The lack of low-frequency information and a good initial model can seriously affect the success of full-waveform inversion (FWI), due to the inherent cycle skipping problem. Computational low-frequency extrapolation is in principle the most direct way to address this issue. By considering bandwidth extension as a regression problem in machine learning, we have adopted an architecture of convolutional neural network (CNN) to automatically extrapolate the missing low frequencies. The band-limited recordings are the inputs of the CNN, and, in our numerical experiments, a neural network trained from enough samples can predict a reasonable approximation to the seismograms in the unobserved low-frequency band, in phase and in amplitude. The numerical experiments considered are set up on simulated P-wave data. In extrapolated FWI (EFWI), the low-wavenumber components of the model are determined from the extrapolated low frequencies, before proceeding with a frequency sweep of the band-limited data. The introduced deep-learning method of low-frequency extrapolation shows adequate generalizability for the initialization step of EFWI. Numerical examples show that the neural network trained on several submodels of the Marmousi model is able to predict the low frequencies for the BP 2004 benchmark model. Additionally, the neural network can robustly process seismic data with uncertainties due to the existence of random noise, a poorly known source wavelet, and a different finite-difference scheme in the forward modeling operator. Finally, this approach is not subject to strong assumptions on signals or velocity models of other methods for bandwidth extension and seems to offer a tantalizing solution to the problem of properly initializing FWI.

Seismic wave arrival time measurements form the basis for numerous downstream applications. State‐of‐the‐art approaches for phase picking use deep neural networks to annotate seismograms at each station independently, yet human experts annotate seismic data by examining the whole network jointly. Here, we introduce a general‐purpose network‐wide phase picking algorithm based on a recently developed machine learning paradigm called Neural Operator. Our model, called Phase Neural Operator, leverages the spatio‐temporal contextual information to pick phases simultaneously for any seismic network geometry. This results in superior performance over leading baseline algorithms by detecting many more earthquakes, picking more phase arrivals, while also greatly improving measurement accuracy. Following similar trends being seen across the domains of artificial intelligence, our approach provides but a glimpse of the potential gains from fully‐utilizing the massive seismic data sets being collected worldwide.

Full-waveform inversion (FWI) strongly depends on an accurate starting model to succeed. This is particularly true in the elastic regime: The cycle-skipping phenomenon is more severe in elastic FWI compared to acoustic FWI due to the short S-wave wavelength. In this article, we extend our work on extrapolated FWI (EFWI) by proposing to synthesize the low frequencies of multicomponent elastic seismic records and use those “artificial” low frequencies to seed the frequency sweep of elastic FWI. Our solution involves deep learning: we can either train the same convolutional neural network (CNN) on two training datasets, one with vertical components and one with horizontal components of particle velocities, or train with two components together, to extrapolate the low frequencies of elastic data for 2-D elastic FWI. The architecture of this CNN is designed with a large receptive field by dilated convolution. Numerical examples on the Marmousi2 model show that the 2–4 Hz low-frequency data extrapolated from band-limited data above 4 Hz provide good starting models for elastic FWI of P- and S-wave velocities. In addition, we study the generalization ability of the proposed neural network from acoustic to elastic data. For elastic test data, collecting the training dataset by elastic simulation shows better extrapolation accuracy than acoustic simulation, i.e., a smaller generalization gap.

SUMMARY: Full-waveform inversion (FWI) relies on low-frequency data to succeed if a good initial model is unavailable. However, field seismic data excited by active sources are typically band-limited above 3 Hz. By extrapolated FWI, we can start inversion from computational low frequencies extrapolated from band-limited data. However, low-frequency extrapolation with deep learning is challenging for field data since a neural network trained on synthetic data usually generalizes poorly on real seismic data. Here we use a semi-supervised learning method to extrapolate low frequencies for field data by training with real data without real labels. Specifically, by training CycleGAN with unpaired images of field 4–10 Hz band-limited and synthetic 0–4 Hz low-frequency shot gathers, we can extrapolate the 0–4 Hz low frequencies for the field data band-limited above 4 Hz. The source wavelet for the simulation of synthetic low-frequency data is used as the source in FWI using the extrapolated data. The inverted velocity model using only the extrapolated low frequencies is comparable to the tomography model. Our method strengthens the ability of FWI for mapping fine Earth structures by mitigating the cycle-skipping problem effectively.

Fault zones accommodate relative motion between tectonic blocks and control earthquake nucleation. Nanocrystalline fault rocks are ubiquitous in “principal slip zones” indicating that these materials are determining fault stability. However, the rheology of nanocrystalline fault rocks remains poorly constrained. Here, we show that such fault rocks are an order of magnitude weaker than their microcrystalline counterparts when deformed at identical experimental conditions. Weakening of the fault rocks is hence intrinsic, it occurs once nanocrystalline layers form. However, it is difficult to produce “rate weakening” behavior due to the low measured stress exponent, n, of 1.3 ± 0.4 and the low activation energy, Q, of 16,000 ± 14,000 J/mol implying that the material will be strongly “rate strengthening” with a weak temperature sensitivity. Failure of the fault zone nevertheless occurs once these weak layers coalesce in a kinematically favored network. This type of instability is distinct from the frictional instability used to describe crustal earthquakes.

Passive seismic interferometry is a vastly generalized blind deconvolution question, where different paths through the Earth correspond to different channels called Green's functions; the sources are completely incoherent and not shared by the channels, and the question is to estimate paths (channels) that are not present in the dataset. SI, turning noise to signal, has numerous applications, from monitoring industrial activities to crustal structure investigation. No standard method of signal processing will solve SI. Instead, domain scientists resort to a simple cross-correlation operation, a.k.a. correlogram, which can retrieve the Green's function directly, but only under restrictive assumptions of ergodicity (energy equipartitioning) of the random process generating the seismic source. However, in practice, correlograms are not equal to the empirical Green's function, because these assumptions are generally far from being satisfied in realistic situations. In the framework of supervised learning, we propose to train deep neural networks (NNs) to overcome two limitations of correlation-based SI: the temporal limitation of passive recordings and the spatial limitation of the random source distribution. Deep NNs are trained to implicitly find the relationship between the empirical Green's functions and the correlograms and then used to extract the correct Green's functions from ambient noise. The input of the network is correlograms (a virtual shot gather), and the desired output is the empirical Green's function (the active shot gather). The NN can often retrieve Green's functions from 5-min passive recordings with acceptable accuracy in our synthetic example. Although an exact estimation of the source locations may not be necessary, a prior knowledge of the source directionality (through a preliminary beamforming step) is helpful when training the NN to mitigate the challenges associated with inhomogeneous source distributions (directional wave fields). In this work, all the numerical examples are based on the retrieval of P-wave reflections in the exploration scale and are conducted on synthetic data. We use a modified ResNet in our numerical experiments.