During the processes of reservoir stimulation, fluids are injected into a specific area underground. The high-pressure condition created by the fluid injection causes rocks to crack to release the built-up stress, resulting in small earthquakes called microseismic events. Detecting these events in seismic recordings and locating them back to their subsurface locations are important for understanding the subsurface conditions such as fracture networks and fluid flow pathways. This knowledge is critical for applications like carbon storage, geothermal energy extraction, and oil/gas production. Traditional approaches for microseismic event detection and location often suffer from manual intervention and/or heavy computation, while current machine learning-assisted approaches typically address detection and location separately. These limitations prevent the potential for real-time microseismic monitoring, which is crucial for scientists and engineers to make instant, informed decisions, like optimization of injection strategies. Here, we proposed a machine learning-based procedure for simultaneously detecting and locating microseismic events within a single framework, using a conventional Convolutional Neural Network and an encoder-decoder Transformer. Tests on synthetically-generated and field-collected passive seismic data illustrate the accuracy, efficiency, and potential of the proposed method, which could pave the way for real-time monitoring of microseismic events in the future.

Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to obtain the desired high-resolution model with FWI. To address this challenge, we propose a new paradigm for FWI regularized by generative diffusion models. Specifically, we pre-train a diffusion model in a fully unsupervised manner on a prior velocity model distribution that represents our expectations of the subsurface and then adapt it to the seismic observations by incorporating the FWI into the sampling process of the generative diffusion models. What makes diffusion models uniquely appropriate for such an implementation is that the generative process retains the form and dimensions of the velocity model. Numerical examples demonstrate that our method can outperform the conventional FWI with only negligible additional computational cost. Even in cases of very sparse observations or observations with strong noise, the proposed method could still reconstruct a high-quality subsurface model. Thus, we can incorporate our prior expectations of the solutions in an efficient manner. We further test this approach on field data, which demonstrates the effectiveness of the proposed method.

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence and the need to perform additional, potentially expensive, training for different PDE parameters. To solve this limitation, we introduce latentPINN, a framework that utilizes latent representations of the PDE parameters as additional (to the coordinates) inputs into PINNs and allows for training over the distribution of these parameters. Motivated by the recent progress on generative models, we promote the use of latent diffusion models to learn compressed latent representations of the PDE parameters distribution and act as input parameters to NN functional solutions. We use a two-stage training scheme in which the first stage, we learn the latent representations for the distribution of PDE parameters. In the second stage, we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the PDE parameters. We test the approach on a class of level set equations given by the nonlinear Eikonal equation. We specifically share results corresponding to three different sets of Eikonal parameters (velocity models). The proposed method performs well on new phase velocity models without the need for any additional training.

Microseismic source imaging plays a significant role in passive seismic monitoring. However, such a process is prone to failure due to the aliasing problem when dealing with sparse measured data. Thus, we propose a direct microseismic imaging framework based on physics-informed neural networks (PINNs), which can generate focused source images, even with very sparse recordings. We use the PINNs to represent a multi-frequency wavefield and then apply the inverse Fourier transform to extract the source image. Specially, we modify the representation of the frequency-domain wavefield to inherently satisfy the boundary conditions (the measured data on the surface) by means of the hard constraint, which helps to avoid the difficulty in balancing the data and PDE losses in PINNs. Furthermore, we propose the causality loss implementation with respect to depth to enhance the convergence of PINNs. The numerical experiments on the Overthrust model show that the method can admit reliable and accurate source imaging for single- or multiple- sources and even in passive monitoring settings. Then, we further apply our method on the hydraulic fracturing field data, and demonstrate that our method can correctly image the source.

Physics-informed neural networks (PINNs) have attracted a lot of attention in scientific computing as their functional representation of partial differential equation (PDE) solutions offers flexibility and accuracy features. However, their training cost has limited their practical use as a real alternative to classic numerical methods. Thus, we propose to incorporate multi-resolution hash encoding into PINNs to improve the training efficiency, as such encoding offers a locally-aware (at multi resolution) coordinate inputs to the neural network. Borrowed from the neural representation field community (NeRF), we investigate the robustness of calculating the derivatives of such hash encoded neural networks with respect to the input coordinates, which is often needed by the PINN loss terms. We propose to replace the automatic differentiation with finite-difference calculations of the derivatives to address the discontinuous nature of such derivatives. We also share the appropriate ranges for the hash encoding hyperparameters to obtain robust derivatives. We test the proposed method on three problems, including Burgers equation, Helmholtz equation, and Navier-Stokes equation. The proposed method admits about a 10-fold improvement in efficiency over the vanilla PINN implementation.

Uncertainty quantification is crucial to inverse problems, as it could provide decision-makers with valuable information about the inversion results. For example, seismic inversion is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data. It is therefore of paramount importance to quantify the uncertainties associated to the inversion process to ease the subsequent interpretation and decision making processes. Within this framework of reference, sampling from a target posterior provides a fundamental approach to quantifying the uncertainty in seismic inversion. However, selecting appropriate prior information in a probabilistic inversion is crucial, yet non-trivial, as it influences the ability of a sampling-based inference in providing geological realism in the posterior samples. To overcome such limitations, we present a regularized variational inference framework that performs posterior inference by implicitly regularizing the Kullback-Leibler divergence loss with a CNN-based denoiser by means of the Plug-and-Play methods. We call this new algorithm Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) and demonstrate its ability in producing high-resolution, trustworthy samples representative of the subsurface structures, which we argue could be used for post-inference tasks such as reservoir modelling and history matching. To validate the proposed method, numerical tests are performed on both synthetic and field post-stack seismic data.

Several techniques have been proposed over the years for automatic hypocenter localization. While those techniques have pros and cons that trade-off computational efficiency and the susceptibility of getting trapped in local minima, an alternate approach is needed that allows robust localization performance and holds the potential to make the elusive goal of real-time microseismic monitoring possible. Physics-informed neural networks (PINNs) have appeared on the scene as a flexible and versatile framework for solving partial differential equations (PDEs) along with the associated initial or boundary conditions. We develop HypoPINN -- a PINN-based inversion framework for hypocenter localization and introduce an approximate Bayesian framework for estimating its predictive uncertainties. This work focuses on predicting the hypocenter locations using HypoPINN and investigates the propagation of uncertainties from the random realizations of HypoPINN's weights and biases using the Laplace approximation. We train HypoPINN to obtain the optimized weights for predicting hypocenter location. Next, we approximate the covariance matrix at the optimized HypoPINN's weights for posterior sampling with the Laplace approximation. The posterior samples represent various realizations of HypoPINN's weights. Finally, we predict the locations of the hypocenter associated with those weights' realizations to investigate the uncertainty propagation that comes from those realisations. We demonstrate the features of this methodology through several numerical examples, including using the Otway velocity model based on the Otway project in Australia.

Machine learned tasks on seismic data are often trained sequentially and separately, even though they utilize the same features (i.e. geometrical) of the data. We present StorSeismic, as a framework for seismic data processing, which consists of neural network pre-training and fine-tuning procedures. We, specifically, utilize a neural network as a preprocessing model to store seismic data features of a particular dataset for any downstream tasks. After pre-training, the resulting model can be utilized later, through a fine-tuning procedure, to perform tasks using limited additional training. Used often in Natural Language Processing (NLP) and lately in vision tasks, BERT (Bidirectional Encoder Representations from Transformer), a form of a Transformer model, provides an optimal platform for this framework. The attention mechanism of BERT, applied here on a sequence of traces within the shot gather, is able to capture and store key geometrical features of the seismic data. We pre-train StorSeismic on field data, along with synthetically generated ones, in the self-supervised step. Then, we use the labeled synthetic data to fine-tune the pre-trained network in a supervised fashion to perform various seismic processing tasks, like denoising, velocity estimation, first arrival picking, and NMO. Finally, the fine-tuned model is used to obtain satisfactory inference results on the field data.