Prediction of S-wave velocity models from surface waves using deep learning

Surface wave (SW) methods extract dispersion properties of wavefields propagating through a seismic array (1D or 2D). This is achieved by analysing the phase velocity versus frequency (or wavelength) data. Afterwards, an inversion process is performed to construct near-surface S-wave velocity models. Among the SW methods, multichannel analysis of SWs (MASW) is commonly used for engineering applications, analysing dispersion characteristics by generating a dispersion image. However, classical MASW depends on the manual picking of dispersion curves, which can lead to subjective outcomes and require time and effort to obtain precise results. To avoid these pitfalls, many studies, including deep-learning techniques, have focused on automating the process. Similarly, we propose a deep-learning-based algorithm that estimates the S-wave velocity directly from the dispersion image of SWs. This algorithm consists of a convolutional neural network (CNN) designed to directly yield S-wave velocity profiles and a fully connected network (multi-layer perceptron) added to regularize predictions. Unlike typical SW techniques, the proposed approach does not incorporate prior information such as layer count and thickness. To ensure successful training, we modified the loss function to exploit the normalized mean squared error. The training dataset was generated by modelling synthetic shot gathers and transforming them into dispersion images for various 1D stratified velocity structures. After a sample is fed to the CNN network for inversion, the inversion network's output subsequently goes through an additional simple neural network (NN) to regularize the predicted S-wave velocity model (which is the post-processing step). The combined usage of deep-learning-based SW inversion with NN-based post-processing was assessed using test data. The proposed algorithm achieved an average relative error of approximately 7.49% in predicting the S-wave velocity and was successfully applied to the field data. Additionally, we discuss its performance on noisy data as well as its applicability to out-of-training data. Numerical examples demonstrated that the proposed method is robust to noise, whereas it requires additional training to handle data beyond the distribution of the training data.