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Deep Learning Tomography
Dr. Amir Adler
Shell Technology Center Amsterdam
5.11.2019
1
Collaborators
2
Tomaso Poggio Mauricio Araya-Polo Stuart Farris Joseph Jennings
MIT Shell Stanford Stanford
Agenda
3
• Seismic Tomography: Forward & Inverse Problems
• Tomography via Empirical Risk Minimization
• The Deep Learning Approach
• Feature Selection: Hand-Crafted vs. Raw Data
• Image Reconstruction: FC vs. RNN Architectures
• Conclusions
Marine Seismic Survey for
Oil & Gas Exploration
4
Schuster, Seismic Inversion, SEG, 2017.

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The Forward and Inverse Problems
5
Velocity Model
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The Scientific Computing, Applied and Industrial Mathematics (SCAIM) Seminar at University of British Columbia. October 2019.

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Trainset Generation Workflow
Shots
Waveform
and
Locations
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Geometry
Acoustic Wave
Propagation
Forward Model
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𝐝𝑖 − seismic data resulting from model 𝐦𝑖
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 Input
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Number Input Features
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2 Spectrograms 2D CNN Multiple FC 2D CNN
3 Spectrograms 2D CNN RNN + FC 2D CNN
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 Recurrent cells are designed for processing time series data.
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VMB results of 4 models with salt bodies: 1st row ground truth (GT); 2nd row CNN
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dimensions of each model are 70 x 90 pixels, representing depth (vertical axis) and
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Network Type CNN RNN LSTM GRU
Number of coefficients in recurrent layer 0 655,872 2,623,488 1,967,616
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• Learn a collection of 1D filters, each processes a single seismic trace in the
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Use raw seismic traces as inputs to 1D CNN:
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Tomography from Raw Data Volume
Conclusions
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We Are Here
Network Capacity
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1) Comparable good performance of the evaluated architectures for
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features directly from raw data
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required to maximize performance with complex velocity models
Publications
39
 M. Araya-Polo, J. Jennings, A. Adler, T. Dhalke,
"Deep Learning Tomography", in The Leading Edge, 2018.
 A. Adler, M. Araya-Polo, T. Poggio,
"Deep Recurrent Architectures for Seismic Tomography",
in EAGE Conference & Exhibition, 2019.
 M. Araya-Polo, A. Adler, J. Jennings, S. Farris, "Fast and
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Deep Learning Tomography

  • 1. Deep Learning Tomography Dr. Amir Adler Shell Technology Center Amsterdam 5.11.2019 1
  • 2. Collaborators 2 Tomaso Poggio Mauricio Araya-Polo Stuart Farris Joseph Jennings MIT Shell Stanford Stanford
  • 3. Agenda 3 • Seismic Tomography: Forward & Inverse Problems • Tomography via Empirical Risk Minimization • The Deep Learning Approach • Feature Selection: Hand-Crafted vs. Raw Data • Image Reconstruction: FC vs. RNN Architectures • Conclusions
  • 4. Marine Seismic Survey for Oil & Gas Exploration 4 Schuster, Seismic Inversion, SEG, 2017.
  • 5. The Forward and Inverse Problems 5 Velocity Model A 2D or 3D model of subsurface layers, where each grid point is the corresponding acoustic wave propagation velocity (m/s)
  • 6. The Forward Problem 6   noise spacedatatomodelvelocityfrommappingF (unknown)modelocitytruth velground dataseismicrecorded     n m d   nmd  F
  • 7. The Inverse Problem 7     functionloss, spacedatatomodelvelocityafrommapping~F dataseismicrecorded modelvelocitypredictedˆ     L m d m   mdm m ~F,minargˆ ~ L
  • 8. Tomography via Empirical Risk Minimization 8     trainsetaoverriskempiricalminimalofsensein the"best" Tbydefinedspacefunctionin thebest""for theSearch: ?vectorparametersset thetoHow: ,Tˆ (function)operatorTomography,TDesign        A Q dm d
  • 9. Trainset Generation Workflow Shots Waveform and Locations Geophones Array Geometry Acoustic Wave Propagation Forward Model 𝐦𝑖, 𝐝𝑖 𝑖=1 𝑁 idVelocity Models Generator Seismic Data Ground Truth Velocity Model Trainset 𝐦𝑖
  • 10. Tomography via Empirical Risk Minimization 10 𝛼 = arg min 𝛼 1 𝑁 𝑖=1 𝑁 𝐿 𝐦𝑖, T 𝐝𝑖, 𝛼 𝑤ℎ𝑒𝑟𝑒: 𝐦𝑖, 𝐝i i=1 𝑁 − dataset with 𝑁 examples 𝐦𝑖 − ground truth i−th velocity model 𝐝𝑖 − seismic data resulting from model 𝐦𝑖 T X,𝛼 − Tomography operator, parameterized by 𝛼 L •,• −loss function
  • 11. Empirical Risk Minimization with MSE Loss 11     modelsstacked-columnhererepresentˆ,where , 1 minargˆ :taskregressionaobtainWe ˆˆ,lossErrorSquaredthechoosingBy 1 2 2 2 2 mm dm mmmm    N i ii T N L  
  • 12. The Potential of Deep Learning 12 Network Capacity (i.e Function Space)
  • 13. High-Level Deep Learning Solution 13  Input  Hand-crafted: Semblance cube  Hand-crafted: Spectrograms of raw seismic data  Raw seismic data  Features Extraction: Convolutional layers  Image Reconstruction: Fully connected vs. recurrent layers  Super-Resolution: Optional convolutional layers
  • 14. Evaluated Architectures 14 Number Input Features Extraction Image Reconstruction Super- Resolution 1 Semblance cube 3D CNN Multiple FC None 2 Spectrograms 2D CNN Multiple FC 2D CNN 3 Spectrograms 2D CNN RNN + FC 2D CNN 4 Spectrograms 2D CNN LSTM + FC 2D CNN 5 Spectrograms 2D CNN GRU + FC 2D CNN 6 Raw Data 1D CNN Multiple FC 2D CNN 7 Raw Data 1D CNN RNN + FC 2D CNN 8 Raw Data 1D CNN LSTM + FC 2D CNN 9 Raw Data 1D CNN GRU + FC 2D CNN 10 Raw Data 3D CNN Multiple FC None
  • 15. Network Training Workflow 15 Deep Neural Network 𝐦𝑖, 𝐝𝑖 𝑖=1 𝑁 Predicted Velocity Model 𝐦𝑖 Learning Algorithm (SGD) Loss Seismic Gather 𝐝𝑖 𝐦𝑖 Data Label Trainset
  • 16. Semblance-Based Architecture 16 Employ Semblance velocity analysis to the raw data, and obtain a Semblance cube: Time x Velocity x Midpoint
  • 22. Spectrograms-Based Architecture 22 Takahashi, Naoya, et al. "Deep Convolutional Neural Networks and Data Augmentation for Acoustic Event Detection“, in Interspeech 2016. Number of sensors Use Spectrogram images of seismic traces as input to 2D CNN:
  • 23. The Spectrogram 23Reveals temporal changes in frequency content
  • 26. Recurrent Architectures for Image Reconstruction 26  Recurrent cells are designed for processing time series data.  Natural candidates for seismic data processing  Real-life product: Google’s motion sense radar in Pixel 4  We evaluated three recurrent architectures, based on:  Recurrent Neural Network (RNN) cells  Long Short Term Memory (LSTM) cells  Gated Recurrent Unit (GRU) cells
  • 27. Recurrent Architectures for Image Reconstruction 27 RNN Cell
  • 30. Spectrogram-Based Architectures 30 VMB results of 4 models with salt bodies: 1st row ground truth (GT); 2nd row CNN (non-recurrent); 3rd row RNN; 4th row LSTM; and 5th row GRU results. The dimensions of each model are 70 x 90 pixels, representing depth (vertical axis) and lateral offset (horizontal axis).
  • 31.  Dataset: 9,600 gathers for training and 2,400 for testing  Each gather: 3 x 17 = 51 seismic traces  Noiseless data Spectrogram-Based Architectures 31 Network Type CNN RNN LSTM GRU Number of coefficients in recurrent layer 0 655,872 2,623,488 1,967,616 Total number of coefficients 7,182,728 1,557,896 3,525,512 2,869,640 Percentage of coefficients vs. CNN network 100% 21.68% 49.08% 39.95% SSIM (averaged on 2,400 velocity models) 0.8199 0.8210 0.8378 0.8414 MSE (averaged on 2,400 velocity models) 0.0018 0.0019 0.0014 0.0013
  • 32. Learning Features from Raw Traces 32 • Learn a collection of 1D filters, each processes a single seismic trace in the time domain. • Proposed [1,2] as a superior alternative to Spectrogram-based Deep Learning, in the context of Automatic Speech Recognition. 1. Y. Hoshen, R. J. Weiss and K. W. Wilson, "Speech acoustic modeling from raw multichannel waveforms," in IEEE ICASSP, 2015. 2. T. N. Sainath et al., "Multichannel Signal Processing With Deep Neural Networks for Automatic Speech Recognition," in IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 25, no. 5, 2017.
  • 33. Raw Data-Based Architecture 33 Use raw seismic traces as inputs to 1D CNN:
  • 34. Raw Data-Based Baseline Recurrent Architecture 34 Use raw seismic traces as inputs to 1D CNN:
  • 35. Spectrograms vs. Raw Data 35  Dataset: 9,600 gathers for training and 2,400 for testing  Each gather: 3 x 51 = 153 seismic traces  Noiseless & Noisy data
  • 36. Tomography from Raw Data Volume  Reshape gather to 3D volume: Time x Receivers x Shots Time Receivers Shots 3D CNN Layers Fully - Connected Layers Features Extractions Image Reconstruction 34 Predicted Model
  • 37. 37 Tomography from Raw Data Volume
  • 38. Conclusions 38 We Are Here Network Capacity (i.e Function Space) 1) Comparable good performance of the evaluated architectures for relatively simple velocity models with salt and additive noise 2) No killer architecture, some advantage with recurrent layers, learn features directly from raw data 3) Massive amounts of data, and increased network capacity are required to maximize performance with complex velocity models
  • 39. Publications 39  M. Araya-Polo, J. Jennings, A. Adler, T. Dhalke, "Deep Learning Tomography", in The Leading Edge, 2018.  A. Adler, M. Araya-Polo, T. Poggio, "Deep Recurrent Architectures for Seismic Tomography", in EAGE Conference & Exhibition, 2019.  M. Araya-Polo, A. Adler, J. Jennings, S. Farris, "Fast and Accurate Seismic Tomography via Deep Learning", in Deep Learning: Algorithms and Applications, Springer, 2020.