Machine learning algorithm has been applied to shear wave velocity (Vs) inversion in surface wave tomography, where a set of starting 1‐D Vs profiles and their corresponding synthetic dispersion curves are used in network training. Previous studies showed that the performance of such trained network is dependent on the diversity of the training data set, which limits its application to previously poorly understood regions. Here, we present an improved semi‐supervised algorithm‐based network that takes both model‐generated and observed surface wave dispersion data in the training process. The algorithm is termed Wasserstein cycle‐consistent generative adversarial networks (Wasserstein Cycle‐GAN [Wcycle‐GAN]). Different from conventional supervised approaches, the GAN architecture enables the inclusion of unlabeled data (the observed surface wave dispersion) in the training process that can complement the model‐generated data set. The cycle‐consistency and Wasserstein metric significantly improve the training stability of the proposed algorithm. We benchmark the Wcycle‐GAN method using 4,076 pairs of fundamental mode Rayleigh wave phase and group velocity dispersion curves derived in periods from 3 to 16 s in Southern California. The final 3‐D Vs model given by the best trained network shows large‐scale features consistent with the surface geology. The resulting Vs model has reasonable data misfits and provides sharper images of structures near faults in the top 15 km compared with those from conventional machine learning methods.
A machine learning based method is developed for 1-D shear wave velocity (Vs) inversion to include observed dispersion data into the training process • The Wasserstein Cycle-GAN algorithm is used to improve training stability and spatial continuity of the output 3-D Vs model • The final Vs model shows reasonable data misfits, sharper images of major faults, and is consistent with the largescale surface geology
We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ( χ2) waveform misfit of one is achieved and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.
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