Rapid construction of Rayleigh wave dispersion curve based on deep learning

Abstract

Introduction:The dispersion curve of the Rayleigh-wave phase velocity (VR) is widely utilized to determine site shear-wave velocity (Vs) structures from a distance of a few metres to hundreds of metres, even on a ten-kilometre crustal scale. However, the traditional theoretical-analytical methods for calculating VRs of a wide frequency range are time-consuming because numerous extensive matrix multiplications, transfer matrix iterations and the root searching of the secular dispersion equation are involved. It is very difficult to model site structures with many layers and apply them to a population-based inversion algorithm for which many populations of multilayers forward modelling and many generations of iterations are essential.Method:In this study, we propose a deep learning method for constructing the VR dispersion curve in a horizontally layered site with great efficiency. A deep neural network (DNN) based on the fully connected dense neural network is designed and trained to directly learn the relationships between Vs structures and dispersion curves. First, the training and validation sets are generated randomly according to a truncated Gaussian distribution, in which the mean and variance of the Vs models are statistically analysed from different regions’ empirical relationships between soil Vs and its depth. To be the supervised dataset, the corresponding VRs are calculated by the generalized reflection-transmission (R/T) coefficient method. Then, the Bayesian optimization (BO) is designed and trained to seek the optimal architecture of the deep neural network, such as the number of neurons and hidden layers and their combinations. Once the network is trained, the dispersion curve of VR can be constructed instantaneously without building and solving the secular equation.Results and Discussion:The results show that the DNN-BO achieves a coefficient of determination (R2) and MAE for the training and validation sets of 0.98 and 8.30 and 0.97 and 8.94, respectively, which suggests that the rapid method has satisfactory generalizability and stability. The DNN-BO method accelerates the dispersion curve calculation by at least 400 times, and there is almost no increase in computation expense with an increase in soil layers.