Shallow seismic surface-wave waveform inversion with U-net and a hybrid loss function

Summary Shear-wave (S-wave) velocity is one of the key seismic parameters for environmental and engineering geophysics. Surface waves dominate the shallow-seismic wavefield, and the accurate estimation of S-wave velocity model from surface waves has been a research focus in near-surface geophysics. Full-waveform inversion (FWI) favors high resolution by using the full information recorded in the waveform, but faces challenges such as high nonlinearity and high computational cost. In recent years, the rapid advancement of deep learning methods, particularly convolutional neural networks (CNNs) provided new approaches for geophysical inversion. Here, we propose a novel shallow-seismic FWI method, namely the Mean squared error and Edge-loss U-net (MEU-net), by using a U-net architecture and a hybrid loss function containing mean squared error, edge loss, and peak signal-to-noise ratio simultaneously. The MEU-net achieves an end-to-end estimation of S-wave velocity model from the input seismograms. The inclusion of three complementary misfits in the hybrid loss function enables a comprehensive consideration of the point-to-point fitness, quality of boundary reconstruction, and overall variation of the reconstructed subsurface model. We train the MEU-net with 6400 models, whose corresponding multiple shot gathers are simulated by solving the elastic wave equation numerically. Synthetic examples show that our proposed MEU-net outperforms the conventional approach that uses an MSE loss function with a fully convolutional network in the accuracy of the results. Furthermore, we use a transfer learning strategy with fine-tuning pre-trained models on a small-scale dataset to improve the generalization of MEU-net. We apply the MEU-net to field data acquired in Krauthausen, Germany. We used a deconvolution technique to adapt the field data to our simulated data that uses a different source wavelet. The estimated subsurface model shows nice agreement with the cone penetration test result, proving relatively high accuracy in the result. The field example validates the effectiveness of our proposed MEU-net and shows its ability in characterizing near-surface models from seismic waveform with end-to-end deep learning approaches.