[STT52-P02] An application of reversible-jump MCMC method for simultaneous determinations of 1-D velocity structures and hypocenters around a fault (I): Formulation
A 1-D velocity model is generally constructed based on seismological and/or geological knowledge [e.g., Sakai et al., 2004]. Three-dimensional analyses, i.e., tomographic inversion, would detect those heterogeneous structures if a large amount of seismological observations were obtained. In other words, with small dataset of seismic records, it is difficult to know a presence of structural boundary and velocity structures of each seismological/geological unit around a fault without obvious surface exposure of them. Therefore, in our series of presentation (this study and Shiina and Kano [this meeting]), we propose a Bayesian-based approach for simultaneous determination of hypocenters of earthquakes and 1-D velocity structures around a fault. Additionally, our approach assigns each station to a specific velocity model.
This study uses a reversible-jump Markov chain Monte Carlo (rj-MCMC) method to estimate 1-D velocity models and hypocenters of earthquakes. In an analysis of seismic velocity structure of Earth’s interior, the rj-MCMC method can change a number of discrete units, i.e., grid, block, or layer, and investigate P- and S-wave velocities of the discrete units. Bodin and Sambridge  adopted this method to estimate a two-dimensional velocity structure. Based on their formulation, we developed the rj-MCMC approach; layered velocity structures and hypocenters are simultaneously determined when given a number of 1-D velocity models.
In this presentation, we will summarize formulations of the developed method in detailed. An application of this method for synthetic data sets will be summarized by Shiina and Kano [this meeting].