Source-linked AI summary
InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs
Yue Wu, Youzuo Lin
TL;DR
FWI is computationally expensive and can produce low-resolution inversions because it is ill-posed and vulnerable to local minima. The paper addresses this by learning a direct seismic-to-velocity inverse mapping with an encoder-decoder CNN and CRF refinement. Experiments on synthetic datasets report accurate, efficient, and noise-robust inversion.
Problem
FWI is a nonlinear, ill-posed inverse problem whose gradient-based computational techniques are expensive and often yield unsatisfactory resolution for small structures.
Method
InversionNet directly approximates f^-1 with an encoder-decoder CNN, while a locally connected CRF refines velocity values near boundaries and faults.
Results
The CNN-CRF model obtains the best results on two synthetic velocity datasets and demonstrates robustness to additive noise.
Takeaways & Limitations
The experiments support direct data-driven reconstruction of subsurface velocity models from seismic measurements without using the underlying forward physics.
Takeaways & Limitations
Data-driven inversion depends strongly on training data and can require substantial data even when regressed parameters are correlated.
Abstract
from arXiv · showhide
Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator $f$ maps the subsurface velocity structures to seismic signals. The existing computational methods for solving full-waveform inversion are not only computationally expensive, but also yields low-resolution results because of the ill-posedness and cycle skipping issues of full-waveform inversion. To resolve those issues, we employ machine-learning techniques to solve the full-waveform inversion. Specifically, we focus on applying the convolutional neural network~(CNN) to directly derive the inversion operator $f^{-1}$ so that the velocity structure can be obtained without knowing the forward operator $f$. We build a convolutional neural network with an encoder-decoder structure to model the correspondence from seismic data to subsurface velocity structures. Furthermore, we employ the conditional random field~(CRF) on top of the CNN to generate structural predictions by modeling the interactions between different locations on the velocity model. Our numerical examples using synthetic seismic reflection data show that the propose CNN-CRF model significantly improve the accuracy of the velocity inversion while the computational time is reduced.
1 INTRODUCTION
FWI is an important but difficult inverse problem, motivating data-driven approaches that directly reconstruct subsurface velocity from seismic measurements. InversionNet combines an encoder-decoder CNN with a CRF to improve structural predictions, and experiments report accurate, more efficient inversion.
- FWI supports applications including geoscience subsurface characterization and medical breast cancer detection.
- Data-driven inverse-problem methods include end-to-end CNN regression, representation learning, iterative refinement, and analytical methods paired with denoisers.
- Unlike related neural-network studies that add prior knowledge or model forward propagation, InversionNet directly reconstructs FWI models from seismic measurements.
- InversionNet uses an encoder to represent seismic data and a decoder to produce subsurface velocity models despite their differing dimensions.
- A CRF is coupled with the CNN to enhance boundaries and faults that per-pixel CNN losses may capture poorly.
- Synthetic-data experiments compare InversionNet with physics-driven baselines and report accurate inversion with improved computational efficiency.
2 BACKGROUND
Physics-driven FWI uses wave-equation modeling and gradient-based optimization, but can be expensive and produce inadequate resolution. Data-driven methods learn seismic-to-velocity mappings, trading explicit training-data independence for substantial data requirements.
- Physics-Driven Techniques: Physics-driven FWI infers subsurface models using governing physics, including acoustic or elastic wave equations and forward modeling operators.
- Physics-Driven Techniques: The inverse problem minimizes data misfit between recorded waveforms and forward-modeling results, with regularization controlling the solution.
- Physics-Driven Techniques: Tikhonov regularization favors smooth models, whereas total variation is incorporated to preserve sharp interfaces in piecewise-constant velocity structures.
- Physics-Driven Techniques: The TV regularization parameter λ balances regularization against data misfit; excessive λ over-regularizes, while insufficient λ under-regularizes inversion.
- Physics-Driven Techniques: Gradient-based physics-driven techniques are computationally expensive and often provide unsatisfactory resolution for small structures.
- Data-Driven Techniques: Data-driven FWI trains on seismic measurements paired with velocity models, then predicts velocity models for new seismic data.
- Data-Driven Techniques: Unlike physics-driven methods, machine-learning solutions depend strongly on training data and may require substantial data even when parameters are correlated.
3 METHODOLOGY
InversionNet maps seismic data to subsurface velocity models with an encoder-decoder CNN, then uses a locally connected CRF to model interactions and refine structural predictions. Mean-field inference makes the CRF computationally tractable, with overall linear complexity under the stated conditions.
- 3 METHODOLOGY: The forward model maps subsurface model m to seismic data x, while InversionNet approximates the inverse mapping from x to m.The encoder-decoder architecture translates between the seismic-data and velocity-model domains.
- 3.1 Encoder: The encoder uses convolution blocks to extract and compress seismic features into a high-dimensional vector before decoding them into velocity models.Initial convolutions incorporate temporal features, and the final convolution compresses the feature map into a single vector.
- 3.2 Decoder: The decoder combines transposed convolutions and regular convolutions to double resolution and refine the upsampled feature maps.Each deconvolution block uses 4×4 kernels with stride 2, followed by a 3 × 3 convolution.
- 3.3 Conditional Random Fields: A locally connected CRF is placed on the decoder’s final feature map to model interactions between velocity-model outputs.The local graph connects each node to all nodes within a d × d window, while unary and pairwise potentials model individual predictions and output interactions.
- 3.3 Conditional Random Fields: Mean-field factorization approximates the CRF distribution instead of exact inference, reducing the stated exact O(n^3) cost.The approximate distributions are iteratively updated from the CNN’s unary predictions, with w constrained to remain nonnegative.
- 3.3.3 Computational Cost Analysis: O(cd^2n) is the CRF complexity for c mean-field iterations, window size d, and n nodes; because c << n and d^2 << n, it is O(n).The same complexity applies to both inference and learning phases under the stated assumptions.
4 EXPERIMENTAL SETTINGS
The experiments use two synthetic velocity-model datasets, corresponding synthetic seismic measurements, and nearest-neighbor checks to evaluate training-set representativeness. Models are trained with a CNN backbone followed by CRF optimization and assessed with depth-estimation metrics.
- Datasets: FlatVel contains 36,000 100 × 100 velocity models, while CurvedVel contains 50,000 100 × 150 models.The datasets represent flat and curved subsurface layers, respectively.
- Seismic data: Synthetic seismic measurements are generated by forward modeling velocity models with multiple sources, receivers, and finite-difference wave propagation.CurvedVel uses three sources and 150 receivers; both displacement directions are used as training inputs.
- Training-set assessment: Nearest-neighbor comparisons check whether training models resemble test models without being nearly identical, helping assess distribution coverage and memorization risk.The reported neighbors share similarities but differ in velocity values, fault orientation, and layer location.
- Implementation: Training uses a piecewise strategy that first learns the CNN backbone and then optimizes the CRF parameters.The implementation uses separate training and testing pairs for FlatVel and CurvedVel.
- Evaluation metrics: Evaluation adopts depth-estimation metrics including mean absolute error, relative error, log10 error, and accuracy at multiple thresholds.The supplied metric passages list thresholded accuracy values including t = 1.01, 1.02, 1.05, and 1.10.
- Evaluation results: On CurvedVel, data-driven methods outperform physics-driven baselines, with the CNN coupled to the CRF producing the best results.CurvedVel provides a more challenging curved-layer setting than FlatVel.
5 EXPERIMENTAL RESULTS
Experiments on synthetic FlatVel and CurvedVel data show that data-driven models outperform physics-driven baselines, with CNN-CRF generally producing the most accurate reconstructions and improved structural detail. Additional tests indicate robustness to noise and some generalization beyond the training distributions.
- FlatVel: The physics-driven FWI-PRE and FWI-MTV baselines require more prediction time and produce higher errors than the data-driven models on FlatVel.FWI-PRE performs worst, while FWI-MTV improves inversion but still produces artifacts in sparse deep and boundary regions.
- FlatVel: CNN captures boundaries and faults better than the physics-driven models, while CNN-CRF further refines within-layer values and improves deep and boundary regions.The CRF uses d = 20 in the plotted result and enforces consistency across each layer.
- CurvedVel: On CurvedVel, data-driven methods outperform physics-driven baselines despite decreased accuracy, and CNN-CRF yields the best results among the data-driven models.The curved layers create irregular reflections and imbalanced data coverage, making inversion more challenging.
- CurvedVel: CNN-CRF produces more accurate CurvedVel values within layers and significantly better captures the geologic fault, although deep-region fault reconstructions remain incomplete.The reconstruction retains some boundary artifacts.
- Effectiveness of Conditional Random Field: The CRF alleviates inversion artifacts in homogeneous regions and provides better characterization of subsurface structure than CNN alone.Figure 10 compares mean absolute errors between CNN and CNN-CRF against ground truth on FlatVel and CurvedVel.
- Robustness and Generalization: InversionNet remains robust to some additive Gaussian noise levels and produces promising reconstructions for unseen fault configurations and smoothly varying velocity models.Multiple-fault reconstructions retain reasonable overall velocity but show degraded fault shape and velocity; smooth-model tests capture overall geologic features and velocity trends.
6 CONCLUSIONS
The paper develops a CNN-CRF data-driven method for full-waveform inversion and reports the best results on two synthetic velocity datasets, along with robustness to additive noise.
- Method: The CNN encoder-decoder maps seismic waves from multiple receivers to subsurface velocity models, while a locally connected CRF refines values near boundaries and faults.The encoder produces a high-dimensional feature vector and the decoder converts it into a velocity model.
- Results: CNN-CRF obtains the best results on the two synthetic velocity datasets and demonstrates robustness to additive noise.The conclusion presents these experiments as evidence of potential for solving full-waveform inversion problems.