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Deep-learning inversion: a next generation seismic velocity-model building method

Fangshu Yang, Jianwei Ma

arXiv:1902.06267v1physics.geo-phcs.LGeess.SP

TL;DR

Seismic velocity models are essential for high-resolution imaging, yet conventional tomography and FWI are time consuming, computationally expensive, and reliant on human interaction. The paper uses a supervised deep FCN to map raw multi-shot seismic data directly to P-wave velocity models, with promising performance in synthetic experiments and negligible prediction cost after training.

  • Problem

    Velocity-model building is essential for seismic imaging, but conventional methods face computational inefficiency, subjective human factors, and low-frequency limitations.

  • Method

    A supervised deep fully convolutional neural network learns a nonlinear mapping from raw multi-shot seismic data to corresponding P-wave velocity models.

  • Results

    The proposed method shows promising performance compared with conventional FWI in synthetic experiments, including more realistic input-data scenarios.

  • Takeaways & Limitations

    Once a generalized network is built, prediction costs are negligible, offering a possible faster approach for velocity inversion.

  • Takeaways & Limitations

    The approach requires an expensive training process, and conventional inversion remains constrained by low-frequency components and ill-posedness.

Abstract

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Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information has traditionally been derived by tomography or full-waveform inversion (FWI), which are time consuming and computationally expensive, and they rely heavily on human interaction and quality control. We investigate a novel method based on the supervised deep fully convolutional neural network (FCN) for velocity-model building (VMB) directly from raw seismograms. Unlike the conventional inversion method based on physical models, the supervised deep-learning methods are based on big-data training rather than prior-knowledge assumptions. During the training stage, the network establishes a nonlinear projection from the multi-shot seismic data to the corresponding velocity models. During the prediction stage, the trained network can be used to estimate the velocity models from the new input seismic data. One key characteristic of the deep-learning method is that it can automatically extract multi-layer useful features without the need for human-curated activities and initial velocity setup. The data-driven method usually requires more time during the training stage, and actual predictions take less time, with only seconds needed. Therefore, the computational time of geophysical inversions, including real-time inversions, can be dramatically reduced once a good generalized network is built. By using numerical experiments on synthetic models, the promising performances of our proposed method are shown in comparison with conventional FWI even when the input data are in more realistic scenarios. Discussions on the deep-learning methods, training dataset, lack of low frequencies, and advantages and disadvantages of the new method are also provided.

INTRODUCTION

Velocity-model building is essential for seismic exploration and imaging, but conventional approaches face computational, data, and human-intervention limitations. The paper proposes a fully convolutional network that reconstructs P-wave velocity models directly from raw seismic data.

  • Accurate velocity models are prerequisites for reverse-time migration and other seismic imaging techniques.
  • Tomography and FWI reconstruct subsurface velocity using seismic measurements, governing physics, and numerical optimization.
  • Conventional methods can be limited by insufficient low-frequency information, computational inefficiency, subjective human factors, and expensive iterative refinement.
  • Earlier machine-learning studies demonstrated velocity or subsurface-parameter prediction from synthetic seismic data, including high-resolution approximations and noise-tolerant inversion.
  • The proposed FCN reconstructs P-wave velocity models directly from raw multi-shot seismic data by learning a nonlinear data-to-model mapping.
  • The method requires expensive training, but prediction cost becomes negligible after training and can support velocity inversion in more realistic seismic-data scenarios.

Basic inversion problem

The basic inversion problem models seismic wave propagation and seeks subsurface velocity parameters that explain measured data. Because the forward operator is nonlinear and surveys are imperfect, the resulting optimization is generally ill-posed.

  • The constant-density 2D acoustic wave equation describes wave amplitude using velocity, spatial derivatives, time, and a source signal.
  • The forward operator H maps a velocity model v to wavefield data u and is usually nonlinear.
  • Classical inversion minimizes an objective comparing modeled and measured seismic data, with d denoting measurements and f the objective function.
  • Adjoint-state gradients and iterative optimization algorithms are used to minimize the inversion objective.
  • Nonlinearity in H and imperfect surveys make the optimization generally ill-posed, with solutions that are non-unique and unstable.

A review of the FCN

The FCN maps seismic data directly to velocity models through a learned nonlinear function. Training uses paired synthetic data and optimization, while prediction applies the trained network to unknown models.

  • Convolution, nonlinear activation, subsampling, and soft-max operations form the network's principal computational components.
  • The network represents a nonlinear mapping whose inputs and outputs are denoted by x and y, with learnable convolutional weights and biases.
  • The FCN performs end-to-end learning by mapping seismic inputs from the data domain to outputs in the model domain.
  • Supervised training uses paired synthetic seismic data and ground-truth velocity models generated with an acoustic-wave-equation forward model.
  • After training, the learned network predicts unknown velocity models from new seismic data, although the described prediction inputs are synthetic traces rather than field data.
  • The network minimizes prediction error against ground-truth velocity values using back propagation and stochastic gradient descent with mini-batches.

Architecture of the network

The proposed network modifies a UNet-style FCN for seismic velocity-model building. It combines multi-shot inputs, encoder–decoder feature extraction, skip connections, and direct data-to-model domain projection.

  • The method adopts and modifies the UNet architecture for automatic seismic velocity-model building from raw seismic data.
  • The encoder–decoder network uses max-pooling for contraction and transposed convolution for expansion, increasing receptive field with depth.
  • Skip layers combine local shallow feature maps with global deep feature maps to support precise localization.
  • Training synthesizes velocity models and seismic data, updates parameters with Adam, and prediction synthesizes new data before estimating a velocity model.
  • Different shot gathers from the same model are assigned as input channels and fed together to increase data redundancy.
  • The output is resized and reduced to one channel so the network directly maps seismic data in (x, t) to a velocity model in (x, z).

NUMERICAL EXPERIMENTS AND RESULTS

The numerical experiments evaluate data preparation, supervised training, prediction, transfer learning for SEG salt models, and comparison with FWI on a GPU workstation.

  • The experiments train the network on simulated datasets and predict unknown velocity models using the learned network.
  • A pretrained network from simulated models initializes training on the SEG salt dataset through transfer learning.
  • The SEG testing process compares the proposed method with FWI using numerical experiments on the stated workstation configuration.

Data preparation

The study prepares synthetic velocity models and seismic inputs for supervised inversion, then evaluates predictions on simulated and SEG salt models under clean, noisy, and amplitude-scaled conditions.

  • Data preparation: The simulated training dataset contains 1600 velocity samples with layered backgrounds and embedded salt bodies on 201×301 grids.
  • Data preparation: The SEG dataset derives 2D salt models from a 3D reference model, but limited extraction provides only 130 velocity models.
  • Data preparation: Training inputs are generated with finite-difference acoustic modeling using 29 sources and 301 evenly spaced receivers.
  • Robustness: With 5% Gaussian noise, predictions remained acceptable, but some superficial background layers diverged from ground truth and other noise types remain for future study.
  • Data preparation: Testing uses 100 simulated and 10 SEG velocity samples whose geological structures resemble those in training while remaining excluded from it.
  • Results: The FCN produced a generally good match to ground truth and comparable results to FWI while preserving most geological structures.
  • Results: 37 min for FWI versus 2 s per FCN prediction after 1078 min of training, making prediction time more than 1000 times lower.
  • Robustness: Doubling testing-data amplitude produced predictions consistent with those from original inputs, supporting the reported adaptive and stable inversion behavior.

Inversion for SEG salt dataset

The SEG salt experiments show that the proposed network can predict velocity models from seismic data rapidly, including noisy and higher-amplitude inputs. Its performance was slightly below FWI in one test, while transfer learning improved predictions.

  • Comparison with FWI: The proposed method yielded slightly lower performance than FWI in the compared SEG salt test, attributed to the small number of training datasets.The SEG salt training set contained fewer datasets than the simulated-model training set.
  • Transfer learning: Predictions using a pre-trained initialized network were better than predictions from a randomly initialized network.The pre-trained network was trained on the simulated dataset before SEG salt inversion.
  • Noisy and perturbed inputs: The network’s predictions were generally close to ground-truth velocities for noisy seismic data, although slightly below those from clean data.Higher-amplitude inputs produced no difference in prediction results.
  • Computational cost: 43 min trained the network for all SEG salt-model inversions, while each prediction required only 2 s of GPU time.FWI required 25 min for one SEG salt velocity-model inversion.
  • Practical uses: The numerical experiments support velocity inversion directly from raw seismic shot gathers without initial velocity models.The method can also provide initial models for FWI or travel-time tomography and support on-site quality control.
  • Computational cost: Most computational cost occurs once during training and can be handled offline, making post-training prediction costs negligible relative to physical-based inversion.The method avoids iterative searches for optimal solutions.

DISCUSSION

The discussion presents deep-learning velocity inversion as promising but strongly dependent on training-data coverage and testing conditions. Experiments examine dataset size, shot count, missing low frequencies, and transfer learning as determinants of generalization.

  • Evaluation caveat: Quantitative evaluations may be misleading because testing results were averaged over 10 selected networks during training.The authors identify training-shot effects and other performance factors for future investigation.
  • Training dataset: The network’s capability depends on the training dataset, whose structures should resemble those in the predicted models.Larger, diverse training sets generally produce more powerful networks but require longer training.
  • Generalization: SEG salt predictions were lower-performing than FWI when only 10 training samples without salt were used, leaving sediment vague.The network learned these models less effectively than other salt models.
  • Training shots: All tested shot-count cases had training losses converging to zero, suggesting applicability with arbitrary training shots, although the 1-shot case was somewhat unstable.Testing used 1-, 13-, 21-, 27-, and 29-shot configurations.
  • Low frequencies: Removing low frequencies reduced the clarity of structure boundaries and made background velocity layers vaguer than predictions from complete data.The network still predicted most parts of the velocity model.
  • Low frequencies: Retraining with low-frequency-missing seismic data produced slightly better predictions than the corresponding test, but they remained below predictions using complete data.The retraining data were processed using the same approach as the low-frequency-missing testing data.
  • Generalization: The method’s robustness across complex or real models remains difficult to test directly because performance relies on dataset similarity.The discussion frames broader application as requiring further training-set diversity and transfer learning.
  • Transfer learning: Transfer learning was applied when new training models were similar to simulated models, improving learning with pre-trained initialization.The pre-trained network was intended to represent nonlinear input-output mapping rather than merely memorize dataset characteristics.

CONCLUSION

The study presents supervised end-to-end deep learning as an alternative to conventional FWI for reconstructing subsurface velocity models directly from seismic data. Numerical experiments indicate promising reconstruction quality under more realistic conditions, while reducing prediction costs and human intervention after training.

  • CONCLUSION: The method is presented as a possible alternative to conventional FWI-based velocity inversion.The approach uses supervised learning and a fully convolutional network rather than the conventional local-based inversion formulation.
  • CONCLUSION: The proposed formulation uses a fully convolutional network to reconstruct subsurface parameters from seismic data rather than performing local-based inversion.The network produces a subsurface model after training, using seismic data as input.
  • CONCLUSION: Numerical experiments showed that deep learning can approximate the inverse of a difficult nonlinear operator for seismic model building.The learned network still computes satisfactory velocity profiles when seismic data are under more realistic conditions.
  • CONCLUSION: Compared with FWI, reconstruction costs become negligible after network training, with little human intervention and no initial velocity setup.The loss function is measured in the model domain, and prediction does not require generating seismograms.
  • CONCLUSION: A large-scale, diverse training set is important, while future work targets more complex models, field data, and integration with physical inversion approaches.The authors propose generative adversarial learning, transfer learning, and hybrid network designs, but further studies are required for large problems and field applications.
  • CONCLUSION: Further studies are required to adapt the methods to large problems, field data, and other applications.This statement defines the current scope boundary of the reported work.
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