11:15 AM - 11:30 AM
[STT43-03] An introduction of the MCMC method to a Joint Hypocenter Determination problem: Implications for an approximate JHD method
Keywords:Hypocenter detemination, MCMC method, JHD method
The location of an earthquake hypocenter, which is one of the fundamental pieces of information in seismology, is generally determined using the arrival times of P and S waves. Since expected arrival times also vary depending on the subsurface structure, an approach that jointly determines subsurface structure and station correction terms is often applied to obtain reliable locations of the earthquake hypocenters.
The Joint Hypocenter Determination (JHD) method is an approach utilized to simultaneously determine the hypocenter locations with other model parameters. An alternate optimization scheme between the hypocenter locations and the other model parameters is known as the approximate JHD method [e.g., Pujol, 2000; Sakai et al., 2005]. For example, in the approximate JHD method for determining hypocenter locations and station correction terms, the following steps are performed. First, hypocenter locations are determined without station correction terms. Second, residuals at each station are averaged and adopted the average values as the station correction terms. Then, hypocenter locations are relocated using the updated station correction terms. These procedures are repeated to converge the results. Finally, we obtained the hypocenter locations and the station correction terms.
Recently, the Markov Chain Monte Carlo (MCMC) method has developed as a novel approach to solving inverse problems across various fields, involving the JHD [e.g., Lomax et al., 2000; Ryberg and Haberland, 2019]. The MCMC method explores the posterior probability distribution of model parameters and has the advantage of quantifying their uncertainties. In this method, the model parameters are generally selected randomly for updating. However, the random scan may decrease computational efficiency, as the number of earthquakes is often significantly larger than the number of stations. To address this issue, Shiina et al. [under review], who investigated the aftershock distribution of the 2024 Noto Peninsula Earthquake, Japan, introduced the Metropolise within Gibbs algorithm with systematic scan in the MCMC method.
Analogies exist between the approximate JHD method and the MCMC method with systematic scan in their analytical procedures. Therefore, in this presentation, we examine the relationship between the two methods for the joint determinations between the hypocenter location and the station correction terms. Specifically, we demonstrate that an MCMC method involving the systematic scans and the block Gibbs sampling algorithm can be interpreted as a extension of the approximate JHD method to the Bayesian inference.
The Joint Hypocenter Determination (JHD) method is an approach utilized to simultaneously determine the hypocenter locations with other model parameters. An alternate optimization scheme between the hypocenter locations and the other model parameters is known as the approximate JHD method [e.g., Pujol, 2000; Sakai et al., 2005]. For example, in the approximate JHD method for determining hypocenter locations and station correction terms, the following steps are performed. First, hypocenter locations are determined without station correction terms. Second, residuals at each station are averaged and adopted the average values as the station correction terms. Then, hypocenter locations are relocated using the updated station correction terms. These procedures are repeated to converge the results. Finally, we obtained the hypocenter locations and the station correction terms.
Recently, the Markov Chain Monte Carlo (MCMC) method has developed as a novel approach to solving inverse problems across various fields, involving the JHD [e.g., Lomax et al., 2000; Ryberg and Haberland, 2019]. The MCMC method explores the posterior probability distribution of model parameters and has the advantage of quantifying their uncertainties. In this method, the model parameters are generally selected randomly for updating. However, the random scan may decrease computational efficiency, as the number of earthquakes is often significantly larger than the number of stations. To address this issue, Shiina et al. [under review], who investigated the aftershock distribution of the 2024 Noto Peninsula Earthquake, Japan, introduced the Metropolise within Gibbs algorithm with systematic scan in the MCMC method.
Analogies exist between the approximate JHD method and the MCMC method with systematic scan in their analytical procedures. Therefore, in this presentation, we examine the relationship between the two methods for the joint determinations between the hypocenter location and the station correction terms. Specifically, we demonstrate that an MCMC method involving the systematic scans and the block Gibbs sampling algorithm can be interpreted as a extension of the approximate JHD method to the Bayesian inference.