⚡ electrical engineering

Physics-guided Fully Convolutional Network using attenuation information for viscoacoustic velocity model prediction

This study proposes a physics-guided Fully Convolutional Network that incorporates attenuation information as an auxiliary input to significantly improve the accuracy and robustness of viscoacoustic velocity model reconstruction compared to conventional data-driven approaches, while also demonstrating the method's sensitivity to the precision of the attenuation data.

Original authors: Nelson Ricardo Coelho Flores Zuniga, Viatcheslav Ivanovich Priimenko

Published 2026-09-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nelson Ricardo Coelho Flores Zuniga, Viatcheslav Ivanovich Priimenko

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep beneath the Earth's surface, hidden from direct view, lie the complex structures that hold oil, gas, and water. To find these resources, geoscientists send sound waves into the ground and listen for the echoes that bounce back. These echoes carry a map of the underground world, but reading that map is notoriously difficult. The rocks and fluids they pass through do more than just reflect sound; they also absorb energy, causing the waves to weaken and change shape as they travel. This weakening, known as attenuation, is a physical clue about the material the wave passed through, much like how a voice sounds different when spoken through a thick curtain versus a thin sheet of glass. For decades, scientists have tried to use these echoes to build accurate pictures of underground speed, which is essential for locating reservoirs, but the process is often hindered by the very complexity of the rocks themselves.

A team of researchers has developed a new way to help computers solve this puzzle. They created a specialized artificial intelligence system designed to look at seismic data and predict the speed of sound underground with greater accuracy. The key innovation in their work is teaching the computer to pay attention not just to the shape of the sound waves, but also to the information about how much energy those waves lost along the way. By feeding the system this extra layer of physical detail, they found it could reconstruct the underground map more faithfully than systems that only looked at the wave shapes. This approach offers a promising path toward clearer images of the Earth's interior, potentially making the search for energy resources more efficient and reliable.

The researchers focused on a specific type of computer network called a Fully Convolutional Network, which is excellent at recognizing patterns in images and data. In their study, they trained this network using a massive library of ten thousand synthetic underground models. These models were computer-generated versions of a famous geological test site known as Marmousi II, which contains complex layers of rock, faults, and fluid-filled pockets. For each model, the team simulated what the seismic data would look like if real instruments were recording it on the surface. They then split the task into two groups. The first group trained a standard network using only the seismic waveforms. The second group, the experimental one, received the same waveforms but with an added ingredient: a map of the energy loss, or attenuation, associated with each wave. This extra map was derived from the physics of how sound travels through the specific rocks in the simulation.

The results showed that giving the computer this extra physical information made a measurable difference. When the researchers tested the networks on new, unseen models, the version that used the attenuation data produced a more accurate picture of the underground speed. The error in its prediction dropped by nearly fourteen percent compared to the standard version. This improvement was not uniform across the entire map; it was most dramatic in specific areas, such as gas-filled sand pockets and water channels, where the error reduction reached nearly fifty percent in some spots. The researchers also compared their best-performing network against a traditional physics-based method called Full-Waveform Inversion, which is a standard but computationally heavy technique. In these specific simulations, the new network produced a clearer result than the traditional method, though the authors caution that this comparison depends heavily on how the traditional method was set up and does not mean the new approach is universally superior in all real-world scenarios.

However, the study also revealed that this advantage comes with a condition. The extra information is only helpful if it is accurate. When the researchers deliberately introduced errors into the attenuation data—simulating a situation where the energy loss was estimated incorrectly—the performance of the improved network began to degrade. With a ten percent error in the extra data, the benefit shrank, and with a twenty percent error, the network actually performed worse than the standard version that ignored the extra data entirely. This finding highlights a critical reality: the new method relies on the quality of the physical clues it is given. It is not a magic fix that works regardless of input quality, but rather a tool that amplifies accuracy when the underlying physical data is reliable.

The researchers also tested how well the system held up when the seismic data itself was noisy, simulating the messy conditions often found in real field recordings. Even when the data was contaminated with noise, the network using the attenuation information still outperformed the standard one, though the margin of improvement narrowed as the noise increased. Furthermore, they ran the training process multiple times with different random starting points to ensure the results were consistent and not just a lucky accident. The improved performance held steady across all these trials, confirming that the benefit of the extra physical information was real and repeatable. The cost of this improvement was modest, adding only about seven percent to the time required to train the computer, while the actual process of making a prediction remained fast, taking only a few seconds per model.

Ultimately, this work demonstrates that combining data-driven learning with specific physical knowledge can lead to better results in geophysical imaging. The study does not claim to have solved the problem of underground imaging for every possible geological setting, as the tests were conducted on computer-generated models based on a single geological family. The authors note that future work will need to test this approach on different types of rock formations and real-world field data to see if the benefits translate beyond the controlled environment of the simulation. Nevertheless, the findings offer a clear proof of concept: by guiding artificial intelligence with the laws of physics—specifically how energy dissipates through the Earth—scientists can build more accurate maps of the hidden world below our feet.

Technical Summary: Physics-guided Fully Convolutional Network using Attenuation Information for Viscoacoustic Velocity Model Prediction

Problem Statement
Accurate reconstruction of seismic velocity models in attenuative media remains a significant challenge. Conventional data-driven approaches typically infer subsurface properties from seismic waveforms without explicitly exploiting information related to seismic energy dissipation. In complex geological settings, this omission limits the ability of neural networks to resolve structures where attenuation provides critical complementary physical information. While recent deep learning studies have focused on estimating the quality factor ( $Q$ ) itself, there is a gap in utilizing attenuation-related information as an auxiliary input to improve the primary task of velocity model prediction.

Methodology
The authors propose a Physics-guided Fully Convolutional Network (FCN) that incorporates seismic attenuation information as an auxiliary input feature to assist in viscoacoustic velocity model reconstruction.

Architecture: The study employs a U-Net based FCN encoder-decoder architecture. The network uses 3×3 convolutional kernels, progressive feature channel expansion (64 to 1024), max-pooling, and transposed convolutions for upsampling. Skip connections preserve high-resolution spatial information.
Input Formulation: Two configurations are compared in a controlled ablation experiment:
1. Baseline FCN: Takes only seismic data ( $D_n$ ) as input.
2. Attenuation-Informed FCN: Takes seismic data ( $D_n$ ) concatenated with an attenuation-related matrix ( $A_n$ ) derived from the constant- $Q$ viscoacoustic formulation (Kjartansson, 1979).
  Crucially, the network output in both cases is the subsurface velocity model; $Q$ is not a prediction target but an auxiliary physical feature.
Dataset: The training dataset consists of 10,000 velocity models derived from the Marmousi II model, augmented with horizontal flipping and fault-like structures. Each model is associated with five finite-difference-generated shot gathers (100 receivers, 5 sources) and corresponding attenuation parameter matrices.
Training & Optimization: The network is trained using the Adam optimizer with a learning rate of $1.0 \times 10^{-3}$ , L2 regularization, and early stopping based on validation loss. The loss function is the Mean Squared Error (MSE) between predicted and reference velocity models.
Evaluation: Performance is measured using Root Mean Squared Error (RMSE) on an independent test set of 250 models. The study includes a Full-Waveform Inversion (FWI) result as a physics-based reference (not a direct competitor). Robustness is tested via seismic noise (20 dB and 10 dB SNR), sensitivity is tested via perturbations in the attenuation input (10% and 20%), and repeatability is assessed through five independent training runs with statistical validation (Wilcoxon signed-rank test).

Key Contributions

Auxiliary Physical Feature Integration: The study introduces attenuation-related information not as a prediction target, but as a complementary physical feature to enhance FCN-based velocity reconstruction.
Controlled Ablation: By keeping the architecture, dataset, and optimization strategy identical between the baseline and proposed configurations, the study isolates the specific contribution of attenuation information to velocity prediction.
Comprehensive Robustness Analysis: The work evaluates the method's sensitivity to seismic noise, uncertainty in the auxiliary attenuation input, and variability in network initialization, providing a nuanced view of the method's reliability.
Regional Performance Characterization: The analysis moves beyond global metrics to evaluate reconstruction accuracy across specific geological regions (e.g., gas sands, water channels, oil sands).

Results

Global Accuracy: Incorporating attenuation information reduced the global RMSE from 0.0237 (Baseline) to 0.0204 (Proposed), a 13.9% reduction. The attenuation-informed FCN also outperformed the FWI reference (RMSE 0.0249) under these specific synthetic conditions.
Regional Variability: The improvement was not uniform. The largest RMSE reductions occurred in Gas Sand 1 (GS1, ~48.8% reduction) and Water-Wet Sand Channels (WWSC, ~34.9% reduction). Smaller but consistent improvements were observed in other regions (e.g., ~8.5% in Oil Sand 2).
Robustness to Noise: The proposed method maintained lower errors than the baseline under noisy conditions, though the relative benefit decreased as noise increased (10.9% reduction at 20 dB SNR; 6.8% at 10 dB SNR).
Sensitivity to Input Uncertainty: The method is sensitive to the accuracy of the auxiliary input. A 10% perturbation in the attenuation matrix increased RMSE to 0.0226, and a 20% perturbation increased it to 0.0259 (exceeding the baseline error). This indicates that inaccurate attenuation estimates can negate the benefits of the approach.
Repeatability and Convergence: Five independent training runs confirmed the statistical significance of the improvement ( $p < 0.05$ ). The attenuation-informed FCN converged stably, reaching a lower minimum validation loss with only a marginal increase in training epochs compared to the baseline.
Computational Cost: Training time increased by approximately 6.94% (an additional ~1.87 hours) due to the extra input channels. Inference time remained efficient at ~11 seconds per case.

Significance and Claims
The paper claims that attenuation-related information serves as a valuable complementary physical constraint for FCN-based velocity reconstruction in viscoacoustic media. The study demonstrates that explicitly providing energy dissipation information allows the network to better map seismic wavefields to velocity structures, particularly in complex reservoir settings like gas sands and water channels.

However, the authors maintain a modest scope regarding their claims:

The results are restricted to the Marmousi II-derived model family and do not claim universal generalization to all geological settings without further validation.
The method is not presented as a universally robust inversion strategy; its efficacy is contingent on the accuracy of the auxiliary attenuation input. If the attenuation information is significantly inaccurate, the performance degrades.
The comparison with FWI is intended as a physics-based reference for error magnitude rather than a definitive proof of superiority, given the fundamentally different inversion strategies (iterative vs. learned mapping).

In conclusion, the proposed framework offers a basis for further investigation using independent geological models and field data, highlighting that while attenuation information improves reconstruction, its utility is bounded by the quality of the seismic observations and the reliability of the attenuation estimates.

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