arXiv subjects

Tariq Alkhalifah

Publications and source records attributed to Tariq Alkhalifah.

At least 55 records · Page 3Linked to original sources

arXiv2025

A new practical and effective source-independent full-waveform inversion with a velocity-distribution supported deep image prior: Applications to two real datasets

Full-waveform inversion (FWI) is an advanced technique for reconstructing high-resolution subsurface physical parameters by progressively minimizing the discrepancy between observed and predicted seismic data. However, conventional FWI encounters challenges in real data applications, primarily due to its conventional objective of direct measurements of the data misfit. Accurate estimation of the source wavelet is essential for effective data fitting, alongside the need for low-frequency data and a reasonable initial model to prevent cycle skipping. Additionally, wave equation solvers often struggle to accurately simulate the amplitude of observed data in real applications. To address these challenges, we introduce a correlation-based source-independent objective function for FWI that aims to mitigate source uncertainty and amplitude dependency, which effectively enhances its practicality for real data applications. We develop a deep-learning framework constrained by this new objective function with a velocity-distribution supported deep image prior, which reparameterizes velocity inversion into trainable parameters within an autoencoder, thereby reducing the nonlinearity in the conventional FWI's objective function. We demonstrate the superiority of our proposed method using synthetic data from benchmark velocity models and, more importantly, two real datasets. These examples highlight its effectiveness and practicality even under challenging conditions, such as missing low frequencies, a crude initial velocity model, and an incorrect source wavelet.

physics.geo-ph↗

arXiv2025

Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields

Physics-Informed Neural Networks (PINNs) have gained increasing attention for solving partial differential equations, including the Helmholtz equation, due to their flexibility and mesh-free formulation. However, their low-frequency bias limits their accuracy and convergence speed for high-frequency wavefield simulations. To alleviate these problems, we propose a simplified PINN framework that incorporates Gabor functions, designed to capture the oscillatory and localized nature of wavefields more effectively. Unlike previous attempts that rely on auxiliary networks to learn Gabor parameters, we redefine the network's task to map input coordinates to a custom Gabor coordinate system, simplifying the training process without increasing the number of trainable parameters compared to a simple PINN. We validate the proposed method across multiple velocity models, including the complex Marmousi and Overthrust models, and demonstrate its superior accuracy, faster convergence, and better robustness features compared to both traditional PINNs and earlier Gabor-based PINNs. Additionally, we propose an efficient integration of a Perfectly Matched Layer (PML) to enhance wavefield behavior near the boundaries. These results suggest that our approach offers an efficient and accurate alternative for scattered wavefield modeling and lays the groundwork for future improvements in PINN-based seismic applications.

physics.geo-ph↗

arXiv2025

A generative foundation model for an all-in-one seismic processing framework

Seismic data often face challenges in their utilization due to noise contamination, incomplete acquisition, and limited low-frequency information, which hinder accurate subsurface imaging and interpretation. Traditional processing methods rely heavily on task-specific designs to address these challenges and fail to account for the variability of data. To address these limitations, we present a generative seismic foundation model (GSFM), a unified framework based on generative diffusion models (GDMs), designed to tackle multi-task seismic processing challenges, including denoising, backscattered noise attenuation, interpolation, and low-frequency extrapolation. GSFM leverages a pre-training stage on synthetic data to capture the features of clean, complete, and broadband seismic data distributions and applies an iterative fine-tuning strategy to adapt the model to field data. By adopting a target-oriented diffusion process prediction, GSFM improves computational efficiency without compromising accuracy. Synthetic data tests demonstrate GSFM surpasses benchmarks with equivalent architectures in all tasks and achieves performance comparable to traditional pre-training strategies, even after their fine-tuning. Also, field data tests suggest that our iterative fine-tuning approach addresses the generalization limitations of conventional pre-training and fine-tuning paradigms, delivering significantly enhanced performance across diverse tasks. Furthermore, GSFM's inherent probabilistic nature enables effective uncertainty quantification, offering valuable insights into the reliability of processing results.

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arXiv2025

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network

Physics-informed neural networks (PINNs) face significant challenges in modeling multi-frequency wavefields in complex velocity models due to their slow convergence, difficulty in representing high-frequency details, and lack of generalization to varying frequencies and velocity scenarios. To address these issues, we propose Meta-LRPINN, a novel framework that combines low-rank parameterization using singular value decomposition (SVD) with meta-learning and frequency embedding. Specifically, we decompose the weights of PINN's hidden layers using SVD and introduce an innovative frequency embedding hypernetwork (FEH) that links input frequencies with the singular values, enabling efficient and frequency-adaptive wavefield representation. Meta-learning is employed to provide robust initialization, improving optimization stability and reducing training time. Additionally, we implement adaptive rank reduction and FEH pruning during the meta-testing phase to further enhance efficiency. Numerical experiments, which are presented on multi-frequency scattered wavefields for different velocity models, demonstrate that Meta-LRPINN achieves much fast convergence speed and much high accuracy compared to baseline methods such as Meta-PINN and vanilla PINN. Also, the proposed framework shows strong generalization to out-of-distribution frequencies while maintaining computational efficiency. These results highlight the potential of our Meta-LRPINN for scalable and adaptable seismic wavefield modeling.

cs.LG↗

arXiv2025

Deep learning enhanced initial model prediction in elastic FWI: application to marine streamer data

Low-frequency data are essential to constrain the low-wavenumber model components in seismic full-waveform inversion (FWI). However, due to acquisition limitations and ambient noise it is often unavailable. Deep learning (DL) can learn to map from high frequency model updates of elastic FWI to a low-wavenumber model update, producing an initial model estimation as if it was available from low-frequency data. We train a FusionNET-based convolutional neural network (CNN) on a synthetic dataset to produce an initial low-wavenumber model from a set of model updates produced by FWI on the data with missing low frequencies. We validate this DL-fused approach using a synthetic benchmark with data generated in an unrelated model to the training dataset. Finally, applying our trained network to estimate an initial low-wavenumber model based on field data, we see that elastic FWI starting from such a 'DL-fused' model update shows improved convergence on real-world marine streamer data.

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arXiv2024

DeFault: Deep-learning-based Fault Delineation Using the IBDP Passive Seismic Data at the Decatur CO2 Storage Site

The carbon capture, utilization, and storage (CCUS) framework is an essential component in reducing greenhouse gas emissions, with its success hinging on the comprehensive knowledge of subsurface geology and geomechanics. Passive seismic event relocation and fault detection serve as indispensable tools, offering vital insights into subsurface structures and fluid migration pathways. Accurate identification and localization of seismic events, however, face significant challenges, including the necessity for high-quality seismic data and advanced computational methods. To address these challenges, we introduce a novel deep learning method, DeFault, specifically designed for passive seismic source relocation and fault delineating for passive seismic monitoring projects. By leveraging data domain-adaptation, DeFault allows us to train a neural network with labeled synthetic data and apply it directly to field data. Using DeFault, the passive seismic sources are automatically clustered based on their recording time and spatial locations, and subsequently, faults and fractures are delineated accordingly. We demonstrate the efficacy of DeFault on a field case study involving CO2 injection related microseismic data from the Decatur, Illinois area. Our approach accurately and efficiently relocated passive seismic events, identified faults and aided in the prevention of potential geological hazards. Our results highlight the potential of DeFault as a valuable tool for passive seismic monitoring, emphasizing its role in ensuring CCUS project safety. This research bolsters the understanding of subsurface characterization in CCUS, illustrating machine learning's capacity to refine these methods. Ultimately, our work bear significant implications for CCUS technology deployment, an essential strategy in combating climate change.

physics.geo-ph↗

arXiv2024

Joint Microseismic Event Detection and Location with a Detection Transformer

Microseismic event detection and location are two primary components in microseismic monitoring, which offers us invaluable insights into the subsurface during reservoir stimulation and evolution. Conventional approaches for 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; such limitations hinder the potential for real-time microseismic monitoring. We propose an approach to unify event detection and source location into a single framework by adapting a Convolutional Neural Network backbone and an encoder-decoder Transformer with a set-based Hungarian loss, which is applied directly to recorded waveforms. The proposed network is trained on synthetic data simulating multiple microseismic events corresponding to random source locations in the area of suspected microseismic activities. A synthetic test on a 2D profile of the SEAM Time Lapse model illustrates the capability of the proposed method in detecting the events properly and locating them in the subsurface accurately; while, a field test using the Arkoma Basin data further proves its practicability, efficiency, and its potential in paving the way for real-time monitoring of microseismic events.

physics.geo-ph↗

arXiv2024

Propagating the prior from shallow to deep with a pre-trained velocity-model Generative Transformer network

Building subsurface velocity models is essential to our goals in utilizing seismic data for Earth discovery and exploration, as well as monitoring. With the dawn of machine learning, these velocity models (or, more precisely, their distribution) can be stored accurately and efficiently in a generative model. These stored velocity model distributions can be utilized to regularize or quantify uncertainties in inverse problems, like full waveform inversion. However, most generators, like normalizing flows or diffusion models, treat the image (velocity model) uniformly, disregarding spatial dependencies and resolution changes with respect to the observation locations. To address this weakness, we introduce VelocityGPT, a novel implementation that utilizes Transformer decoders trained autoregressively to generate a velocity model from shallow subsurface to deep. Owing to the fact that seismic data are often recorded on the Earth's surface, a top-down generator can utilize the inverted information in the shallow as guidance (prior) to generating the deep. To facilitate the implementation, we use an additional network to compress the velocity model. We also inject prior information, like well or structure (represented by a migration image) to generate the velocity model. Using synthetic data, we demonstrate the effectiveness of VelocityGPT as a promising approach in generative model applications for seismic velocity model building.

physics.geo-ph↗

arXiv2024

Conditional Image Prior for Uncertainty Quantification in Full Waveform Inversion

Full Waveform Inversion (FWI) is a technique employed to attain a high resolution subsurface velocity model. However, FWI results are effected by the limited illumination of the model domain and the quality of that illumination, which is related to the quality of the data. Additionally, the high computational cost of FWI, compounded by the high dimensional nature of the model space, complicates the evaluation of model uncertainties. Recent work on applying neural networks to represent the velocity model for FWI demonstrated the network's ability to capture the salient features of the velocity model. The question we ask here is how reliable are these features in representing the observed data contribution within the model space (the posterior distribution). To address this question, we propose leveraging a conditional Convolutional Neural Network (CNN) as image prior to quantify the neural network uncertainties. Specifically, we add to the deep image prior concept a conditional channel, enabling the generation of various models corresponding to the specified condition. We initially train the conditional CNN to learn (store) samples from the prior distribution given by Gaussian Random Fields (GRF) based perturbations of the current velocity model. Subsequently, we use FWI to update the CNN model representation of the priors so that it can generate samples from the posterior distribution. These samples can be used to measure the approximate mean and standard deviation of the posterior distribution, as well as draw samples representing the posterior distribution. We demonstrate the effectiveness of the proposed approach on the Marmousi model and in a field data application.

physics.geo-ph↗

arXiv2024

Controllable seismic velocity synthesis using generative diffusion models

Accurate seismic velocity estimations are vital to understanding Earth's subsurface structures, assessing natural resources, and evaluating seismic hazards. Machine learning-based inversion algorithms have shown promising performance in regional (i.e., for exploration) and global velocity estimation, while their effectiveness hinges on access to large and diverse training datasets whose distributions generally cover the target solutions. Additionally, enhancing the precision and reliability of velocity estimation also requires incorporating prior information, e.g., geological classes, well logs, and subsurface structures, but current statistical or neural network-based methods are not flexible enough to handle such multi-modal information. To address both challenges, we propose to use conditional generative diffusion models for seismic velocity synthesis, in which we readily incorporate those priors. This approach enables the generation of seismic velocities that closely match the expected target distribution, offering datasets informed by both expert knowledge and measured data to support training for data-driven geophysical methods. We demonstrate the flexibility and effectiveness of our method through training diffusion models on the OpenFWI dataset under various conditions, including class labels, well logs, reflectivity images, and the combination of these priors. The performance of the approach under out-of-distribution conditions further underscores its generalization ability, showcasing its potential to provide tailored priors for velocity inverse problems and create specific training datasets for machine learning-based geophysical applications.

physics.geo-ph↗

arXiv2024

Signal Enhancement in Distributed Acoustic Sensing Data Using a Guided Unsupervised Deep Learning Network

Distributed Acoustic Sensing (DAS) is a promising technology introducing a new paradigm in the acquisition of high-resolution seismic data. However, DAS data often show weak signals compared to the background noise, especially in tough installation environments. In this study, we propose a new approach to denoise DAS data that leverages an unsupervised deep learning (DL) model, eliminating the need for labeled training data. The DL model aims to reconstruct the DAS signal while simultaneously attenuating DAS noise. The input DAS data undergo band-pass filtering to eliminate high-frequency content. Subsequently, a continuous wavelet transform (CWT) is performed, and the finest scale is used to guide the DL model in reconstructing the DAS signal. First, we extract 2D patches from both the band-pass filtered data and the CWT scale of the data. Then, these patches are converted using an unrolling mechanism into 1D vectors to form the input of the DL model. The architecture of the proposed DL network is composed of several fully-connected layers. A self-attention layer is further included in each layer to extract the spatial relation between the band-pass filtered data and the CWT scale. Through an iterative process, the DL model tunes its parameters to suppress DAS noise, with the band-pass filtered data serving as the target for the network. We employ the log cosh as a loss function for the DL model, enhancing its robustness against erratic noise. The denoising performance of the proposed framework is validated using field examples from the San Andreas Fault Observatory at Depth (SAFOD) and Frontier Observatory for Research in Geothermal Energy (FORGE) datasets, where the data are recorded by a fiber-optic cable. Comparative analyses against three benchmark methods reveal the robust denoising performance of the proposed framework.

physics.geo-ph↗

arXiv2024

Discovery of physically interpretable wave equations

Using symbolic regression to discover physical laws from observed data is an emerging field. In previous work, we combined genetic algorithm (GA) and machine learning to present a data-driven method for discovering a wave equation. Although it managed to utilize the data to discover the two-dimensional (x,z) acoustic constant-density wave equation u_tt=v^2(u_xx+u_zz) (subscripts of the wavefield, u, are second derivatives in time and space) in a homogeneous medium, it did not provide the complete equation form, where the velocity term is represented by a coefficient rather than directly given by v^2. In this work, we redesign the framework, encoding both velocity information and candidate functional terms simultaneously. Thus, we use GA to simultaneously evolve the candidate functional and coefficient terms in the library. Also, we consider here the physics rationality and interpretability in the randomly generated potential wave equations, by ensuring that both-hand sides of the equation maintain balance in their physical units. We demonstrate this redesigned framework using the acoustic wave equation as an example, showing its ability to produce physically reasonable expressions of wave equations from noisy and sparsely observed data in both homogeneous and inhomogeneous media. Also, we demonstrate that our method can effectively discover wave equations from a more realistic observation scenario.

physics.geo-ph↗

arXiv2024

Ensemble Deep Learning for enhanced seismic data reconstruction

Seismic data often contain gaps due to various obstacles in the investigated area and recording instrument failures. Deep learning techniques offer promising solutions for reconstructing missing data parts by leveraging existing information. However, self-supervised methods frequently struggle with capturing under-represented features such as weaker events, crossing dips, and higher frequencies. To address these challenges, we propose a novel ensemble deep model along with a tailored self-supervised training approach for reconstructing seismic data with consecutive missing traces. Our model comprises two branches of U-nets, each fed from distinct data transformation modules aimed at amplifying under-represented features and promoting diversity among learners. Our loss function minimizes relative errors at the outputs of individual branches and the entire model, ensuring accurate reconstruction of various features while maintaining overall data integrity. Additionally, we employ masking while training to enhance sample diversity and memory efficiency. Application on two benchmark synthetic datasets and two real datasets demonstrates improved accuracy compared to a conventional U-net, successfully reconstructing weak events, diffractions, higher frequencies, and reflections obscured by groundroll. However, our method requires a threefold of training time compared to a simple U-net. An implementation of our method with TensorFlow is also made available.

physics.geo-ph↗

arXiv2024

Robust Full Waveform Inversion with deep Hessian deblurring

Full Waveform Inversion (FWI) is a technique widely used in geophysics to obtain high-resolution subsurface velocity models from waveform seismic data. Due to its large computation cost, most flavors of FWI rely only on the computation of the gradient of the loss function to estimate the update direction, therefore ignoring the contribution of the Hessian. Depending on the level of computational resources one can afford, an approximate of the inverse of the Hessian can be calculated and used to speed up the convergence of FWI towards the global (or a plausible local) minimum. In this work, we propose to use an approximate Hessian computed from a linearization of the wave-equation as commonly done in Least-Squares Migration (LSM). More precisely, we rely on the link between a migrated image and a doubly migrated image (i.e., an image obtained by demigration-migration of the migrated image) to estimate the inverse of the Hessian. However, instead of using non-stationary compact filters to link the two images and approximate the Hessian, we propose to use a deep neural network to directly learn the mapping between the FWI gradient (output) and its Hessian (blurred) counterpart (input). By doing so, the network learns to act as an approximate inverse Hessian: as such, when the trained network is applied to the FWI gradient, an enhanced update direction is obtained, which is shown to be beneficial for the convergence of FWI. The weights of the trained (deblurring) network are then transferred to the next FWI iteration to expedite convergence. We demonstrate the effectiveness of the proposed approach on two synthetic datasets and a field dataset.

physics.geo-ph↗

arXiv2024

Microseismic source imaging using physics-informed neural networks with hard constraints

Microseismic source imaging plays a significant role in passive seismic monitoring. However, such a process is prone to failure due to aliasing when dealing with sparsely 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 inverse Fourier transform to extract the source image. To be more specific, we modify the representation of the frequency-domain wavefield to inherently satisfy the boundary conditions (the measured data on the surface) by means of a 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. Compared with the time-reversal method, the results of the proposed method are consistent with numerical methods but less noisy. Then, we further apply our method to hydraulic fracturing monitoring field data, and demonstrate that our method can correctly image the source with fewer artifacts.

physics.geo-ph↗

arXiv2024

Meta-PINN: Meta learning for improved neural network wavefield solutions

Physics-informed neural networks (PINNs) provide a flexible and effective alternative for estimating seismic wavefield solutions due to their typical mesh-free and unsupervised features. However, their accuracy and training cost restrict their applicability. To address these issues, we propose a novel initialization for PINNs based on meta learning to enhance their performance. In our framework, we first utilize meta learning to train a common network initialization for a distribution of medium parameters (i.e. velocity models). This phase employs a unique training data container, comprising a support set and a query set. We use a dual-loop approach, optimizing network parameters through a bidirectional gradient update from the support set to the query set. Following this, we use the meta-trained PINN model as the initial model for a regular PINN training for a new velocity model in which the optimization of the network is jointly constrained by the physical and regularization losses. Numerical results demonstrate that, compared to the vanilla PINN with random initialization, our method achieves a much fast convergence speed, and also, obtains a significant improvement in the results accuracy. Meanwhile, we showcase that our method can be integrated with existing optimal techniques to further enhance its performance.

physics.geo-ph↗

arXiv2024

A self-supervised learning framework for seismic low-frequency extrapolation

Full waveform inversion (FWI) is capable of generating high-resolution subsurface parameter models, but it is susceptible to cycle-skipping when the data lack low-frequency. Unfortunately, the low-frequency components (< 5.0 Hz) are often tainted by noise in real seismic exploration, which hinders the application of FWI. To address this issue, we develop a novel self-supervised low-frequency extrapolation method that does not require labeled data, enabling neural networks to be trained directly on real data. This paradigm effectively addresses the significant generalization gap often encountered by supervised learning techniques, which are typically trained on synthetic data. We validate the effectiveness of our method on both synthetic and field data. The results demonstrate that our method effectively extrapolates low-frequency components, aiding in circumventing the challenges of cycle-skipping in FWI. Meanwhile, by integrating a self-supervised denoiser, our method effectively performs simultaneously denoising and low-frequency extrapolation on noisy data. Furthermore, we showcase the potential application of our method in extending the ultra-low frequency components of the large-scale collected earthquake seismogram.

physics.geo-ph↗

arXiv2023

PINNslope: seismic data interpolation and local slope estimation with physics informed neural networks

Interpolation of aliased seismic data constitutes a key step in a seismic processing workflow to obtain high quality velocity models and seismic images. Building on the idea of describing seismic wavefields as a superposition of local plane waves, we propose to interpolate seismic data by utilizing a physics informed neural network (PINN). In the proposed framework, two feed-forward neural networks are jointly trained using the local plane wave differential equation as well as the available data as two terms in the objective function: a primary network assisted by positional encoding is tasked with reconstructing the seismic data, whilst an auxiliary, smaller network estimates the associated local slopes. Results on synthetic and field data validate the effectiveness of the proposed method in handling aliased (coarsely sampled) data and data with large gaps. Our method compares favorably against a classic least-squares inversion approach regularized by the local plane-wave equation as well as a PINN-based approach with a single network and pre-computed local slopes. We find that introducing a second network to estimate the local slopes whilst at the same time interpolating the aliased data enhances the overall reconstruction capabilities and convergence behavior of the primary network. Moreover, an additional positional encoding layer embedded as the first layer of the wavefield network confers to the network the ability to converge faster improving the accuracy of the data term.

physics.geo-ph↗