SEP-189 (2023)

Rustam Akhmadiev, Hassan Almomin, Milad Bader, Biondo Biondi, Robert Clapp, Thomas A. Cullison, Stuart Farris, Paige Given, Haipeng Li, Jingxiao Liu, Hae Young Noh, Julio Oliva Frigerio, Min Jun Park, Cedric Richard, Rahul Sarkar, Joseph Stitt, Martijn van den Ende, Jonathan Voyles

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SEP-189 Reports (Password Protected) (June, 2023)

Distributed acoustic sensing (DAS)

Source footprint elimination in full-waveform inversion by model extension: Application to elastic guided waves recorded by distributed acoustic sensing in unconventional reservoir
Milad Bader, Robert G. Clapp, Kurt T. Nihei, and Biondo Biondi
Source footprints represent an inherent problem to full-waveform inversion (FWI). They are caused by the high data sensitivity to the model parameters in the vicinity of the seismic sources and can be exacerbated by source-related errors in the modeling operator. We propose a simple, effective, and efficient method to remove source footprints in FWI when sources are located near or inside the volume of interest while robustly updating the model in their vicinity. The method uses illumination redundancy and extends the model along sources. Each source updates one component of the extended model, and a regularization term ensures that these components are mutually consistent, except for their respective footprints. We illustrate the effectiveness of our method on the elastic inversion of synthetic guided waves. We show its robustness in the presence of source-related errors and its superiority over other well-known approaches, such as illumination compensation by inverse pseudo-Hessian and gradient preconditioning. We apply the method to a field distributed acoustic sensing dataset with elastic guided waves generated by perforation shots in an unconventional shale reservoir. The method is able to retrieve localized reservoir anomalies with higher elastic velocities, indicating possible lower pore pressure or tighter shale regions.

Automated and Continuous Near-surface characterization using a DAS-based Vehicle Tracking Method
Siyuan Yuan, Jingxiao Liu, Hae Young Noh, Robert Clapp, and Biondo Biondi
This study proposes a novel method for detecting spatial subsurface heterogeneity and rain-induced soil saturation changes in the San Francisco Bay Area. Our approach utilizes vehicles as cost-effective surface-wave sources that excite wavefield recorded by a roadside Distributed Acoustic Sensing (DAS) array. Leveraging a Kalman filter vehicletracking algorithm, we can automatically track hundreds of vehicles each day, allowing us to extract space-time windows of high-quality surface waves. By constructing highly accurate virtual shot gathers from these waves, we can perform time-lapse surface-wave analyses with high temporal and spatial resolutions. Our method enables accurate and efficient monitoring of both spatial near-surface heterogeneity and daily soil saturation changes.

Spatial Deep Deconvolution U-Net for Traffic Analyses with Distributed Acoustic Sensing
Siyuan Yuan, Martijn van den Ende, Jingxiao Liu, Hae Young Noh, Robert Clapp, Cedric Richard, and Biondo Biondi
Distributed Acoustic Sensing (DAS) that transforms city-wide fiber-optic cables into a large-scale strain sensing array has shown the potential to revolutionize urban traffic monitoring by providing a fine-grained, scalable, and low-maintenance monitoring solution. However, there are challenges that limit DAS’s real-world usage: noise contamination and interference among closely traveling cars. To address the issues, we introduce a self-supervised U-Net model that can suppress background noise and compress car-induced DAS signals into high-resolution pulses through spatial deconvolution. To guide the design of the approach, we investigate the fiber response to vehicles through numerical simulation and field experiments. We show that the localized and narrow outputs from our model lead to accurate and highly resolved car position and speed tracking. We evaluate the effectiveness and robustness of our method through field recordings under different traffic conditions and various driving speeds. Our results show that our method can enhance the spatial-temporal resolution and better resolve closely traveling cars. The spatial deconvolution U-Net model also enables the characterization of large-size vehicles to identify axle numbers and estimate the vehicle length. Monitoring large-size vehicles also benefits imaging deep earth by leveraging the surface waves induced by the dynamic vehicle-road interaction.

Elastic Full-Waveform Inversion of Distributed Acoustic Sensing Data: Modeling, Inversion, and Parameterization
Haipeng Li and Biondo L. Biondi
In this study, we investigate the numerical modeling strategy and elastic Full-waveform Inversion (FWI) for Distributed Acoustic Sensing (DAS) data. We quantify the impact of different discretization schemes on DAS waveform modeling and observe varying error magnitudes. Using the deviated fiber, we analyze the directional sensitivity of DAS acquisition in a heterogeneous model. In addition, we compare the effectiveness of three parameterization schemes used in the DAS FWI: Velocity-Density, ModuliDensity, and Impedance-Density. Our results based on anomaly models indicate that the velocity-density parameterization outperforms the other schemes in suppressing crosstalks. Moreover, we apply the Porosity, Clay content, and Water saturation (PCS) parameterization that directly links elastic FWI with rock physics in the time-lapse inversion. The results based on the PCS parameterization more accurately recover time-lapse changes than the velocity-density scheme. This study shows the potential advantage of FWI on the DAS data for subsurface imaging and monitoring, particularly in challenging environments where traditional seismic acquisition methods may be limited or costly.

Estimating Dark Fiber Effective-Coupling from Passively Recorded Seismic Data
Jonathan Voyles, Robert G Clapp, and Biondo Biondi
A critical issue challenging the widespread adoption of distributed acoustic sensing (DAS) data is understanding the coupling between the fiber optic cable and the Earth. Understanding and estimating the coupling is a crucial processing step in seismic imaging, velocity estimation, event detection, and much more. Here, we develop an algorithm to automatically estimate the effective coupling of a given fiber optic cable deployment leveraging passive seismicity. Effective coupling can be thought of as the physical coupling between the fiber and the Earth combined with near-surface effects. Passive seismicity offers a wide frequency band of signal without requiring an active source. We present two different methods to estimate effective coupling; one that compares the seismic response of the fiber to that of a nearby seismometer and one that compares the seismic response of the fiber to itself. We test our algorithm on the Stanford DAS array for various earthquakes to estimate effective coupling as a function of distance along the fiber. We package the algorithm with its various methods into an open-source python package for use by the scientific community.

Waveform modeling and inversion 

Seismic modeling using SBP operators
Milad Bader
This article is the draft Chapter 2 of my thesis, in which I describe how to numerically model elastic waves in isotropic and vertical transverse isotropy (VTI) media using summation-by-parts and simultaneous approximation terms framework. I include the numerical injection of vector and moment tensor sources. I compare my numerical solution with known analytical solutions. Then, I describe how distributed acoustic sensing data can be modeled in theory and assess the error committed in my simplified approach. Part of this chapter is published in Bader et al. (2023).

Formulation and solution of tomographic waveform inversion (TWI)
Julio Oliva Frigerio
Tomographic waveform inversion (TWI) is an inversion method to perform seismic velocity model building. An interesting characteristic of TWI is that it combines elements from a variety of its predecessors, like FWI, WEMVA, TFWI, FWIME, RFWI, into its inverse problem formulation. The purpose of such a combination is to overcome many of the major limitations that these previous algorithms presented by exploring and benefiting from the complementarity that exists between each of them. With this purpose, TWI is built upon extended Born modeling, which takes two sets of variables as input, the velocity model and reflectivity model. This naturally incorporates an extension into the model/parameter space and has a profound significance in the shape of the objective function. All of this makes TWI a unique inverse problem, especially with respect to the shape and characteristics of its objective function as well as the way this inverse problem is solved. Even though a gradient-based strategy is employed to solve TWI as a convex optimization problem, the way one navigates within the model space and relative to the objective function’s surface is special and theoretically appealing. In this sense, what makes TWI immune to convergence to local minima is not the fact that it does not have local minima, but the possibility of solving the inverse problem by always staying within the optimal valley, that in TWI corresponds to the global basin of attraction. In this article I will be present to the elegant theoretical framework of TWI as an inverse problem almost from first principles. The reader will see how the facts mentioned above connect and make up a clear and solid theory.

One-way waveform inversion using variable frequency-extended density and spline interpolation
Rustam Akhmadiev, Robert Clapp and Biondo Biondi
We expand upon the previously proposed method of one-way waveform inversion with a frequency-extended model to accommodate variable density. Frequency-extended density model is used to compute reflectivity and is updated simultaneously with slowness. By utilizing a fine spline grid for the extended density and a coarse grid for the extended slowness model, we are able to achieve accurate data-residual matching and smooth slowness updates. The variability of the model parameters with frequency can be controlled in a similar way. As a result, accurate slowness model can be recovered even from a rough starting model and with no low-frequency components in the data. The proposed method does not require intermediate step of solving a least-squares problem for extended reflectivity and potentially is more computationally attractive. We demonstrate the effectiveness of our approach with synthetic examples.

Deep subsalt velocity model improvement with tomographic waveform inversion (TWI) in the Tiber WATS dataset, Gulf of Mexico
Julio Oliva Frigerio
Tomographic waveform inversion (TWI) has been developed as an inversion method to be employed in challenging scenarios where the other algorithms available, e.g. raybased tomography and FWI with its flavors, would fail. Examples of such scenarios involve elements as potential of convergence to local minima (cycle-skipping), lack of lower frequencies, lack of long enough acquisition offsets and record of diving waves, impossibility of moveout tracking and definition, presence of complex geology such as salt bodies. With the purpose of fostering research and innovation, BP has made public a dataset containing a variety of Tiber WATS seismic data and the corresponding legacy velocity model. The subsalt part of the legacy model is clearly inaccurate and needs improvement. Inversion of this portion of the model contains many - if not all - of the challenges mentioned in the previous paragraph. For this reason, traditional methods are not able to handle inversion of the Tiber subsalt with the seismic data provided. Application of TWI to update the Tiber subsalt has succeeded in improving the quality of the velocity model and the imaging of the subsalt strata, where the reservoir is located. The results of this experiment are an evidence that TWI can provide important and unique contributions in the process of velocity model building in face of complex scenarios.

Some computational aspects of Lippmann-Schwinger equation constrained acoustic waveform inversion
Rahul Sarkar and  Biondo Biondi
We study some computational aspects of inversion using the Lippmann-Schwinger equation as constraint, that has been introduced in Sarkar and Biondi (2022). One key difficulty that arises in the implementation of the second step of the inner iterations, is that the parameter space is real valued, but the operators are complex valued. We show how to handle this case using black-box least squares solvers. Next, we tackle the problem in the precomputation step, where we need to compute Green’s functions, as some of the well-known available direct solvers in Python fail to handle large models (even in 2D). This is ameliorated by using iterative methods.

Tomographic waveform inversion (TWI) with time-lags
Julio Oliva Frigerio and Rustam Akhmadiev
Tomographic waveform inversion (TWI) has been so far formulated with extended images consisting of subsurface-offsets gathers. This formulation has been successful in producing great inversion results in all the applications where TWI was tested. However, there are some cases where using subsurface-offset gathers in TWI is troublesome. One of them is 3D seismic data with full azimuth, which requires computation of 2D horizontal subsurface-offsets, leading to insurmountable memory requirements. The other case is that of datasets containing transmitted/refracted waves, such as diving waves, refractions at critical angles, cross-well data records. To generalize TWI to be able to properly handle these cases along with the previous ones of reflections within a limited azimuth range, a new formulation is proposed, one in which the extended images consist of time-lag common-image gathers. In the search of the new formulation, we discover that kinematic invariance of the extended Born imaging and modeling is not always preserved. To correctly incorporate this observation, TWI’s objective function is rearranged and defined in two ways, depending on the application. The first experiments indicate that the proposed formulation is correct and produces accurate inversion results.

Born scattering from a time-dependent perturbation: motivation and examples
Rahul Sarkar
This article is a draft of Chapter 5 of my thesis. The goal here is to introduce the motivation behind the study of the time-dependent Born scattering problem, and to explain why it arose in the context of seismic inversion. This is a new kind of extended model, a concept which is explained in this chapter more thoroughly, that was discovered while trying to better understand the role of convolutions for time-lag extended models. In this article, I will first briefly discuss the role of extended models in seismic inversion, focusing particularly on the concept of time-lag extension that motivated this study. Then we will introduce the time-dependent Born scattering extension, which is the main contribution of this article. We show how the corresponding common-image gathers can be used to detect velocity errors. We discuss using numerical examples the efficacy of the proposed extension for modeling seismic residuals. Finally we show that the normal operator corresponding to the time-dependent Born scattering phenomenon produces artifacts in the imaging process.

Computing solutions to the Helmholtz equation with horizontal radial symmetry
Rahul Sarkar and Biondo Biondi
We discuss a numerical strategy to compute the solution to the Helmholtz equation in R2 and R3 for a sound speed profile that is only dependent on depth. We discuss the 3D case, where it is the most advantageous, and then state what happens in the 2D case. For the 3D case, the problem is effectively reduced to a 2D problem, which can then be solved using direct matrix factorization techniques. The advantage of the method arises when one needs to solve the Helmholtz equation multiple times for different right hand sides, for such a depth dependent velocity.

Machine learning

Synthetics are all you need
Stuart Farris
This study presents a supervised deep learning approach using convolutional neural networks (CNNs) to recover accurate low-wavenumber earth models from band-limited, narrow-offset seismic field data for full-waveform inversion (FWI) applications. The focus is on the novel, open-source Tiber WATS data from the Gulf of Mexico, obtained from BP in 2010 and made publicly available in 2022. The Tiber field lies beneath an expansive, tabular allochthonous salt body, complicating imaging of geologic layers encapsulating reservoir compartments. CNNs are trained on three different datasets, including field data and two types of synthetic data, to predict low-wavenumber velocity models. Performance is evaluated by comparing velocity predictions to a benchmark legacy model from a CGG multi-client survey, using mean-squared error and structural similarity index measure (SSIM). An unbiased comparison is also conducted through reverse time migration imaging of the results from each model. Results demonstrate the capability of CNNs to effectively learn a mapping from seismic field data to lowwavenumber velocity models and make predictions on unseen data. This highlights the potential of deep learning for tackling industrial-scale problems in geophysics. The study also provides insights into the performance of CNNs trained on synthetic data, informing future geophysical applications.

Exploring the Use of Pre-Injection Seismic Surveys and Unsupervised Deep Learning for Affordable Carbon Storage Monitoring
Min Jun Park, Julio Frigerio, Bob Clapp, and Biondo Biondi
Monitoring stored CO2 is an essential part of a carbon capture and storage project, as it helps to ensure the safety and effectiveness of the project. Among various monitoring methods, a time-lapse (or 4D) seismic survey can provide a detailed analysis of injected CO2 plumes by allowing for the repeated measurement of subsurface changes over time. However, the subtle changes in the subsurface induced by injected CO2 pose a significant challenge for time-lapse seismic monitoring, particularly in environments with low signal-to-noise ratios. This highlights the need for robust time-lapse monitoring techniques to accurately identify subsurface changes even in the presence of noise. Such noise-robust methods may also reduce monitoring costs by potentially lowering data quality requirements. To address this issue, we propose an unsupervised deep learning-based CO2 monitoring system, which can recognize CO2 response among the time-lapse noise. Specifically, we adopt a Deep-Support Vector Data Description scheme, an unsupervised anomaly detection approach that allows us to learn time-lapse noise characteristics from pre-injection surveys. We then use this knowledge to distinguish the CO2-induced signal from the time-lapse noise. In this study, we evaluate the effectiveness of our proposed approach using both 2D synthetic and 3D field data from the Aquistore project. In synthetic examples, we simulate the random near-surface effects to introduce the time-lapse noise and compare the monitoring performance between the proposed method and conventional time-lapse imaging. In the field data example from Aquistore, we use two pre-injection surveys to learn the characteristics of the time-lapse noise and then use this information to identify the CO2 plumes in two post-injection surveys. Our results from both synthetic and field data demonstrate that learning the time-lapse noise characteristics can lead to more accurate identification of the CO2 response.

Automatic Microseismic Event Detection for Enhanced Geothermal through Transfer Learning of Convolutional Neural Networks
Paige Given, Robert G. Clapp, and Biondo Biondi
In this study, we apply transfer learning of our automatic microseismic event detection algorithm trained on unconventional reservoir data. The algorithm takes DAS data as input and outputs the probability of a microseismic event occurring within a given 250-millisecond by 400-meter sliding window across large datasets. We tested our algorithm on the Utah Department of Energy FORGE Geothermal 2022 DAS dataset and achieved an accuracy of over 99% in detecting 636 microseismic events, missing only one instance. Further analysis of the singular missed event revealed that it had lower amplitudes than most events and did not actually house an event, but rather trailing seismicity. Our study demonstrates that accurate, cost-effective, and efficient analysis methods can be implemented in the geothermal field, promoting the use of this sustainable resource.

Leveraging Adversarial Regularization in Geophysical Inverse Problems: How Can a Convolutional Neural Network Tackle the Model Null Space Challenge?
Joseph Stitt, Robert Clapp, and Biondo Biondi
This paper introduces a novel approach utilizing neural network-based regularizers to enhance Dix inversion accuracy with synthetic and field RMS velocity data. Improving geophysical inverse problem-solving is vital for reliable information extraction and uncertainty quantification. Regularization techniques stabilize ill-posed problems by penalizing high-value model parameters. Deep learning algorithms enable data-driven geophysical inversion. The authors use an adversarial regularizer to constrain inverse solutions, limiting model possibilities to realistic scenarios and excluding incoherent models. After training on simple undulated layers, accurate wavenumber content was added to near-surface layers and the chalk layer top, but with artifacts. Training on a North Sea dataset reflective of subsurface geology, the 2D Netherlands F3 model slice displayed improved resolution of sedimentary bedding and chalk layer boundaries. Deeper layers were less resolved, but some faulted layers were apparent. The adversarial regularizer effectively enhanced both synthetic and field data resolution, providing high-wavenumber updates for complex geometric boundaries. Future work includes acoustic and elastic full-waveform inversion to mitigate crosstalk effects, using synthetic models and well data. A promising three-parameter input regularizer term example is provided.

Rock Physics Modeling Using Machine Learning
Hassan Almomin
Rock physics is the study of the correlations between rock properties and their elastic characteristics. Rock physics models (RPMs) are equations that convert these rock properties into elastic attributes. The current RPMs, however, exhibit limitations in fully capturing the intricate details and complexity of real rocks. This report focuses on a review and assessment of these conventional RPMs, while highlighting their limitations and potential areas of improvement. To address these identified limitations, this paper investigates the potential of machine/deep learning algorithms. A few examples in existing literature reveal how these advanced algorithms have been utilized to build more accurate rock physics relationships between various properties. The literature demonstrates the success of various machine learning algorithms in generating realistic synthetic wells and seismic volumes, which can be employed to train models for a range of geophysical applications. This makes machine learning a potentially invaluable tool for the oil and gas industry. Looking forward, the paper proposes the development of various machine learning networks as part of future work, to further enhance rock physics modeling and applications.

Cloud and reproducibility

Efficient Cloud Migration: Harnessing Terraform, Containers, and Python Packages for a Smooth Transition
Robert G. Clapp
This article presents an approach to migrating from on-premises infrastructure to the cloud, utilizing Terraform, containers, and Python-based software. Terraform, an infrastructure-as-code tool, enables streamlined provisioning and maintenance of cloud resources. Containers, such as Docker and Singularity, provide isolated, reproducible environments for simplified application deployment. In addition, two innovative Python packages are introduced to aid the migration process. The first, auto-launch, automates the launching of Jupyter notebooks, Docker containers, and Singularity containers on Slurm batch clusters in the cloud, ensuring consistency across environments. The second, sep-python, efficiently reads and writes seismic regular cubes on both conventional disks and object stores, simplifying data access and manipulation for geophysical analysis. By employing these tools and packages, we hope effectively transition applications to the cloud, reaping benefits such as improved scalability, flexibility, and cost-efficiency.

Chasing Reproducibility
Thomas A. Cullison and Robert G. Clapp
Research publications should be reproducible, including all computations used for generating results. However, maintaining a computationally reproducible framework can be challenging, particularly when developing research codes within a rapidly changing computational landscape. We discuss some of these challenges and the steps SEP is taking to keep pace with reproducibility in an evolving computational landscape.