hasting (M-H) method to sample the probability density function. The M-H method, however, require long Markov chain because of the ideal acceptance ration is around 20-30%. Therefore, the large dimensional problem requires the very long mixing time.
To overcome such problem, we investigate the new estimation approach for single rectangular fault model based on the Hamiltonian Monte Carlo (HMC) method. HMC is a MCMC method that uses the derivatives of the density function being sampled to generate efficient transitions spanning the posterior. It uses an approximate Hamiltonian dynamics simulation based on numerical integration which is then corrected by performing a Metropolis acceptance step. To calculate the numerical integration, we adopted the leapfrog integrator, which is a numerical integration algorithm. During the leapfrog integrator, we need to assume the discretization time (e) and number of steps (L). To estimate the appropriate number of leapfrog (L), we adopted the no-U-turn sampler (NUTS). We also assumed the discretization time (e) as 10-4 which was determined by try-and-error. The model parameter vector that contains fault parameters of a single rectangular fault model (Okada 1992). To optimize amount of each step size for unknown parameters, we installed logit transformation for all unknown parameters except for latitude and longitude.
We applied the developed approach to numerical experience which was under the optimum site coverage. Obtained results clearly shows the rapid convergence (~1000 steps) which clearly shorter step number compared with M-H method. We will show the more detail of our developed method and results for more realistic site coverage.
To overcome such problem, we investigate the new estimation approach for single rectangular fault model based on the Hamiltonian Monte Carlo (HMC) method. HMC is a MCMC method that uses the derivatives of the density function being sampled to generate efficient transitions spanning the posterior. It uses an approximate Hamiltonian dynamics simulation based on numerical integration which is then corrected by performing a Metropolis acceptance step. To calculate the numerical integration, we adopted the leapfrog integrator, which is a numerical integration algorithm. During the leapfrog integrator, we need to assume the discretization time (e) and number of steps (L). To estimate the appropriate number of leapfrog (L), we adopted the no-U-turn sampler (NUTS). We also assumed the discretization time (e) as 10-4 which was determined by try-and-error. The model parameter vector that contains fault parameters of a single rectangular fault model (Okada 1992). To optimize amount of each step size for unknown parameters, we installed logit transformation for all unknown parameters except for latitude and longitude.
We applied the developed approach to numerical experience which was under the optimum site coverage. Obtained results clearly shows the rapid convergence (~1000 steps) which clearly shorter step number compared with M-H method. We will show the more detail of our developed method and results for more realistic site coverage.