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 exist...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.展开更多
Let K = $ k(\sqrt \theta ) $ be a real cyclic quartic field, k be its quadratic subfield and $ \tilde K = k(\sqrt { - \theta } ) $ be the corresponding imaginary quartic field. Denote the class numbers of K, k and $ \...Let K = $ k(\sqrt \theta ) $ be a real cyclic quartic field, k be its quadratic subfield and $ \tilde K = k(\sqrt { - \theta } ) $ be the corresponding imaginary quartic field. Denote the class numbers of K, k and $ \tilde K $ by h K , h k and {417-3} respectively. Here congruences modulo powers of 2 for h ? = h K /h K and $ \tilde h^ - = h_{\tilde K} /h_k $ are obtained via studying the p-adic L-functions of the fields.展开更多
基金Science and Technology Development Fund of the Macao SAR under research grant SKL-IOTSC-2018-2020the Research Committee of University of Macao under Research Grant MYRG2016-00029-FST。
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 10771111)
文摘Let K = $ k(\sqrt \theta ) $ be a real cyclic quartic field, k be its quadratic subfield and $ \tilde K = k(\sqrt { - \theta } ) $ be the corresponding imaginary quartic field. Denote the class numbers of K, k and $ \tilde K $ by h K , h k and {417-3} respectively. Here congruences modulo powers of 2 for h ? = h K /h K and $ \tilde h^ - = h_{\tilde K} /h_k $ are obtained via studying the p-adic L-functions of the fields.
