Development and numerical tests of a Bayesian approach to inferring shallow velocity structures using microtremor arrays
Ikuo Cho 1 4 Takaki Iwata 2 3
+ Author Affiliations
- Author Affiliations
1 Geological Survey of Japan, AIST, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8567, Japan.
2 College of Community Development, Tokiwa University, 1-430-1 Miwa, Mito, Ibaraki 310-8585, Japan.
3 Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan.
4 Corresponding author. Email: ikuo-chou@aist.go.jp
Exploration Geophysics 49(6) 881-890 https://doi.org/10.1071/EG18011
Submitted: 17 January 2018 Accepted: 19 January 2018 Published: 19 March 2018
Journal compilation © ASEG 2018 Open Access CC BY-NC-ND
Abstract
We propose an empirical Bayesian approach to inferring shallow (depth ranges from a few to several tens of metres) S-wave velocity structures using microtremor arrays and execute numerical tests to assess the feasibility of this approach. In our approach, the estimate of the S-wave structure (posterior) is derived from an empirical S-wave structure model (prior) and phase velocities of Rayleigh waves obtained with microtremor arrays. In other words, we aim to find a model that is close to the empirical model and is able to explain phase velocities with a 1D surface-wave theory. The inversion is stabilised by the constraints from the prior model so that model parameterisation with many thin layers can be adopted. The velocity structure is individually estimated for each of two cases (assumptions): the case where we assume fundamental-mode dominance and the case where we take into account the higher modes. Optimal values of the model parameters (e.g. a thickness parameter) are found, based on Akaike’s Bayesian Information Criterion (ABIC), and the choice of the better assumption of the surface-wave theory is also based on ABIC. Numerical tests, where synthetic data is generated from a horizontally stratified two-layer model, indicate that the relative weight between a prior model and the observed data is appropriately adjusted by ABIC. It is revealed that a value of the thickness parameter required to reproduce the given two-layer model is successfully found by ABIC. We also suggest that we can make a plausible choice of the assumption of the surface-wave theory with ABIC, unless observation error is extremely large.
Key words: arrays, inversion, modelling, passive, shallow, surface wave, velocity.
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