SEP168 -- TABLE OF CONTENTS |

Permanent dense seismic arrays are costly to install and maintain using traditional point sensors. Fiber optic Distributed Acoustic Sensing (DAS) arrays show promise as a low-cost alternative that can be left in place with thousands of sensors run by a single power source. However, the trenching process used in some surface DAS arrays can be costly and logistically prohibitive in some cases. To mitigate these issues, we designed an experiment to investigate the potential for fibers in slim holes underground, with an eye towards repurposing existing telecommunications infrastructure. Our experiment has three primary goals: ambient noise interferometry, earthquake detection, and recording active seismic shooting. In August 2016, 2.4 km of fiber optic cable was deployed in a two-dimensional array in existing telecommunications conduits underneath the Stanford University campus. This array has been continuously recording since Sep. 3, 2016, and is planned to continue for at least one year in the current configuration, known as the ``Stanford DAS Array-1'' or SDASA-1.

Earthquakes analysis using data recorded by the Stanford DAS Array [SRC]

We analyze the data recorded by the ``Stanford DAS Array'' for 6 seismic events cataloged in the USGS online database. Two of these events are man made (blasts at a nearby quarry), and 4 are earthquakes spanning a range from a local event that occurred less than 4 km from the array to a large quake offshore Cape Mendocino in North California. The data from two seismometers installed on Stanford campus at Jasper Ridge help to validate and interpret the data recorded by our DAS array. The analysis of the two quarry-blasts demonstrates that both kinematics and waveforms are recorded by the DAS array with excellent repeatability. We show that the time of the first-break of P-wave arrivals can be reliably measured from the DAS array, notwithstanding the loose coupling of the fiber-optic cable with the ground, and the known limitations of DAS to record events with particle motion orthogonal to the fiber cable. P-wave waveforms are more challenging to analyze because of the complexity of the wavefield, probably caused by strong local scattering. All the events we analyzed show that kinematics of S and surface waves can be reliably measured from the data recorded by our DAS array. Because of noise and uncertain coupling, it is more challenging to assess the quality of the waveform shapes and amplitudes than the kinematics. We show that that DAS recording of propagating waves with particle displacement orthogonal to the propagation direction are subject to a phase rotation that is dependent on the fiber-cable direction. When we apply an approximate correction for this phase rotation the spatial coherency of S-wave and surface-wave arrivals substantially improves.

Ambient Noise Interferometry on Two-Dimensional DAS Arrays [SRC]

When using three-component geophones for ambient noise tomography, the process of extracting Rayleigh or Love waves requires first rotating data into radial and transverse components, respectively, before cross-correlation. When a two-dimensional distributed acoustic sensing (DAS) array is used, a single straight line can easily have Rayleigh waves extracted via cross-correlation within the line. However, only using straight lines significanly reduces our ray coverage, so we aim to garner meaninful information from all pairs of channels in the array. In practice, cross-correlation and cross-coherence of the data recorded at many pairs of channels in the Stanford DAS Array-1 (SDASA-1) yield coherence waveforms. But, we can not rotate every data point into radial and transverse components, so special treatment must be given to understand the coherent waveforms generated when non-colinear fibers' data are cross-correlated. This is the first extension of ambient noise theory given these geometric constraints.

The search for P-waves at Forties [SRC]

Results from seismic interferometry at Apache Forties indicates the presence of P-wave events hidden in the ambient seismic noise field. I use phase-weighted stacking rather than linear stacking of correlations from quiet time periods to enhance this apparent P-wave energy. From source gathers with a virtual source located near the platform, there are three apparent events in the hydrophone-hydrophone and vertical-vertical geophone correlations between 40 and 80 Hz. From a tau-p transform of these gathers, there are events in the hydrophone component propagating at 1500 m/s and 3000 m/s with 0 s intercept time, while in the vertical-geophone component there are two events propagating at 3000 m/s with different intercept times. To determine the direction in which these events are traveling through the array, I look at source gathers along approximate lines of receivers in the north-south, east-west, and northeast-southwest directions. Using linear moveout with velocity estimated from the tau-p transform, I find that the slower event in the hydrophone correlations appears to be moving across the array from generally northeast to southwest, while the faster events in both component correlations appear to propagate from the platform. Based on the unlikelihood of interface waves traveling at such high velocities, I perform passive fathometry processing on ambient noise records in an attempt to recover body-wave energy. Preliminary results of passive fathometry appear to retrieve the water-column multiple along with some possible reflection events.

Comparing whales to marine seismic sources: low frequency sound generation by fin whales [SRC]

Seismic surveys have been shown to cause behavioral changes in whales and have the potential to cause temporary or permanent physical harm. Whale calls have a similar frequency content to seismic airguns, and hence communication between animals is likely to be disrupted by exploration activities. We demonstrate that whale calls recorded by tags attached to fin whales have comparable amplitude to a marine vibroseis observed at a distance of 100 m and a seismic airgun at 1000 m. In addition, we discuss how whales may generate sound through resonance of their lungs in an analogous fashion to how seismic airguns generate sound through the resonance of the bubble of air ejected from the gun.

The extension of full waveform inversion (FWI) into elastic models can potentially address the limitations of acoustic FWI due to amplitude versus offset effects. I present results of applying an elastic FWI workflow to ocean-bottom nodes data. I show the steps used to pre-process the data and create an initial elastic model for inversion. Then, I apply these inputs into the inversion workflow and show how elastic inversion without pre-conditioning can be dominated by artifacts. Finally, I apply weighting operators in both residual space and image space and present results for the inverted model with data in the range of 2 to 5 Hz.

Preconditioned elastic full waveform inversion using approximated Hessian matrix [SRC]

We describe a simple way of estimating the elements of the Hessian matrix for elastic full waveform inversion (FWI) problems by applying it to spikes in the model space. We explain how to use this estimated matrix to precondition an elastic isotropic FWI problem and show results from a simple one layer model and a more complex subsurface elastic earth. We observe that already a main diagonal approximation is able to increase the inverse problem's convergence rate. This gradient preconditioning allows us to obtain a meaningful inversion result for the deeper part of the model in fewer iterations.

Reciprocity in elastic multi-component data [SRC]

Reciprocity for source and receiver pairs has been routinely adopted in seismic processing to mitigate poor receiver density and improve computational costs. But while its implementation is straightforward for acoustic data, the correct combination of source and receiver components in elastic, multi-component data, can be challenging. We derive the Green's functions for the direct and reciprocal data for a source-receiver pair and show synthetic results demonstrating their equivalence. We also show how an explosive source can be represented as a combination of normal stresses or particle velocities. Finally, we calculate the respective wavelets for each formulation both analytically and by linear inversion.

Phase Only Full Waveform Inversion of Elastic Data Using Acoustic Engine [SRC]

Modeling the elastic earth with acoustic assumptions leads to large amplitude mismatches between observed and predicted data. Matching both amplitude and phase information between elastic field data and acoustic modeled data is more difficult than only matching phase information. Therefore, we attempt to perform acoustic full waveform inversion (FWI) with an objective function designed to favor minimizing phase variation between observed and predicted data.

Level sets are subsets of a domain that have the same value for a certain function. We can use them as a tool to update discrete boundaries of homogeneous bodies, which makes them particularly useful for updating salt models. Often, salt takes complicated geometries which causes a lack of direct illumination, as well as interactions between boundaries. Deriving a formulation of the Hessian which takes into account the level set parametrization should allow for better search directions than simpler methods. We find that by linearizing the velocity model perturbation with respect to the underlying background and level set parameters, we can derive a Hessian application operator suitable for a linear inversion scheme to get an improved search direction for updating the salt boundaries.

Tomographic Full Waveform Inversion for imaging under complex overburden [SRC]

Tomographic Full Waveform Inversion (TFWI) is a waveform inversion technique that uses an extended modeling operator, allowing the predicted data to be in phase with the observed data, even when the starting velocity model is inaccurate. While being robust against cycle-skipping issues inherent to Full Waveform Inversion (FWI), it is still poorly understood whether this technique can be efficient in a complex overburden environment. And if so, which type of model extension is the most adequate to predict and capture the complexity of the waveforms such as the ones reflecting off a top-salt boundary. We first present three synthetic examples that illustrate the issues encountered in complex overburden environments. Then, we review the theoretical framework of TFWI and present our code that allows for space and time-lag extensions. Finally, we test for various model extensions to understand which combination manages to better capture the complexity of a wavefield that is reflected from a top-salt boundary.

An efficient time-lapse full waveform inversion by saving the wavefield at boundaries around the reservoir [SRC]

The need to propagate the source and receiver wavefield over the whole subsurface model is a challenge for time-lapse full-waveform inversion (FWI). We show that by saving the wavefield at the boundary enclosing the reservoir, we can estimate the wavefield around the reservoir after model perturbation. The perturbed wavefield can predict synthetic data at the surface through the pre-computed Green's function. We eliminate the need to propagate the wavefield through the overburden area and therefore accelerate the FWI procedure. Random phase-encoding can be incorporated into our proposed workflow and has the potential to further reduce the computational cost.

Our progress towards linearized waveform inversion with velocity updating (LWIVU) [SRC]

Linearized waveform inversion with velocity updating demands the cooperation of Born modeling and wave-equation migration velocity analysis, both forward modeling operators and their adjoints. We successfully tested both of them for passing both the dot-product test and the linearization test. We previously re-organized the wave-propagation codes to operate with random boundary conditions, thus achieving more efficient RAM usage. Assuming the correctness of the operators after the tests, we use the Born modeling pair to illustrate how to pre-compute the Gauss-Newton Hessian by means of point-spread functions. We have now the elements to assemble a robust code for linearized waveform inversion with velocity updating.

Understanding the difference between full Newton and Gauss-Newton approximation of the full waveform inversion Hessian: a short note [SRC]

We continue the mixed theoretical-computational study of the difference between full Newton and Gauss-Newton approximation of the Hessian matrix in the context of full waveform inversion (FWI) started in the SEP report 160. We also continue to use an acoustic isotropic wave equation approximation during our discussion. We analyze the connection of the residual-dependent component of the full Hessian with the physical double scattering described by the wave equation. We explain how to avoid inversion instabilities of the full Newton Hessian when this matrix is not positive definitive. With the help of a simple two-perturbation model we study the advantages of full Newton compared to the Gauss-Newton approximation.

Incorporating optimal transport in Tomographic Full Waveform Inversion : Theory [SRC]

In recent years, a great deal of work has gone into devising optimization strategies that are more robust to cycle skipping as compared to the conventional Full Waveform Inversion (FWI) objective function. Tomographic full waveform inversion (TFWI) is one such technique that involves the use of a non-physical extension of the whole velocity model and an extended modeling operator that is better capable of modeling the observed data. Inversion algorithms based on this concept have been shown to converge to reasonable models on field data, but with slow convergence rate. Another interesting direction of research that has emerged in this field is based on the use of optimal transport objective functions. These formulations have also been shown to be capable of converging to correct models from relatively inaccurate starting models, leveraging the fact that objective functions based on optimal transport distances are much less susceptible to local minima compared to their L

In the imaging and inversion of long-offset seismic data, it is neccessary to incorporate anisotropy to produce accurate images and subsurface models. Building an anisotropic model is a challenging inverse problem because of the large number of unknown parameters. To reduce the number of unknown parameters, it is common to assume a simple physics, for example, using the acoustic approximation or constant density. This leads to a mismatch in amplitude between the modeled data and the observed data. Estimation of the source wavelet by directly minimizing the inversion's objective function can help to mitigate this mismatch. Adding to the challenge of anisotropic model building is the fact that anisotropic parameters are often of different types, such as velocity, stiffness, or Thomsen's parameters. Consequently, one needs to account for their crosstalk and sensitivity. We follow an established workflow that stochastically simulates these parameters based on rock physics and compaction models. This simulation provides information about the model covariance, which can be used to reduce parameter crosstalk.

GENESIS dataset: 3D initial VTI model for time-lapse reverse time migration [SRC]

We estimate a 3D vertical transverse isotropy (VTI) model for the GENESIS data set based on stable inverse Dix formula. We reprocess the time-lapse seismic data set to attenuate the spatial aliasing problem. The common shot gathers and the common receiver gathers are created to enhance the subsurface illumination because the surveys were conducted with the towed streamers. Time-lapse reverse-time migration (RTM) to the GENESIS data set, with the isotropic velocity model, suggests observable velocity change near the reservoir and the overburden area as a result of production. Time-lapse RTM with the VTI model has also been studied.

We model a land survey data line

Source signature deconvolution of marine seismic data using deterministic modeling of the bubble signature [SRC]

Seismic airguns are not impulsive sources and hence marine seismic data must be designatured before interpretation. We demonstrate how deterministic modeling of the airgun signature can be used to designature field data. A heuristic approach is used to generalize the single airgun model to describe the signature of a small array of closely spaced guns where the bubbles from the different guns coalesce. The simulated signatures are used to designature data from a near-surface survey around a production rig. The results compare favorably to prediction-error filtering and the importance of using the correct source signature is illustrated.

We develop a new inversion scheme for linearized waveform-inversion (LWI) of blended data. We introduce polarization filters, computed from the independently modeled multicomponent data, which filter the blended data at each iteration of the inversion. We compare an approach of polarization filtering based on the Singular Value Decomposition (SVD) to our own new approach in which we extend the application of prediction-error filtering (PEF) to multicomponent data. We show that estimating PEFs using all data components provides the best deblended data which should provide much better imaging during the LWI process.

Fitting while whitening nonstationary residuals [SRC]

While fitting a model to given data, I simultaneously whiten nonstationary residuals in both data space and model space. Last year we learned, in the presence of nonstationary noise in multidimensional space, how to solve three classes of problems: (1) deconvolution, (2) missing data, and (3) simulating data with the nonstationary spectrum of given data. This year I extend that class of problems to a general model

Subsurface model inversion: pushing the limits of resolution [SRC]

Detecting and inverting the imprint of changing subsurface elastic parameters on seismic data lies at the heart of time-lapse seismic imaging for reservoir monitoring. In this work we demonstrate that the recently proposed technique of simultaneous time-lapse full-waveform inversion with a model-difference regularization can be used to extract high-resolution information on magnitude and location of subsurface velocity and stress anomalies, potentially providing valuable input for reservoir monitoring and assessment of geohazards.

Near-surface imaging with ambient noise has grown into an increasingly common tool over the past decade thanks to the virtual source method. However, if non-ideal noise sources are present, experts must manually analyze the noise to look for any issues they suspect, then design filters to remove these non-ideal noises. Up until now, the deployment and maintenance of the receiver array was the primary cost, but this is changing with advancements in Distributed Acoustic Sensing (DAS), an emerging technology that repurposes a fiber optic cable as a series of strain sensors. On the Stanford campus we have shown that we can record seismic waves with fiber optic cables sitting loosely in existing telecommunications conduits. As we look forward at the possibility of easily plugging into unused fibers in telecom bundles on-demand, it is clear that manual selection of non-ideal noise sources is the next bottleneck. Herein we show a variety of methods, mixing traditional signal processing and machine learning, to automatically assist geophysicists in analyzing the ambient noise recorded and selecting non-ideal noises. We demonstrate that we can identify different types of noise using clustering algorithms and that template matching can be used for detecting specific events.

Higher Order Principal Component Analysis for Identifying AVO Anomalies [SRC]

We use principal component analysis (PCA) to identify amplitude versus offset (AVO) anomalies in a legacy 2D seismic data set. The traditional methods of AVO analysis rely on inversion techniques that require simplified models of the subsurface. Simple models of the earth make assumptions that may lead to incorrect hydrocarbon identification. By making no assumptions about the earth model or how waves propagate in the model, PCA could provide a more robust technique for finding AVO anomalies

Based on the SEPlib non-linear solver library described previously, we implement an out-of-core Python-based generic solver for linear/non-linear inverse problems. We closely follow the object-oriented structure of the previous library and add new features in order to handle any programming language describing the application of user-defined operators. Our out-of-core feature addresses many treating memory-intensive inverse problems frequently encountered in geophysical applications. We demonstrate the new solver capability with simple linear problems and a non-linear acoustic isotropic full-waveform inversion (FWI) example.

make, schmake: CMake [SRC]

This year SEP has switched from GNU

Facilitating code distribution: Docker and Generic IO [SRC]

Disseminating research through computational software is of growing importance in academia. The growth of cloud computing and object-oriented programming has led to the development of new paradigms. We take advantage of two of these paradigms, containers and generalized IO, as a new way to distribute. software to SEP sponsors.

SEP168 -- TABLE OF CONTENTS |

2013-9-13