10:45 AM - 11:00 AM
[STT44-01] Bayesian Inversion Analysis of Seismological and Geodetic Data–Basis Function Expansion and Gaussian Process
★Invited Papers
In geophysics, inversion analyses, which estimate unobservable quantities from observational data and theoretical models (observation equations), play an important role. Bayesian inference is effective because available data are limited and noisy in general. In Bayesian inference, prior information on a model is represented as a prior probability distribution, and its posterior probability distribution given data is derived to obtain an estimate and its uncertainty. In this presentation, I introduce and compare two methods–basis function expansion and Gaussian process–in which posterior distributions can be analytically derived for linear inverse problems.
In the basis function expansion (BFE), an estimated quantity is represented as a linear combination of finite (M) fixed basis functions, which results in a finite-dimensional problem on a parameter space. By combining a prior distribution on the model parameters and a likelihood of observational data, the posterior distribution of the model parameters is derived, which gives the predictive distribution of the estimated quantity.
In the Gaussian process (GP), a prior distribution is directly set on an estimated quantity, which leads to an infinite-dimensional problem on a function space. Nevertheless, it is known that when finite (N) data are given, the problem is reduced to finite dimensions and the posterior distribution of the estimated quantity can be derived.
Here, I present two applications: estimation of the strain rate field from GNSS velocity data (Okazaki et al., EPS, 2021) and that of the stress field from CMT data of earthquakes (Okazaki et al., JGR, 2022). The characteristics of the two methods are compared from the four viewpoints: computational cost, model region, hyperparameters, and prior information. In particular, the computational costs of BFE and GP scale with the number of model parameters (M) and data (N), respectively. Therefore, GP is particularly efficient in analyzing high-dimensional models.
In the basis function expansion (BFE), an estimated quantity is represented as a linear combination of finite (M) fixed basis functions, which results in a finite-dimensional problem on a parameter space. By combining a prior distribution on the model parameters and a likelihood of observational data, the posterior distribution of the model parameters is derived, which gives the predictive distribution of the estimated quantity.
In the Gaussian process (GP), a prior distribution is directly set on an estimated quantity, which leads to an infinite-dimensional problem on a function space. Nevertheless, it is known that when finite (N) data are given, the problem is reduced to finite dimensions and the posterior distribution of the estimated quantity can be derived.
Here, I present two applications: estimation of the strain rate field from GNSS velocity data (Okazaki et al., EPS, 2021) and that of the stress field from CMT data of earthquakes (Okazaki et al., JGR, 2022). The characteristics of the two methods are compared from the four viewpoints: computational cost, model region, hyperparameters, and prior information. In particular, the computational costs of BFE and GP scale with the number of model parameters (M) and data (N), respectively. Therefore, GP is particularly efficient in analyzing high-dimensional models.