Development and numerical tests of a Bayesian approach to inferring shallow velocity structures using microtremor arrays
Development and numerical tests of a Bayesian approach to inferring shallow velocity structures using microtremor arrays
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使用微震阵列推断浅层速度结构的贝叶斯方法的开发和数值测试
DOI：
10.1071/eg18011
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发表时间：
2018
影响因子：
0.9
通讯作者：
I. and T. Iwata
中科院分区：
文献类型：
--
作者：
Cho;I. and T. Iwata
我们提出了一个经验贝叶斯方法推断浅（深度范围从几到几十米）的S波速度结构，使用微动阵列和执行数值试验，以评估这种方法的可行性。在我们的方法中，估计的S-波结构（后）来自经验的S-波结构模型（前）和相位速度与微动阵列获得的瑞利波。换句话说，我们的目标是找到一个模型，接近的经验模型，并能够解释相速度与一维表面波理论。反演是稳定的约束条件，从先验模型，使模型参数化与许多薄层可以采用。速度结构分别估计为两种情况下（假设）：的情况下，我们假设基模占主导地位的情况下，我们考虑到更高的模式。基于赤池的贝叶斯信息准则（ABIC），找到模型参数（例如厚度参数）的最佳值，并且表面波理论的更好假设的选择也基于ABIC。数值试验，其中合成数据是从一个水平分层的两层模型，表明先验模型和观测数据之间的相对权重是适当的调整ABIC。结果表明，ABIC成功地找到了再现给定的两层模型所需的厚度参数的值。我们还建议，我们可以作出合理的选择与ABIC表面波理论的假设，除非观测误差非常大。
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.