Bayesian Rayleigh wave inversion with an unknown number of layers

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.

Numerical modeling of flow in continuous bends from Daliushu to Shapotou in Yellow River

The upper reach of the Yellow River from Daliushu to Shapotou consists of five bends and has complex topography. A two-dimensional Re-Normalisation Group （RNG） k-ε model was developed to simulate the flow in the reach. In order to take the circulation currents in the bends into account, the momentum equations were improved by adding an additional source term. Comparison of the numerical simulation with field measurements indicates that the improved two-dimensional depth-averaged RNG k-e model can improve the accuracy of the numerical simulation. A rapid adaptive algorithm was constructed, which can automatically adjust Manning＇s roughness coefficient in different parts of the study river reach. As a result, not only can the trial computation time be significantly shortened, but the accuracy of the numerical simulation can also be greatly improved. Comparison of the simulated and measured water surface slopes for four typical cases shows that the longitudinal and transverse slopes of the water surface increase with the average velocity upstream. In addition, comparison was made between the positions of the talweg and the main streamline, which coincide for most of the study river reach. However, deviations between the positions of the talweg and the main streamline were found at the junction of two bends, at the position where the river width suddenly decreases or increases.