Rapid construction of Rayleigh wave dispersion curve based on deep learning - Cui, Diyu; Shi, Lijing; Gao, Kai (Frontiers in Earth Science, 2023)
The dispersion curve of Rayleigh-wave phase velocity (VR) is widely utilized to determine site Shear-wave velocities (Vs) structures from a few meters to hundred meters, even ten kilometers crustal scale. But the traditional theoretical-analytical methods for calculating VRs of a wide frequency range are time-consuming because many massive matrix multiplications, transfer matrix iterations, and root-searching of secular dispersion equation are involved. It's very difficult to model site structures with many layers and apply them to a population-based inversion algorithm, in which many populations of multilayers forward modeling and many generations of iterations are essential. We propose, in this study, a deep learning method for constructing dispersion curve of VR in a horizontally layered site with great efficiency. A deep neural network (DNN) based on fully connected dense neural network is designed and trained to learn the relationship between Vs structures and dispersion curves directly. First, the training and validation set are generated randomly according to truncated Gaussian distribution, in which the mean and variance of Vs models are statistic analyzed 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 optimizer (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. The results show that the DNN-BO achieved coefficient of determination (R^2) and MAE for the training and validation set are respectively 0.98, 8.30, and 0.97, 8.94, which suggest the rapid method has satisfied generalizability and stability. The DNN-BO method accelerates dispersion curve calculation by at least 400 times and there is almost no increase in computation expense with the increase of soil layers.