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Modeling and inversion

Building pore pressure and rock physics guides to constrain anisotropic waveform inversion [SRC]
Huy Le, Anshuman Pradhan, Nader Dutta, Biondo Biondi, Tapan Mukerji, and Stewart A. Levin
We developed a workflow that combines various sources of information, such as geomechanics, well logs, basin history, and diagenesis, to model pore pressure-velocity relation based on rock physics principles. Our workflow produces velocity templates, which can be used as constraints in any anisotropic waveform inversion process. We apply our workflow to a data set from the Gulf of Mexico. We study the diagenesis of shale, particularly, smectite-illite reaction. From well logs, we build models for velocity-porosity and density-overburden relations. Thermal history is approximated from available Bottom Hole Temperature (BHT) data and depositional history is inferred from interpreted horizons. We use mud weight data to calibrate our pore pressure-velocity transformation. A number of different pore pressure gradient scenarios result in different velocity profiles or templates. Combining with mud weight data, these templates provide bound constraints to waveform inversion. The integration and calibration of many sources of data in our workflow ensure the resulting velocity model is geologically feasible physically plausible.
Waveform inversion of multicomponent blended data with polarization filters [SRC]
Joseph Jennings, Biondo Biondi, Robert G. Clapp, and Shuki Ronen
We present a new algorithm for directly imaging blended data via waveform inversion. The algorithm makes use of the directional information contained within muticomponent blended data by introducing polarization filters at each iteration. We show that with the introduction of these polarization filters, the waveform inversion results contain significantly fewer artifacts than those obtained with conventional waveform inversion of blended data.
Synthesis, processing, and migration of a 2D data from the Gulf of Mexico [SRC]
Huy Le, Stewart A. Levin, and Robert G. Clapp
As a step toward applying our anisotropic waveform inversion methodology developed and presented in previous reports, we synthesized a 2D seismic data set from a 3D cross-shooting data acquired offshore Gulf of Mexico. The data's cross-shooting geometry poses a challenge to 2D processing and migration. Since the source lines and receiver lines are perpendicular, out-of-plane events could degrade image quality. Additionally, there are a number of salt bodies in the data area, which, at some locations, rise up to sea bottom with steep flanks causing imaging problems with short-offset data. We migrated the resulting 2D data with an isotropic velocity. Despite all the limitations, we were able to image reflectors down to four kilometers depth. However, segments of the salt bodies' boundaries could hardly be traced due to low signal to noise ratio in deeper portions of the data.


Classification of wave modes extracted from passive data at Moere Vest [SRC]
Jason P. Chang and Biondo Biondi
By performing multi-component seismic interferometry on passive seismic data from the Moere Vest ocean-bottom node survey, we observe three distinct wave modes from the resulting virtual source gathers: Scholte waves, guided acoustic waves, and critical refractions. Scholte waves are characterized by their dispersive nature, very low frequency content (below 0.5 Hz), slow propagation velocity (500-700 m/s), and relative clarity in the vertical-vertical correlations. Guided acoustic waves trapped between the sea surface and sea bottom are characterized by their dispersive nature, group velocity of approximately 1500 m/s, and relative clarity in the hydrophone-hydrophone correlations. Critical refractions in the vertical-vertical correlations are characterized by their non-dispersive linear moveout and high propagation velocity (4000-5000 m/s). Comparison of these events to critical refractions off the top of basalt in vertical-component receiver gathers from active data reveals similar arrival times and moveout velocities. To enhance the clarity of these refractions, we create virtual super-source gathers for both vertical-vertical and vertical-radial correlations. We find that the critical refraction arrives later in the vertical-radial gathers than in the vertical-vertical gathers, which is also observed in vertical- and radial-component receiver gathers from active data. Forward wavefield propagation suggests that these critical refractions could be generated by low-frequency Scholte waves scattering off the horst-and-graben structure of the top of basalt. Overall, these results lay the foundation for passive subsurface imaging using wave modes beyond interface waves.
Time-lapse changes in ambient noise interferometry and dispersion analysis at the Stanford DAS Array [SRC]
Eileen Martin and Biondo Biondi
Ambient noise interferometry allows us to extract signals that mimick active source surveys without the cost and permitting requirements of a true active survey for near-surface imaging. In many environments, seismic velocities in the near surface may change seasonally, reacting to temperature and saturation, and even subsidence. We analyze time-lapse changes in virtual source response estimates extracted from ambient seismic noise recorded at the Stanford Distributed Acoustic Sensing Array (SDASA-1) between September 2016 and August 2017. Our analysis indicates that only one week of noise is enough to yield stable virtual source response estimates when compared with the estimate from the same full month of noise. The virtual source response estimates we extract throughout one year appear to show an improvement in signal-to-noise-ratio during months when the ground is more saturated. The Rayleigh wave dispersion images show velocities in the same range as active source geotechnical surveys (Thomas et al., 2013). Further, their Rayleigh wave dispersion images suggest changes in near surface velocity tied to those saturation changes. But these apparent velocity changes are also accompanied by power spectrum changes, so further investigation into the ambient noise field is needed before these velocity shifts can be interpereted with certainty.
Sensitivity analysis of distributed acoustic sensing arrays [SRC]
Eileen R. Martin, Biondo Biondi, Gabriel Fabien-Ouellet, and Robert G. Clapp
Distributed acoustic sensing (DAS) measures the average axial strain (strain rate) along a subset of a fiber optic cable, as opposed to the particle displacement (velocity) at a particular small point sensor. In shifting from measuring a vector field to a tensor field, DAS effectively increases the directional sensitivity of measurements of every type of seismic wave when compared to single-component geophones. This switch from vector to tensor quantities leads to a plausible explanation for sign-flips between orthogonal channels seen during some S-wave and surface-wave events in our recordings of earthquakes. We show this through theoretical analysis of planar Rayleigh, Love, P- and S-waves over both infinitesimally small and realistic gauge lengths. We extend the analysis of individual sensor detection of surface waves to inter-receiver cross-correlations of these detections showing even more directionally-dependent sensitivity trends than individual sensors.
Catalog of Northern California earthquakes recorded by DAS [SRC]
Siyuan Yuan, Eileen R. Martin, Jason P. Chang, Steve Cole, and Biondo Biondi
We catalogued more than 800 seismic events recorded at Stanford Distributed Acoustic Sensing Array (SDASA-1) from September 2016 to August 2017. The catalog is being continuously updated as new events occur. We have developed open-source interfaces so that users can query the database and extract earthquake recordings efficiently. Pulling the data via the interfaces, we performed signal repeatability analyses for blasts at nearby Permanente Quarry and nearby weak earthquakes from Ladera and Felt Lake. We found that geographically close events could have repeatable signals in terms of S-wave arrivals and surface-wave phase changes. With rich event recordings, the catalog enables us to extract and characterize distant and weak events, which we will use to quantify our array's sensitivity and study event detection and noise attenuation algorithms in future work.

Velocity estimation

Modified Tomographic Full Waveform Inversion using the variable projection method [SRC]
Guillaume Barnier, Ettore Biondi, and Biondo Biondi
We propose a modified tomographic full waveform inversion (TFWI) optimization scheme that allows us to avoid the original nested-loop approach and reduce the number of inversion parameters. We use the variable projection method to solve for the linear component of the inverse problem. We show the convergence to the correct velocity model on a synthetic dataset lacking frequencies below 10 Hz.
Can full waveform inversion image all scales of the velocity model? [SRC]
Biondo Biondi, Ettore Biondi, and Guillaume Barnier
Full waveform inversion (FWI) reconstructs the velocity model based on the information contained in reflections and diving waves, in addition to a tomographic component that contributes when reflected events are not well focused. The wavenumber-domain analysis of the contributions of each of these elements shows that they are mostly complementary. The illumination patterns in the wavenumber domain are scaled by the data frequency, further expanding the wavenumber-domain region that is illuminated by reflections data. When cycle-skipping is not occurring, FWI applied to wideband data should be able to reconstruct all the scales of the velocity model. Our tests on synthetic datasets support this analysis; however, they also show that FWI applied to wideband data (2.5-30 Hz) with long offsets (up to 9km) is not able to reconstruct a small region of the wavenumber plane close to the origin. For our specific examples, the poorly reconstructed scales have vertical wavelengths longer than 400 m and horizontal wavelengths between 150 m and 600 m.
Representing salt bodies with radial basis functions [SRC]
Taylor Dahlke
In this work we show how radial basis functions can be used to sparsely represent the implicit surface used to represent salt bodies. We show that this methodology is effective even when the model parameter reduction is roughly 2% of the original model size. This is important to making shape optimization effective for 3D velocity models. When the Hessian of a modified FWI objective function is used for shape optimization, we must invert the Newton system for the search direction. When using iterative methods like conjugate gradient for this, the reduction in parameters improves the speed and stability of this inversion.
Using the Hessian of a radial basis formulation for level set inversion [SRC]
Taylor Dahlke, Biondo Biondi, and Robert Clapp
Salt bodies provide complex imaging challenges because of their geometry and reflective properties due to the (often) sharp contrast of wave speed between salt and sediments. Level sets are a useful tool to define and refine discrete boundaries of salt using an implicit surface to describe them. Furthermore, we can represent the implicit surface using a sparse representation based on radial basis functions (RBFs). Using linear operators to map from RBF parameter space to wave speed space, we develop a new formulation of the Full Waveform Inversion (FWI) objective function, and then take the second derivative to get a formulation of its Hessian. We can then solve the corresponding Newton system to find a search direction. The sparse representation offered by the RBF scheme means that a truncated iterative inversion is intrinsically faster due to the large reduction in model parameters that we need to solve for. We demonstrate the efficacy of using the Gauss-Newton approximation of this Hessian, as well as explore the limitations of using the full Hessian formulation for finding a search direction.
Implementing Wave-Equation Migration Velocity Analysis Within Linearized Waveform Inversion with Velocity Updating: Considerations and Challenges [SRC]
Alejandro Cabrales-Vargas
Wave-Equation Migration Velocity Analysis is one of the fundamental processes for performing Linearized Waveform Inversion with Velocity Updating, and also the most computationally intense. We recently proposed the implementation of the former by means of employing Random Boundary Conditions for storage alleviation, at the cost of performing extra wavefield propagations. We show the result of this implementation. However, the scattered source wavefield and the scattered receiver wavefield depend on the direction of propagation of the corresponding wavefields that originate them. Therefore, the source wavefield must propagate forward in time when scattering. Likewise, the receiver wavefield must propagate backward in time when scattering. This restriction leads to the fact that we require twelve propagations per iteration plus one, instead of the eight iterations plus one that we had initially expected. Additionally, Random Boundary Conditions can introduce random noise that could potentially harm the inversion result if they are not properly implemented.
A 2D Helmholtz equation solver library based on C++ and SuiteSparse [SRC]
Rahul Sarkar and Biondo Biondi
We developed a 2D Helmholtz equation solver library in C++ based on the SuiteSparse library for sparse linear algebra. The solver library was successfully tested for correctness in this paper by running a suite of simple 2D examples. We first used the library to solve the Helmholtz equation in a homogenous medium for different frequency bands. The test was then repeated for an inhomogenous two layer medium, for the same frequency bands. We also performed Born linearization tests with the code and demonstrated that the error is quadratic in the magnitude of the velocity perturbation, in agreement with the theoretical prediction. Finally we performed extended linearized Born forward modeling tests using the Helmholtz code to demonstrate its use in Tomographic Full Waveform Inversion (TFWI) applications.

Deconvolution and signal processing

Permian Basin High Density Land Acquisition Experimental Dataset [SRC]
Stuart Farris and Rustam Akhmadiev
An experimental, high density land survey has been made available to the Stanford Exploration Project. Herein describes an overview of the dataset including survey parameters and employed wavelet removal techniques. Wave modes are identified in prelimanry shot gathers and possible research directions are discussed.
Multichannel data: separating independent causes [SRC]
Jon Claerbout and Kaiwen Wang
The algorithm for blind deconvolution of a nonstationary time series of vector components (i.e. multichannel) has three stages: (1) Linear-least-squares multichannel prediction-error filtering, (2) Cholesky factorization of the zero-lag covariance matrix, and (3) Rotation angle scanning for maximum sparsity.
Short Note: PEF swapping positive with negative lags [SRC]
Stewart A. Levin
Jon Claerbout recently hypothesized that inserting negative filter lags opposite a gap in positive filter lags could produce interesting and useful filters. Here I prove that, indeed, such filters lead to controlled autocorrelation width and may provide properties beyond those of conventional gapped deconvolution.
Short Note: Time variable prediction without mathematics [SRC]
Jon Claerbout
With almost no math, a quick trick leads to l1 norm nonstationary decon.


C++11 non-linear solver [SRC]
Robert G. Clapp, Stuart Farris, Taylor Dahlke, and Eileen Martin
Inverse problems such as velocity estimation from reflection/refraction data are inherently non-linear. We developed a library to address non-linear problems using C++11. We demonstrate the library on two simple examples.
SEPlib CMake update [SRC]
Stewart A. Levin
SEPlib is now built with CMake. This report covers the futher changes made to the source tree in order to fully support Linux and Mac OS X platforms.

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