Deep learning inversion of Rayleigh-wave dispersion curves with geological constraints for near-surface investigations

SUMMARY With the emergence of massive seismic data sets, surface wave methods using deep learning (DL) can effectively obtain shear wave velocity (Vs) structure for non-invasive near-surface investigations. Previous studies on DL inversion for deep geophysical investigation have a reference model to generate the training data set, while near-surface investigations have no model. Therefore, we systematically give a set of training data set generation processes. In the process, we use both prior information and the observed data to constrain the data set so that the DL inversion model can learn the local geological characteristics of the survey area. Because the space of inverted Vs models is constrained and thus narrowed, the inversion non-uniqueness can be reduced. Furthermore, the mean squared error, which is commonly used as loss function, may cause a poor fitting accuracy of phase velocities at high frequencies in near-surface applications. To make the fitting accuracy evenly in all frequency bands, we modify the loss function into a weighted mean squared relative error. We designed a convolutional neural network (CNN) to directly invert fundamental-mode Rayleigh-wave phase velocity for 1-D Vs models. To verify the feasibility and reliability of the proposed algorithm, we tested and compared it with the Levenberg–Marquardt (L-M) inversion and neighbourhood algorithm (NA) using field data from the Lawrence experiment (USA) and the Wuwei experiment (China). In both experiments, the inverted Vs models by CNN are consistent with the borehole information and are similar to that from existing methods after fine tuning of model parameters. The average root mean squares errors (RMSEs) of the CNN, NA and L-M methods are also similar, except in the Lawrence experiment, the RMSE of CNN is 17.33 m s−1 lower than previous studies using the L-M method. Moreover, the comparison of different loss functions for the Wuwei experiment indicates that the modified loss function can achieve higher accuracy than the traditional one. The proposed CNN is therefore ideally suited for rapid, repeated near-surface subsurface imaging and monitoring under similar geological settings.