The global demand for unconventional energy sources such as geothermal energy and white hydrogen requires new exploration techniques for precise subsurface structure characterization and potential reservoir identification. The magnetotelluric (MT) method is crucial for these tasks, providing critical information on the distribution of subsurface electrical resistivity at depths ranging from hundreds to thousands of meters. However, traditional iterative algorithm-based inversion methods require the adjustment of multiple parameters, demanding time-consuming and exhaustive tuning processes to achieve proper cost function minimization. Recent advances have incorporated deep learning algorithms for MT inversion, primarily based on supervised learning, and large labeled datasets are needed for training. This work utilizes TensorFlow operations to create a differentiable forward MT operator, leveraging its automatic differentiation capability. Moreover, instead of solving for the subsurface model directly, as classical algorithms perform, this letter presents a new deep unsupervised inversion algorithm guided by physics to estimate 1-D MT models. Instead of using datasets with the observed data and their respective model as labels during training, our method employs a differentiable modeling operator that physically guides the cost function minimization, making the proposed method solely dependent on observed data. Therefore, the optimization algorithm updates the network weights to minimize the data misfit. We test the proposed method with field and synthetic data at different acquisition frequencies, demonstrating that the resistivity models obtained are more accurate than those calculated using other techniques. Our implementation is available athttps://github.com/PAULGOYES/MT_guided1DInversion.git.

Seismologists recognize the localization of earthquakes as a primary and complex task. Determining the seismic event’s location is essential for analyzing seismic activity. The event’s location is inverted from seismic waves recorded by receivers at the surface or in a borehole. Although numerous methods have been developed to solve this problem, they face computational and physics limitations. This study introduces a data-driven approach using Fourier neural operators (FNOs) for real-time microseismic event localization. The proposed method aims to construct a resolution-invariant model that can be rapidly evaluated with a single forward pass, eliminating the need for retraining. Initially, a 2-D FNO model is trained to solve the eikonal equation and tested on both simple and complex velocity models such as the Marmousi model. The method achieves high accuracy in identifying event locations, even for complex settings. Finally, the proposed approach is applied to field data from Utah Frontier Observatory for Research in Geothermal Energy (FORGE), demonstrating its potential for industrial applications. By applying FNO to the actual microseismic dataset obtained from the operational well within the enhanced geothermal system (EGS) setting, the research showcases the model’s capability to accurately determine hypocenter locations. Through this study, we validate the effectiveness of FNO in source localization under realistic conditions, accounting for challenges such as partial data coverage. Our approach paves the way for real-time microseismic monitoring, as the trained FNO model can be promptly evaluated to determine the source location, facilitating real-time decision-making to ensure the safe and efficient development of subsurface operations.

Distributed acoustic sensing (DAS) has emerged as a widely used technology in various applications, including borehole microseismic monitoring, active source exploration, and ambient noise tomography. Compared with conventional geophones, the fiber optic cable has unique characteristics that allow it to withstand high-temperature and high-pressure environments. However, due to its high sensitivity, the obtained seismic records are often corrupted with unavoidable background noise, which introduces more uncertainty in the subsequent seismic data processing and interpretation. Thus, the development of robust denoising techniques for DAS data is crucial to minimize the impact of noise and enhance the reliability of seismic data processing and interpretation. In this work, we propose a ground-truth-free method for strong background noise suppression in DAS vertical seismic profiling (DAS-VSP) data. Compared to existing deep learning (DL) methods, the proposed approach demonstrates promising generalizability in handling field examples across different surveys. The proposed method consists of four stages: training set extension with a patching scheme, feature selection with a kurtosis-based method, denoising with a deep image prior (DIP)-based unsupervised neural network, and an unpatching approach for denoised data reconstruction. Numerical experiments conducted on synthetic data and several profiles from the Utah FORGE project and the Groß Schönebeck site demonstrate that the proposed method can effectively suppress most of the background noise while preserving hidden signals. Furthermore, the unsupervised learning (USL) approach is unconditionally generalizable when applied to vastly different field data because it does not require pre-labeled datasets for training. The codes related to this article are fully open-source viahttps://github.com/cuiyang512/Unsupervised-DAS-Denoising.

Seismic traveltime is critical information conveyed by seismic waves, widely used in various geophysical applications. Conventionally, the simulation of seismic traveltime involves solving the eikonal equation. However, the efficiency of traditional numerical solvers is hindered, as they are typically capable of simulating seismic traveltime for only a single source at a time. Recently, deep learning tools, particularly physics-informed neural networks (PINNs), have proven effective in simulating seismic traveltimes for multiple sources. Nonetheless, PINNs face challenges such as limited generalization capabilities across different models and difficulties in training convergence. To address these issues, we have developed a method for simulating multisource seismic traveltimes in variable velocity models using a deep learning technique, known as the physics-informed Fourier neural operator (PIFNO). The PIFNO-based method for seismic traveltime generator takes both velocity and background traveltime as inputs, generating the perturbation traveltime as the output. This method incorporates a factored eikonal equation as the loss function and relies solely on physical laws, eliminating the need for labeled training data. We demonstrate that our proposed method is not only effective in calculating seismic traveltimes for velocity models used during training but also shows promising prediction capabilities for test velocity models. We validate these features using velocity models from the Sibsbee2A velocity and OpenFWI dataset.

For large-scale seismic exploration in areas that lack even basic infrastructure, wired geophones are impractical because of the huge effort involved and their high deployment and operating costs. A network of wireless geophones capable of recording and transmitting data could be an inexpensive solution. However, a typical seismic survey can generate hundreds of terabytes of raw seismic data per day. It takes a huge amount of energy to transmit this massive amount of data from geophones to the on-site data collection center, thus making the transformation from pre-wired to wireless geophones a significant challenge. To reduce data traffic to the data center without putting additional strain on the geophone, a standalone and lightweight compressive sensing (CS) method is proposed in this work. The method takes advantage of the inherent sparsity in the seismic data to enable the geophone to sense data in a compressed manner. This significantly reduces the amount of data that needs to be recorded/transmitted by the geophone, making it energy efficient. However, instead of employing conventional optimization-based CS reconstruction methods, we propose an efficient implementation of a deep convolutional neural network (DCNN). This network processes the compressed data received at the collection center without any a priori assumptions about the underlying seismic signal statistics, making it appropriate for a wide range of seismic data. The use of CS for energy-efficient sensing and transmission combined with powerful DCNN for reconstruction yields a system that could achieve signal-to-noise ratio (SNR) of around 30 dB with a compression gain of 16 on a field data set. Finally, when compared with other methods, the proposed approach demonstrates significant superiority in maximizing compression gain and reconstruction quality for both synthetic and real field data sets.

Wavefield computation constitutes the majority of the computational cost for seismic applications, including reverse-time migration and full waveform inversion (FWI). One of the popular approaches is to solve for the wavefields in the frequency domain by using the Helmholtz equation. However, Helmholtz solvers require inversion of a large stiffness matrix that can become computationally intractable for large 3D models or in the case of modeling high frequencies. Recently, researchers have explored the potential of physics-informed neural networks (PINNs) in solving the Helmholtz equation with limited success. While a number of attractive features have been demonstrated for the PINN-based Helmholtz solvers, their large training cost has been the main impediment in their widespread adoption for wavefield computations. The large training cost is mainly due to the spectral bias of neural networks, which poses difficulty in training the PINN model for high-frequency wavefields. In this work, I employ Kronecker neural networks (KNNs) that form a general framework for neural networks with adaptive activation functions. I, specifically, implement it using a standard feed-forward neural network employing a composite activation function formed by using the inverse tangent (atan), exponential linear unit (elu), locally adaptive sine (l-sin), and locally adaptive cosine (l-cos) activation functions. Thanks to the oscillatory noise added by the sine and cosine terms, the network is able to explore more and learn faster. This allows the network to get rid of saturation regions from the output of each layer and overcome slow convergence. Through numerical tests, the efficacy of the proposed approach in fast and accurate wavefield modeling in the frequency domain is demonstrated.

There has been a recent rise in the uses and applications of passive seismic data, such as tomographic imaging, volcanic monitoring, and hydrocarbon exploration. Consequently, the sharp increase in passive seismic applications requires real-time event detection capabilities with high accuracy. Proper analysis of such events depends largely on the signal-to-noise ratio improvement through noise suppression techniques. Recent advances in the fields of signal processing and deep learning coupled with the available computational resources provide a great opportunity to address this challenge. In this work, a workflow is proposed where a residual deep neural network is customized and employed to detect passive seismic events. The automated detection is followed by a denoising step to extract the signal of interest from background noise using an IIR Wiener filter. The proposed method does not require any prior knowledge of the signal/noise, and therefore, it can work with various types of signals/noises. Another benefit of the proposed detection method is that the deep neural network is trained only on synthetic seismic data without the need to use real data in the training process. Nevertheless, it exhibits high accuracy in detecting and denoising events from real passive seismic data sets. In particular, field seismic data is recorded in northern Saudi Arabia and used to test the complete detection and denoising method. The detection method proved its capability of detecting events automatically in large data sets and in real time (due to off-line training).

The eikonal equation plays an important role across multidisciplinary branches of science and engineering. In geophysics, the eikonal equation, and its characteristics, are used in addressing two fundamental questions pertaining to seismic waves: what paths do the seismic waves take (its spreading)? and how long do they take? There have been numerous attempts to solve the eikonal equation, which can be broadly categorized as finite-difference and physics informed neural network (PINN) based approaches. While the former has been developed and optimized over the years, it still inherits some numerical inaccuracies and also the cost scales exponentially with the velocity model size. More importantly, it requires upwind calculations to satisfy the viscosity solution. PINNs, on the other hand, have shown great promise due to several features allowing for higher accuracy and scalability than conventional approaches. In this paper, we demonstrate another unique feature of PINN solutions, specifically its flexibility resulting from the global nature of its NN functional optimization, allowing for functional gradients referred to as automatic differentiation. This feature allows us to overcome the inability of conventional methods to handle large areas of missing information (gap) in the velocity model. We find empirically that the PINNs interpolation-extrapolation inherent capability enables us to circumvent a scenario when traveltime modelling is performed on velocity models containing gaps. Such a capability is crucial when performing traveltime modelling using the global tomographic Earth velocity model.

The microseismic monitoring technique is widely applied to petroleum reservoirs to understand the process of hydraulic fracturing. Geophones continuously record the microseismic events triggered by fluid injection on the Earth’s surface or in monitoring wells. The microseismic event localization precision has a large impact on the performance of the technique. Deep learning has achieved significant progress in computer vision and natural language processing in recent years. We propose to use a deep convolutional neural network (CNN) to directly map the field records to their event locations. The biggest advantage of deep learning methods over conventional methods is that they can efficiently predict the characteristics of a huge amount of recorded data without human intervention. Thus, we use a CNN to predict the event location of field microseismic data that were recorded during a hydraulic fracturing process of a shale gas play in Oklahoma, the United States. We use synthetic data with extracted field noise from the records to train CNN. The synthetic training data allow us to produce the corresponding labels, and the extracted noise from the field data reduces the difference between the field and synthetic data. We use a correlation preprocessing step to avoid the need for event detection and picking of arrivals. We demonstrate that the proposed approach provides accurate microseismic event locations at a much faster speed than traditional imaging methods, such as time-reversal imaging. Comparison with an existing study on the same data is presented to evaluate the performance of the trained neural network.