Bayesian Rayleigh wave inversion with an unknown number of layers
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EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION
Earthq Eng & Eng Vib (2020) 19: 875-886
October, 2020
DOI: https://doi.org/10.1007/s11803-020-0601-y
Bayesian Rayleigh wave inversion with an unknown number of layers Ka-Veng Yuen† and Xiao-Hui Yang‡ State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental Engineering, University of Macau, 999078, Macao, China
Abstract: Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics.
However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.
Keywords:
Bayesian model class selection; generalized r/t coefficients algorithm; genetic algorithm; inversion of Rayleigh wave; number of layers
1 Introduction Due to their efficiency, flexibility and simplicity, surface wave methods have been widely utilized by earthquake engineers, civil engineers and geophysics scientists (Zhou et al., 2009; Lu et al., 2012a, 2012b; Jahromi and Karkhaneh, 2019). Surface wave exploration has been recognized as an attractive method for estimating S-wave velocity, which is a critical seismic parameter for various applications in engineering, environmental, groundwater and other near surface studies (Hou et al., 2007; Özener, 2012; Ren et al., 2013; Beneldjouzi and Laouami, 2015; Ba et al., 2017; Pamuk et al., 2017; Xie and Zhang, 2017; Zhou et al., 2017; Zhang et al., 2018; Liu et al., 2019). In contrast to body waves, surface waves are dispersive. As a type of surface wave, Rayleigh waves are generated by the interference Correspondence to: Xiao-Hui Yang, State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental Engineering, University of Macau, 999078, Macao, China Tel: +853-6391584 E-mail: [email protected] † Professor; ‡PhD Candidate Supported by: Science and Technology Development Fund of the Macao SAR under research grant SKL-IOTSC-2018-2020 and the Research Committee of University of Macau under Research Gr
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