Author: Denis Avetisyan
A new deep learning approach dramatically speeds up full waveform inversion by intelligently focusing on the most informative seismic data.
This work combines compressed learning and representation learning to accelerate full waveform inversion and improve reconstruction quality using a reduced dataset.
Despite advances in computational power, full waveform inversion (FWI) remains limited by the prohibitive cost of processing massive seismic datasets. This paper, ‘Accelerated Full Waveform Inversion by Deep Compressed Learning’, introduces a deep learning workflow that intelligently reduces data dimensionality via compressed and representation learning. By learning from a corpus of subsurface models, the proposed method selects a minimal, yet consequential, subset of seismic data for inversion, consistently outperforming random sampling. Could this hierarchical data selection approach unlock practical, large-scale 3D FWI for complex subsurface imaging?
The Relentless Pursuit of Subsurface Detail
Full Waveform Inversion (FWI), a cornerstone of detailed subsurface imaging, presents a substantial computational challenge. The technique aims to create high-resolution velocity models by minimizing the difference between simulated and observed seismic waveforms, but this requires solving the Wave Equation iteratively for numerous source locations and frequencies. This process becomes exceptionally demanding as the desired resolution increases, because the number of calculations scales rapidly with it. Furthermore, complex geological features – such as salt domes, faults, or steep dips – introduce significant multiples and scattering that further complicate the inversion process and demand even greater computational resources. Consequently, applying traditional FWI to large-scale, structurally complex areas often proves impractical or requires prohibitive amounts of processing time, limiting its effectiveness in many real-world exploration and monitoring scenarios.
Constructing precise subsurface velocity models is paramount for high-resolution seismic imaging, yet this process is intrinsically challenged by the sheer volume of data involved – collections of seismic traces known as Shot Gathers. These datasets, representing echoes from deep within the Earth, can reach terabytes in size, demanding efficient computational strategies for storage, access, and processing. Traditional methods often struggle with such scale, requiring substantial time and resources. Consequently, researchers are actively developing innovative approaches – including advanced data compression techniques, parallel computing architectures, and machine learning algorithms – to manage these vast datasets. The goal is to accelerate velocity model building without sacrificing accuracy, ultimately enabling clearer and more detailed images of subsurface geological structures and improving the success of resource exploration and monitoring efforts.
Full Waveform Inversion (FWI) relies fundamentally on solving the Wave Equation – a mathematically complex task that becomes exponentially more demanding with increasing resolution. Accurately simulating wave propagation through the Earth’s subsurface requires discretizing space and time into millions, even billions, of computational grid points. Each point necessitates solving a series of complex differential equations, demanding immense processing power and memory. As the desired resolution of the subsurface image increases – revealing finer geological features – the number of grid points grows dramatically, quickly exceeding the capabilities of even the most powerful supercomputers. This computational burden limits the feasibility of high-resolution FWI, hindering the ability to accurately characterize complex subsurface structures and posing a significant challenge for resource exploration and monitoring.
Squeezing Information from the Noise
Compressed Sensing (CS) is a signal processing technique that allows for the accurate reconstruction of a signal from significantly fewer samples than traditionally required by the Nyquist-Shannon sampling theorem. This is achieved by exploiting sparsity – the prevalence of signals possessing representations with only a few non-zero coefficients in a chosen basis. Instead of measuring the signal’s amplitude at regular intervals, CS utilizes optimized measurement matrices to capture the signal’s essential information in a compressed form. Reconstruction is then performed using algorithms like l_1 minimization, which promotes sparse solutions. The reduction in required measurements directly translates to lower data acquisition costs and a substantial decrease in computational load for signal processing and inversion tasks, particularly beneficial in large-scale applications like seismic data processing where datasets are often massive.
Autoencoders, a type of neural network, facilitate dimensionality reduction of seismic Shot Gathers – high-dimensional data representing recorded acoustic waves – by learning a compressed representation termed the Latent Space. This process involves training the autoencoder to reconstruct the original Shot Gather from this lower-dimensional Latent Space representation. The network learns to identify and retain the most salient features within the data, discarding redundant or noisy information. The resulting Latent Space representation, typically significantly smaller in size than the original Shot Gather, effectively captures the essential information required for subsequent seismic processing and inversion tasks, enabling computational efficiency without substantial loss of data fidelity.
Compressed Learning extends the principles of Compressed Sensing to machine learning tasks, specifically optimizing the seismic inversion process. Traditional inversion methods often involve computationally expensive iterative procedures to estimate subsurface parameters from observed seismic data. Compressed Learning reframes this as a learning problem where a model is trained to directly map undersampled seismic data to the desired subsurface representation. This is achieved by incorporating data fidelity terms, enforcing sparsity constraints – often leveraging L_1 regularization – and utilizing optimization algorithms designed for machine learning. By learning an efficient mapping, the computational cost associated with iterative inversion is reduced, and the process can be significantly accelerated without substantial loss of accuracy. This approach allows for real-time or near-real-time inversion, which is crucial for applications like time-lapse seismic monitoring and full waveform inversion.
Joint Optimization: A (Slightly) More Elegant Solution
Deep Compressed Learning (DCL) integrates principles from Compressed Learning and deep neural networks to concurrently optimize two critical aspects of seismic velocity model building: shot selection and model construction. Traditional methods often treat these as separate, sequential steps. DCL, however, formulates an integrated optimization framework where the selection of informative shot gathers is directly linked to the iterative refinement of the velocity model. This joint optimization leverages the efficiency of Compressed Learning – reducing the number of required shots – while benefiting from the representational power of deep neural networks to learn complex relationships between shot gathers and the underlying velocity structure, ultimately leading to improved model accuracy and reduced computational cost.
The implementation of binary weights, facilitated by the Straight-Through Estimator (STE), significantly improves the efficiency of shot gather selection within the Deep Compressed Learning framework. Rather than utilizing full-precision weights, the network operates with binary values (+1 or -1), reducing memory requirements and computational load during forward propagation. The STE addresses the non-differentiability of the sign function by allowing gradients to flow directly through the binary activation during backpropagation, enabling effective training despite the discrete weight values. This approach allows for rapid identification of the most informative shot gathers – those that contribute most to the accurate construction of the velocity model – by effectively acting as a sparse selection mechanism.
Operation within the Latent Space significantly reduces computational demands by transforming high-dimensional data into a lower-dimensional representation, thereby accelerating the inversion process. This dimensionality reduction is achieved through encoding data into a compact Latent Space, minimizing the number of parameters requiring optimization. Furthermore, the method is compatible with K-Means Clustering, allowing for efficient grouping of similar data points within this Latent Space, which can be leveraged to identify representative shot gathers and further optimize the velocity model building process. This approach enables faster iterations and improved efficiency compared to methods operating directly on the original, high-dimensional data.
The loss function within the Deep Compressed Learning framework quantifies the discrepancy between the predicted and actual subsurface velocity models, serving as the primary driver for iterative refinement. This function, typically a combination of L1 or L2 regularization and data-mismatch terms, is minimized through gradient descent algorithms applied to the network’s parameters. Specifically, the data-mismatch component assesses the difference between observed seismic data and data predicted using the current velocity model, while regularization terms prevent overfitting and promote model stability. Minimization of the overall loss function iteratively adjusts the velocity model, ultimately converging towards a solution that best fits the available seismic data and prior geological knowledge.
Filling the Gaps and Restoring Confidence
Seismic data acquisition often suffers from gaps due to logistical or economic constraints. Recent advancements leverage Conditional Generative Adversarial Networks (Conditional GANs) to address this challenge by reconstructing missing portions of shot gathers. These networks learn to map latent space representations – compressed, efficient encodings of seismic data – back into realistic seismic traces, effectively ‘filling in’ the data gaps. This process doesn’t simply interpolate; the Conditional GAN learns the underlying geological patterns, generating plausible seismic responses conditioned on the available data. The reconstructed shot gathers then allow for more complete and reliable full waveform inversion (FWI), enhancing the resolution and accuracy of subsurface imaging even with limited or sparsely sampled data.
The ability to reconstruct seismic data from its latent space representation significantly bolsters the reliability of Full Waveform Inversion (FWI) in challenging environments. When seismic data is sparse or degraded by noise – conditions frequently encountered in complex geological formations – this reconstruction process provides a robust foundation for accurate subsurface imaging. Studies demonstrate that utilizing this approach yields up to a 3dB improvement in Peak Signal-to-Noise Ratio (PSNR) – a key metric for image quality – even when only 10% of the original data is sampled, vastly outperforming conventional random shot selection techniques. This enhancement translates directly into more stable and trustworthy FWI results, allowing for detailed subsurface characterization where traditional methods struggle.
Evaluations consistently demonstrate that this reconstruction method surpasses random shot selection in terms of data fidelity. Specifically, the approach achieves demonstrably lower Mean Absolute Error (MAE) and significantly higher Structural Similarity Index Metric (SSIM) values when reconstructing seismic data. These metrics indicate a superior ability to accurately recreate the original seismic wavefield, preserving crucial details often lost in traditional data acquisition or when relying on randomly selected shots. The consistently improved scores across various datasets highlight the effectiveness of this technique in enhancing seismic data quality and providing a more reliable foundation for subsequent processing and interpretation, ultimately leading to clearer subsurface imaging.
Leveraging the principles of Acoustic Approximation within the Wave Equation, this research demonstrates a pathway to significantly reduce the computational burden of Full Waveform Inversion (FWI). By intelligently selecting a reduced set of seismic shots – guided by latent space reconstruction of data gaps – the process bypasses the need for exhaustive data coverage. This targeted approach doesn’t merely decrease processing time; it maintains inversion accuracy with fewer computational resources, as visualized in Figure 3. The methodology efficiently approximates wave propagation, enabling robust imaging even with limited data, and promises a substantial acceleration in subsurface model building and monitoring applications where computational efficiency is paramount.
The pursuit of accelerated full waveform inversion, as detailed in this work, inevitably courts the creation of future technical debt. This paper attempts to intelligently select seismic data using deep learning – a valiant effort, certainly. But the system will, without fail, encounter edge cases, unforeseen data anomalies, or simply the relentless pressure of production scale. As Barbara Liskov observed, “It’s one thing to describe an idea, it’s another to make it work.” The elegant compression and representation learning techniques showcased here are merely temporary victories; the system’s true test lies in its resilience against the inevitable chaos that awaits in real-world deployment. Tests, after all, are merely a form of faith, not certainty.
What’s Next?
The promise of accelerated full waveform inversion via intelligent data selection is, predictably, not a resolution, but a shifting of complexity. This work elegantly sidesteps computational bottlenecks, but introduces the unavoidable question of representativeness. Any compression, however ‘deeply learned’, risks discarding signal crucial to nuanced subsurface features. The claim of improved reconstruction quality will be tested, not in the curated examples presented, but when applied to the truly messy, ambiguous data production invariably provides.
The field will, of course, chase further algorithmic cleverness. Expect increasingly elaborate architectures attempting to predict the uncomputable-the perfect subset, the optimal representation. It is worth remembering that any self-healing network simply hasn’t encountered its fatal flaw. The true metric of success won’t be speed, but robustness – the ability to gracefully degrade in the face of incomplete or corrupted data. If a bug is reproducible, the system is stable; its cleverness is irrelevant.
Ultimately, the limitations lie not in the learning, but in the data itself. The pursuit of ‘intelligent’ workflows often obscures the more fundamental need for improved acquisition, better noise reduction, and, perhaps most importantly, a healthy skepticism towards any model claiming to perfectly represent the Earth. Documentation of these models, predictably, remains a collective self-delusion.
Original article: https://arxiv.org/pdf/2601.01268.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2026-01-07 01:15