SEP-179 (2020)

Fracture properties estimation using DAS recording of guided waves in unconventional reservoirs
Ariel Lellouch, Mark Meadows, Tamas Nemeth, and Biondo Biondi
Perforation shots excite guided waves that propagate in a low-velocity unconventional shale reservoir. They have a frequency content of up to 700 Hz and are dispersive. We analyze horizontal cross-well perforation shots recorded by a Distributed Acoustic Sensing array. We observe a dramatic influence on the guided S waves in the form of delayed arrival times, scattering, phase incoherency, and loss of amplitude and frequency, as well as a gradual slowdown of the P waves, as they propagate through a previously stimulated area. Using a simple geometrical analysis of the spatial locations of the distortions in direct S-wave arrivals, we can estimate the half-lengths of the induced fractures, which range from 50-75% of the distance between the perforated well and monitoring well. Furthermore, we show that the propagation disturbances originate from the middle of the stimulated area. Other diffracted signals, notably from frac plugs, are clearly visible in the data. We report the first large-scale utilization of Distributed Acoustic Sensing records of guided waves. Their potential for high-resolution imaging and inversion of subsurface properties before and after hydraulic stimulation opens new possibilities for the use of seismology in optimizing production from unconventional reservoirs. We hope our findings will ignite such a new area of applied seismic imaging.

Full waveform inversion by model extension using a model-space multi-scale approach
Guillaume Barnier and Ettore Biondi
Full waveform inversion by model extension (FWIME) coupled with a modelspace multi-scale approach has the potential to become a robust acoustic-velocity model-building algorithm. It combines the robustness of wave-equation migration velocity analysis (MVA) with the accuracy and resolution of full waveform inversion (FWI). It mitigates the presence of local minima within the conventional FWI objective function by creating improved descent-paths towards the optimal solution. Its consistent and concise mathematical formulation paired with an automatized implementation makes it simple to apply and thus more accessible to a broad range of non-expert users. We test it on two numerical examples to show its ability to recover accurate solutions from cycle-skipped data dominated by (1) reflected events on the Marmousi2 model, and (2) refracted events on the North Sea region of the BP 2004 model.

Elastic-parameter estimation by combining full-waveform inversion by model extension and target-oriented elastic inversion
Ettore Biondi and Guillaume Barnier
We combine two inversion techniques to achieve an accurate wave-equation-based-elastic-parameter estimation workflow using pressure data. We first apply fullwaveform inversion by model extension (FWIME), a robust model-building technique, which provides an accurate migration velocity so that flat angle-domain common-image gathers (ADCIGs) can be obtained. Secondly, we employ the retrieved migration velocity to perform a redatuming technique based on an extended least-squares migration process, which allows the reconstruction of elastic pressure data reflected from a target area. These reconstructed data are finally employed within an elastic full-waveform inversion (FWI) procedure to estimate the elastic parameters of the target area. This approach requires a fraction of the computational cost of inverting the entire surface pressure data. We demonstrate the efficacy of this new workflow on elastic pressure data recorded on the Marmousi2 model and where the goal is the estimation of the elastic parameters of a gas reservoir.

Convexity and Scalability of Wavefield Reconstruction Inversion
Stuart Farris
We demonstrate a wave equation based inverse scheme, Wavefield Reconstruction Inversion (WRI), that alters the objective function of Full Waveform Inversion (FWI) by adding a regularization term that enforces a given wave equation to a degree defined by a chosen balancing weight. We illustrate that, by adjusting this wave equation balancing term, we can create a convex objective function while also remaining feasible for 3-dimensional velocity inversions at industrial scale through the use of gradient-based solutions. Our approach is compared to the original method, which uses matrix factorization, and we verify that both methods can avoid the local minima of the FWI objective function.

Tomographic Waveform Inversion
Julio Oliva Frigerio and Biondo Biondi
In this work we propose a waveform inversion formulation that overcomes the major problems of the currently available algorithms in the same class. Our formulation is intuitive and simple to implement. Moreover, the algorithm associated with this formulation is efficient and commercially feasible.

Scaling up machine learning projects: Automated hyperparameter tuning using Bayesian optimization
Fantine Huot, Biondo Biondi, and Gregory Beroza
Implementing machine learning algorithms frequently involves careful tuning of hyperparameters. Unfortunately, this tuning often requires expert experience, rules of thumb, or sometimes brute-force search. Therefore, there is a great appeal to automate the hyperparameter search to optimize the performance of a given learning algorithm to the problem at hand. Herein, we present a modular code base for managing hyperparameter tuning. We consider the hyperparameter tuning problem through the framework of Bayesian optimization, in which a machine learning model's performance is modeled as a sample from a Gaussian process. We demonstrate our methodology through the field data example of tectonic tremor detection and show that the resulting neural network successfully detects tremor events even in low signal-to-noise settings.

Focusing unfocused faults with deep learning and residual migration
Joseph Jennings, Robert Clapp and Biondo Biondi
We present a novel, computationally-efficient approach to seismic image refocusing that relies on prestack Stolt residual depth migration and a deep convolutional neural network (CNN). We generate many residually focused images via prestack Stolt residual migration which are then provided as input to a CNN that selects the optimally focused regions of these images. From these selected images, a refocused image of the subsurface can be reconstructed that will be better suited for tasks such as automatic geologic feature detection. We compare our approach to an existing semblance-based approach and show that our approach is more robust to a lack of subsurface illumination.

Comparison between DAS and geophones -downhole microseismic monitoring of the FORGE geothermal experiment
Ariel Lellouch, Nathaniel J. Lindsey, William L. Ellsworth and Biondo Biondi
We compare the performance of a downhole Distributed Acoustic Sensing (DAS) fiber-optic array with that of conventional geophones. The downhole collocated arrays are part of the FORGE Geothermal experiment, where stimulation of the rock volume in an Enhanced Geothermal System causes microseismic events. The DAS acquisition system yields a 1-m resolution data with 2000 samples/s for the entire length of the well, spanning to a depth of 985 m from the surface. Whereas single DAS channels are substantially noisier than geophones at the same location, their large number and spatial coherency allow for the application of effective array processing techniques. We follow a complete workflow for the fiber-optic array: velocity model building, event detection, event location, and magnitude estimation. Estimated velocity models agree well with sonic logging in a nearby well and map a granitic contact accurately. Detection performance is somewhat worse than geophones and yields a magnitude completeness of -1.4 compared to -1.7 for geophones. Using a single vertical fiber array, we cannot retrieve the azimuth of the events relative to the well. However, we can very accurately estimate their depth and horizontal distance from the array. Magnitude estimation with DAS approaches geophone results to within a standard deviation of M = 0.12. The DAS processing results outperform a regional and local surface array, consolidated with a shallow borehole sensor. Thanks to its cost-effectiveness, robustness and ability to be deployed along an active well, we claim that DAS holds vast potential for long-term monitoring of geothermal fields.

City-scale dark fiber DAS measurements of infrastructure use during the COVID-19 pandemic
Nathaniel J. Lindsey, Siyuan Yuan, Ariel Lellouch, Lucia Gualtieri, Thomas Lecocq, Biondo Biondi
Throughout the recent COVID-19 pandemic when government officials around the world ordered citizens to quarantine inside their homes, real-time measurements about the use of roads, hospitals, grocery stores, and other public infrastructure became vital to accurately forecast viral infection rates and inform future government decisions. Although mobile phone locations provide some information about community-level activity, dense distributed geophysical sensing of ground motions across a city are more complete and also natively anonymous. In this paper, we demonstrate how  fiber-optic Distributed Acoustic Sensing (DAS) connected to a telecommunication cable beneath Palo Alto, CA captured seismic and geodetic signals produced by vehicles during the COVID-19 pandemic outbreak and subsequent quarantine. We utilize DAS strain measurements of roadbed deformation caused by local cars and trucks in an automatic template matching detection algorithm to count the number of vehicles traveling per day over a two-month period around the timing of the San Francisco Bay Area shelter-in-place order. Using a segment of the optical fiber near a major grocery store on Sand Hill Road we find a 50% decrease in vehicle count immediately following the order, but data from near Stanford Hospital showed a far more subtle change due to on-going hospital activities. We compare the information derived from DAS measurements to other quarantine response metrics and find a strong correlation with the relative changes reported by Google and Apple using mobile phone data.

Elastic Full Waveform Inversion of Guided Waves Recorded by DAS in a Shale Reservoir
Milad Bader, Ariel Lellouch, Robert G. Clapp, and Biondo Biondi
Unconventional shale reservoirs can constitute a waveguide for elastic waves excited by perforation shots and recorded by a fiber-optic cable deployed along the well. Thanks to the Distributed Acoustic Sensing measurement, guided waves are recorded with high temporal and spatial resolution. We investigate the application of elastic full waveform inversion to these records, and its ability to characterize small heterogeneities. We show that this inversion is capable of retrieving thin layering within the reservoir as well as horizontally localized heterogeneities, representative of open fractures and faults. In the recorded data, such heterogeneities may appear as a decrease in seismic velocities or a forward/backward scattering.

Denoising Low Frequencies using Expanded Prediction-Error Filters
Milad Bader, Robert Clapp and Biondo Biondi
We use prediction-error filters to attenuate random and coherent noise contaminating low-frequency data. We estimate the filters from the high-frequency component, assuming it has a higher signal-to-noise ratio than the low-frequency component. The axes dilation in the time-space domain compresses the filter spectrum towards the low frequencies and wavenumbers. We cast the low-frequency denoising as a minimization problem, where the expanded filter is the signal predictor. To retain the simplicity of stationary prediction-error filters while adapting to non-stationary dip content, we interpolate filters estimated in non-overlapping patches. We use our method to denoise synthetic shot gathers from the Marmousi model and attenuate shear energy on OBN field data set.

Seismic data interpolation using a POCS-guided deep image prior
Min Jun Park, Joseph Jennings, Bob Clapp, and Biondo Biondi
We present an algorithm for seismic data interpolation that combines the use of a deep image prior (DIP) and projection onto convex sets (POCS). Deep image priors form part of an optimization problem in which they reparameterize the interpolated data as the output of a convolutional network. While they are able to provide accurate reconstructions of seismic data without the need for any training data, they tend to suffer when large gaps are present in the missing data. We observe significant improvements in the reconstructed data when a POCS regularization term is introduced to the DIP. We demonstrate the improvements of our approach on both synthetic and field data.

One-way full-waveform inversion by frequency-domain model extension
Rustam Akhmadiev, Biondo Biondi and Robert Clapp
We pose the problem of full-waveform inversion with model extension in the frequency domain using one-way wave extrapolation operators. This type of extension inevitably leads to the complex-valued model parameters. To take this fact into account, we modify the wave propagation operator and its linearization accordingly using the Wirtinger calculus for complex-valued functions and its derivatives. We continue by presenting the expressions for the modified FWI gradients. Finally, we verify the derivations by applying the extended full-waveform inversion for complex-valued model on a synthetic example.

Modeling of seismic residuals using Born scattering from a time dependent velocity perturbation
Rahul Sarkar, and Biondo Biondi
A common strategy used in extended full waveform inversion is the use of an extended modeling operator that is able to fit the residuals, for an appropriate extended model. Extended models along subsurface offsets and along time-lags have been proposed previously, and demonstrated to work well in an extended inversion framework. We propose a new form of time extension where the extension is performed along the propagation time direction. The main difference of this extension from the existing time-lag extension is that the secondary source can simply be computed as a point wise multiplication, without needing to perform any convolutions. Using simple 2D numerical examples, we explore the modeling capabilities of such an extension in the acoustic regime.

Near-surface Characterization Using a Roadside Distributed Acoustic Sensing Array
Siyuan Yuan, Ariel Lellouch, Robert G. Clapp and Biondo Biondi
Thanks to the broadband nature of the Distributed Acoustic Sensing (DAS) measurement, a roadside section of the Stanford DAS-2 array can record seismic signals from various sources. For example, it measures the earth’s quasi-static deformation caused by the weight of cars (<0.8 Hz) as well as Rayleigh waves induced by earthquakes (<3 Hz) and by dynamic car-road interactions (3-20 Hz). We directly utilize the excited surface waves for shallow shear-wave velocity inversion. Rayleigh waves induced by passing cars have a consistent fundamental mode and a noisier first mode. By stacking dispersion images of 33 passing cars, we obtain stable dispersion images. The frequency range of the fundamental mode can be extended by adding the low-frequency earthquake-induced Rayleigh waves. Thanks to the extended frequency range, we can achieve better depth coverage and resolution for shear-wave velocity inversion. In order to assure clear separation from Love waves and aligning apparent and true phase velocities, we choose an earthquake that is approximately in line with the array. The inverted models match those obtained by a conventional geophone survey, performed using active sources by a geotechnical service company contracted by Stanford University, from the surface until about 50 meters. In order to automate the VS inversion process, we introduce a new objective function that avoids manual dispersion curve picking. We construct a 2-D VS profile by performing independent 1-D inversions at multiple locations along the fiber. From the low-frequency quasi-static deformation recordings, we also invert for a single Poisson’s ratio at each location along the fiber. We observe spatial heterogeneity of both VS and Poisson’s ratio profiles. Our approach is dramatically cheaper than ambient field interferometry and reliable estimates can be obtained more frequently as no lengthy cross-correlations are required.