Merge pull request #10 from slimgroup/tuna

Generative Geostatistical Modeling from Incomplete Well and Imaged Seismic Observations

_quarto.yml

@@ -22,6 +22,8 @@ website:
           text: "WISER: full-Waveform variational Inference via Subsurface Extensions with Refinements"
         - file: Rex2024SEG/paper.qmd
           text: "Velocity Continuation for Common Image Gathers"
+        - file: erdinc2024SEG/abstract.qmd
+          text: "Building subsurface velocity priors from field observations"
   page-footer:
     center:
       - file: license.qmd

erdinc2024SEG/abstract.bib

@@ -0,0 +1,45 @@
+@article{ambient,
+  title={Ambient diffusion: Learning clean distributions from corrupted data},
+  author={Giannis Daras, Kulin Shah, Yuval Dagan, Aravind Gollakota, Alexandros G Dimakis, and Adam Klivans},
+  journal={Advances in Neural Information Processing Systems (NeurIPS)},
+  year={2023}
+}
+
+@conference{rafaelkriging,
+	title = {Generative Seismic Kriging with Normalizing Flows},
+  author = {Rafael Orozco and Mathias Louboutin and Felix J. Herrmann},
+	journal = {Third International Meeting for Applied Geoscience and Energy (IMAGE)},
+	year = {2023},
+	url = {https://slimgroup.github.io/IMAGE2023/BayesianKrig/abstract.html},
+}
+
+@article{basdeep,
+	title = {Shortcutting inversion-based near-surface characterization workflows using deep learning},
+  author = {Bas Peters},
+	journal = {SEG Technical Program Expanded Abstracts 2020},
+	year = {2020},
+  doi = {10.1190/segam2020-3428431.1}
+}
+
+@article{bg,
+	title = {Building complex synthetic models to evaluate acquisition geometries and velocity inversion technologies},
+  author = {C. E. Jones, J. A. Edgar, J. I. Selvage, and H. Crook},
+	journal = {74th EAGE Conference and Exhibition Incorporating EUROPEC 2012},
+	year = {2012},
+  doi = {10.3997/2214-4609.20148575},
+  url = {https://www.earthdoc.org/content/papers/10.3997/2214-4609.20148575}
+}
+
+@article{wang2024controllable,
+      title={Controllable seismic velocity synthesis using generative diffusion models}, 
+      author={Fu Wang and Xinquan Huang and Tariq Alkhalifah},
+      year={2024},
+      doi = {10.48550/arXiv.2402.06277},
+}
+
+@article{yin2023wise,
+  title={WISE: full-Waveform variational Inference via Subsurface Extensions},
+  author={Yin, Ziyi and Orozco, Rafael and Louboutin, Mathias and Herrmann, Felix J},
+  journal={arXiv preprint arXiv:2401.06230},
+  year={2023}
+}

erdinc2024SEG/abstract.qmd

@@ -0,0 +1,74 @@
+---
+title: "Generative Geostatistical Modeling from Incomplete Well and Imaged Seismic Observations"
+
+author:
+  - name: Huseyin Tuna Erdinc
+    orcid: "0009-0006-0752-7202"
+    email: herdinc3@gatech.edu
+    affiliations:
+    - name: Georgia Institute of Technology
+  - name: Rafael Orozco
+    affiliations:
+      name: Georgia Institute of Technology
+  - name: Felix J. Herrmann
+    orcid: "0000-0003-1180-2167"
+    affiliations:
+      - name: Georgia Institute of Technology
+        url: https://slim.gatech.edu/
+affiliations:
+  - id: gatech
+    name: Georgia Institute of Technology
+    url: https://slim.gatech.edu/
+description: | 
+  Creating velocity from field observations.
+bibliography: abstract.bib
+abstract: |
+  Creating velocity from field observations, reproducible at []()
+---
+
+::: hidden
+$$
+    \newcommand{\pluseq}{\mathrel{+}=}
+$$
+:::
+
+## Abstract
+
+Diffusion generative models are powerful frameworks for learning high-dimensional distributions and synthesizing high-fidelity images. However, their efficacy in training predominantly hinges on the availability of complete, high-quality training datasets, a condition that often proves unattainable, particularly in the domain of subsurface velocity-model generation.  In this work, we propose to synthesize proxy subsurface velocities from incomplete well and imaged seismic observations by introducing additional corruptions to the observations during the training phase. In this context, proxy velocity models refer to random realizations of subsurface velocities that are close in distribution to the actual subsurface velocities. These proxy models can be used as priors to train neural networks with simulation-based inference. Our approach facilitates the generation of these proxy velocity samples by utilizing available datasets composed merely of seismic images and 5 (for now) wells per seismic image.After training, our foundation generative model permits the generation of velocity samples derived from unseen RTMs without the need of having access to wells.
+
+## Methodology
+
+Seismic velocity-model synthesis from incomplete measurements with Generative Geostatistical Modeling (GGM) is an ill-posed problem. In addition, acquiring comprehensive realistic velocity-model training datasets from seismic shot data through the process of full-waveform inversion proves to be too costly. Generative models, particularly diffusion models, offer a solution by training conditional neural networks to synthesize plausible samples, that we refer to as proxy models. After training, these proxy models are synthesized through an iterative denoising process, facilitating high-fidelity, high-dimensional sample generation. Our work leverages generative diffusion models by producing proxy velocity models from limited well-log and imaged seismic information. It negates the need of having access to fully-sampled velocity models during training. Well data provides the only incomplete access to the ground-truth velocities.
+
+Unfortunately, this lack of fully-sampled velocity models precludes the use of traditional neural reconstruction methods that rely on having access to fully-sampled training examples [@wang2024controllable]. Inspired by recent work by @ambient, @rafaelkriging and @basdeep, our study adopts an alternative approach that only requires access to sub-sampled velocity models (i.e. well-log data, denoted by the sub-sampling operator $\mathbf{A}$). The sub-sampling corresponds to the action of binary masks with unity columns at locations where well-log data is available. The reconstruction of the fully-sampled proxy velocity models is conditioned on seismic images (denoted by $\mathbf{c}$). The proposed training process is illustrated in @fig-sup and repeatedly involves: selection of a 2D seismic image, $\mathbf{c}$, paired with 5 well logs $\mathbf{y}$ from which the sub-sampling masks, $\mathbf{A}$ are generated. Conditioned on this sub-sampling mask, a more sub-sampled mask, $\mathbf{\widetilde{A}}$ (cf. the masks $\mathbf{A}$ and $\mathbf{\widetilde{A}}$ in @fig-sup) is generated by zeroing out more columns. Given the action of the more sub-sampled mask on noised and scaled complete well-log data, the neural network is trained to denoise and fit the complete well-log data conditioned on the seismic image. Our network is trained by repeating this process over 20,000 denoising iterations on 2 A100 GPUs involving a training dataset of 3000 training samples.
+
+::: {#fig-sup}
+![](figures/IMAGE2024_figure1_new.png)
+
+Training-loss formulation: field observations (RTMs and wells) along with column-wise masks ($\mathbf{A}$) are sampled initially. Conditioned on these masks, further sub-sampling masks ($\mathbf{\widetilde{A}}$) are generated. The neural denoising model $h_\theta$, informed by the sub-sampling masks, noisy sub-sampled well information and RTMs, is trained to reconstruct the complete, noise-free velocity model.
+:::
+
+## Results
+
+@fig-unsup presents results of our generative model for two unseen examples of imaged reflectivities. Given these unseen seismic images (RTMs), our trained neural model synthesizes subsurface velocity models without relying on well data. To validate the quality of our generative samples, comparisons are made between the posterior means (the average of 200 generative samples) and their respective unseen ground-truth test velocity models. These velocity models remained entirely unseen during the training and generative phase. We observe that the posterior means can capture long range structures and produce visually meaningful velocity samples, evidenced by the high Structural Similarity Index (SSIM) scores of 0.88 and 0.91. Furthermore, the conditional posterior variances align closely with particular structures within the velocity models, which underscores the generative model's capacity to accurately reflect the uncertainty due to two factors: the variability in the subsurface prior information captured from wells seen during training and the uncertainty due to the RTM imaging process. From these results, we conclude that our method conditioned on imaged seismic data is capable of producing high-fidelity samples from the underlying distribution for subsurface velocity models. These samples will serve as input to our full-Waveform variational Inference via Subsurface Extensions (WISE) framework [@yin2023wise]. Looking ahead, future directions include expanding our dataset across varied geological settings, inclusion of prompts to guide the sample generation, all geared towards advancing on the road to a seismic-based foundation model for subsurface velocities.
+
+::: {#fig-unsup}
+![](figures/IMAGE2024_figure2_new.png)
+
+The denoising generative model is tested on two previously unseen seismic images. For each case, we fed the corresponding RTM into the network and generated velocity samples (200 samples for each example). Subsequently, we computed both the posterior mean and variance. To assess the accuracy of our model, we included the SSIM between the ground-truth to the posterior means
+:::
+
+
+## Significance
+
+We utilized generative diffusion models to synthesize realistic subsurface velocity model samples. Unlike prior approaches dependent on fully sampled velocity model datasets, our method achieves training with merely $\approx 2$% of velocity information derived from well data and corresponding Reverse Time Migrations (RTMs). After training is completed, our model's sampling mechanism operates without well data, conditioned solely on RTMs to generate velocity samples. The velocity samples produced by our technique are highly beneficial for subsequent tasks such as WISE, which rely on having access to high-fidelity samples of the distribution of subsurface velocity models. Additional material is available at https://slimgroup.github.io/IMAGE2024/.
+
+
+## Acknowledgement {.appendix}
+
+This research was carried out with the support of Georgia Research Alliance and partners of the ML4Seismic Center.
+
+
+## Software availability {.appendix}
+
+## References

index.qmd

@@ -8,6 +8,7 @@ All submissions to the Image24 conference with additional figures, references, .
 
 List of abstracts:
 
+- [VelGen](erdinc2024SEG/abstract.qmd): Building subsurface velocity priors from field observations
 - [Velocity Continuation for Common Image Gathers with Fourier Neural Operators](Rex2024SEG/paper.qmd) A framework to accelerate migration-velocity analysis and uncertainty quantification
 - [Digital twin with control](GahlotLi2024SEG/paper.qmd) A Digital Twin for Geological Carbon Storage with Controlled Injectivity
 - [WISER](yin2024SEG/paper.qmd): full-Waveform variational Inference via Subsurface Extensions with Refinements