Seismic full waveform inversion (FWI) is a powerful technique for generating high-resolution images of the subsurface, leveraging the rich information content within recorded seismic waveforms. However, due to certain limitations in data acquisition and processing, the optimization of seismic FWI is inherently non-linear and non-unique, implying the possibility of multiple solutions that can adequately account for the observed data. Unlike deterministic inversion, which seeks a single best-fit solution, probabilistic inversion explores a range of subsurface model parameters adhering to probability distributions that fit the observations within a given confidence level. In this paper, we introduce a variational autoencoder (VAE)-based probabilistic FWI method to assess the uncertainty associated with subsurface parameters using unsupervised deep learning. By repeatedly sampling the latent representation distributions of the observed data, a set of predicted results that adhering to the subsurface model’s posterior distribution can be reconstructed using the decoder and then calculated for uncertainty quantification. Compared to conventional Markov Chain Monte Carlo-based approaches that require substantial computational costs beyond deterministic FWI, the proposed VAE-based FWI offers the opportunity to assess the uncertainty without additional computational demands. Furthermore, the VAE-based method is benchmarked against other deep learning-based approaches, including AE-based deterministic FWI and dropout-based probabilistic FWI, using 2-D Marmousi and Overthrust models. The comparison reveals that the VAE-based approach offers a more nuanced and comprehensive inversion result compared to the single prediction from the AE-based method. Furthermore, it effectively mitigates the dropout-based method’s tendency to underestimate uncertainty in deeper layers, offering a more reliable assessment of inversion uncertainty.

Low-frequency (LF) information in seismic exploration has long been a subject of great interest because of its association with long-scale subsurface features, which ensures the convergence of seismic inversion toward an accurate solution. However, the absence of LF component in field seismic data is a common occurrence due to restrictions posed by data acquisition equipment and environmental constraints. Thus, the reconstruction of LF information from bandlimited seismic data is a pressing issue. In this paper, we introduce a data-driven deep-learning approach for seismic LF extrapolation within a latent space, which is defined by an autoencoder (AE) in a self-supervised manner. Initially, seismic data undergoes compression into a low-dimensional latent space through the encoder component of AE. Subsequently, LF components are extrapolated within this latent space, which can be later reformulated into the data space using the decoder component of AE. Two training strategies, either synchronous or step-wise, are introduced to train the network by utilizing specific loss designs. In numerical experiments, the Mean Absolute Percentage Errors of the LF extrapolation results for all validation samples, processed via traditional end-to-end strategy without/with an enriched dataset, synchronous, and step-wise training with limited data, register at 52.5%, 20.6%, 13.3%, and 10.6% respectively. The findings attest to the efficacy of the AE in the mitigation of redundant information, thereby streamlining the computational complexity inherent to frequency extrapolation. Notably, the proposed approaches achieve accurate LF extrapolation performance with a limited amount of data.

Full waveform inversion (FWI) stands as the forefront geophysical inversion approach, however, its impediment in practical applications persists due to the absence of prior information and limitations in data acquisition. Addressing this challenge, we introduce implicit FWI (IFWI) which represents subsurface models as continuous and implicit functions, thereby reducing dependency on the initial model with frequency principle in deep learning optimization. Furthermore, through the design of a specialized deep learning model that emphasizes rigorous low-frequency learning, we present a robust IFWI algorithm exhibiting high-resolution reconstruction capabilities, even when low-frequency information is absent in observations, as demonstrated in numerical experiments. Moreover, experimental findings underscore the heightened robustness, reduced data requirements, and strong generalization ability of the proposed robust IFWI algorithm. This highlights its applicability to a variety of subsurface models with diverse acquisition settings, indicating promising potential for practical seismic inversion.

We introduce and analyze the elastic implicit full waveform inversion (EIFWI) of seismic data, which uses neural networks to generate elastic models and perform full waveform inversion. EIFWI carries out inversion by linking two main networks: a neural network that generates elastic models and a recurrent neural network to perform the modeling. The approach is distinct from conventional waveform inversion in two key ways. First, it reduces reliance on accurate initial models relative to conventional FWI. Instead, it invokes general information about the target area, for instance, estimates of means and standard deviations of medium properties in the target area or, alternatively, well-log information in the target area. Second, iterative updating directly affects the weights in the neural network rather than the elastic model. Elastic models can be generated in the first part of the EIFWI process in either of two ways: through the use of a multilayer perceptron (MLP) network or a Bayesian neural network (BNN). Numerical testing is suggestive that the MLP-based EIFWI approach in principle builds accurate models in the absence of an explicit initial model, and the BNN-based EIFWI can give the uncertainty analysis for the prediction results.

First arrival time picking is one of the critical processing steps of acoustic emission (AE)/microseismic (MS) monitoring for studying rock fracture processes. Because of massive monitoring data, the automatic arrival time picking technique is particularly desired. Inspired by recent successful applications of machine learning (ML) in earthquake phase identification, we propose a deep learning (DL)-based P-wave first arrival time picking method named AE Network (AEnet) for laboratory AE monitoring data. Our approach consists of two steps: classification and picking. The convolutional neural network (CNN) is used to classify each sample point of acoustic waveforms into either noise or signal. Different from prior DL-based phase picking studies using raw waveforms, we combine the waveform and high-order statistics as the input to enrich the input data features and accelerate the CNN model learning process. Our approach is examined using the laboratory AE monitoring data and the performance of each component of AEnet is also analyzed. The results show that the CNN model can classify the sample points accurately for the picking procedure. With this classification result, we pick the first arrival time of each trace using the curve fitting method and an unsupervised clustering algorithm. To evaluate the performance of AEnet, we apply Akaike Information Criterion-Short Term Averaging/Long Term Averaging Method (AIC-STA/LTA), one of the most popular and traditional picking methods, on the same waveforms and use the manual picks as the reference. Error analysis results show that AEnet outperforms AIC-STA/LTA.