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Imaging and inversion

Time-lapse inverse scattering theory[SRC]
Musa Maharramov and Biondo Biondi
“Time-lapse inverse scattering theory” that we introduce in this paper focuses on recovering changes in physical models without accurate knowledge of model backgrounds. More specifically, we study the feasibility of recovering low and high-wavenumber components of model perturbation using the traditional Born and Rytov scattering approximations, and establish a connection between the Rytov approximation and phase-only full-waveform inversion (FWI). We provide a theoretical justification for applying regularized simultaneous time-lapse FWI to problems of applied seismology. We demonstrate the method’s sensitivity to realistic production effects in seismic data, and its stability with respect to inaccurate starting models.
Dissection of the full-waveform inversion Hessian [SRC]
Biondo Biondi, Ettore Biondi, Musa Maharramov and Yinbin Ma
We analyze the FWI Hessian and determine that is the combination of two well-understood operators in seismic imaging: 1) the Gauss-Newton Hessian and 2) a differential WEMVA operator. We illustrate this insight with several numerical examples of applying and inverting the different components of the Hessian operator to images originating from the waveform inversion of a simple synthetic dataset. We then discuss possible applications of the theory to making FWI more robust with respect to incorrect starting models, and to speeding-up the application of target-oriented fully non-linear seismic inversion.
SEPLib nonlinear solver library – Manual [SRC]
Ali Almomin, Ettore Biondi, Yinbin Ma, Kaixi Ruan, JosephJennings, Robert Clapp, Musa Maharramov and Alejandro Cabrales-Vargas
We created an SEPLib nonlinear solver library that serves as the infrastructure for many inversion implementations. The library targets gradient-based inversion schemes with a focus on ease of use, flexibility, reusability and expandability. This was achieved by taking advantage of modern language features in object-oriented programing. This manual is divided in three parts. First, we detail what the library components are and explain all the abstract parts. Second, we show how to use each component of the library. Third, we show examples of different inversion implementations.

Modeling and attenuation

Simultaneous inversion of velocity and Q using wave-equation migration analysis [SRC]
Yi Shen
I develop a method for simultaneous inversion of velocity and Q models. This method poses the simultaneous estimation problem as an optimization problem that seeks optimum velocity and Q models by minimizing user-defined image residuals. Numerical tests on a modified SEAM model with two gas clouds demonstrates the necessity of using such simultaneous inversion, when the existent velocity and Q models are inaccurate. The results show that this simultaneous inversion method is able to retrieve both velocity and Q models, as well as correct and compensate the distorted migrated image caused by inaccurate velocities and Q models.
Two-way wave-equation operators for non-constant density acoustic isotropic media [SRC]
Ettore Biondi and Ossian O’Reilly
We derive two-way wave-equation operators in the time domain for isotropic non-constant density media with a finite-difference scheme. We present the chains of linear operators necessary for non-linear modeling, linearized modeling, and non-constant density migration. We also show that radiation patterns obtained from linearized modeling agree with theoretical results. With these correct forward-adjoint operators, multi-parameter full waveform inversion for non-constant density media can be pursued.
Reverse-time migration: Comparing three numerical solvers [SRC]
Alejandro Cabrales-Vargas
I compare the results of three numerical schemes for seismic modeling and reverse-time migration: the rapid expansion method, the Lax-Wendroff method, and the pseudo-analytical method. The rapid expansion method uses coarse time steps without developing instabilities, but it can present frequency dispersion when using coarse grids. Moreover, its implementation is difficult. The Lax-Wendroff method can avoid such limitations at the expense of time step refinement, thereby more Laplacian computations. Both methods allow the representation of the space derivatives either in the spatial domain (finite differences method) or in the Fourier domain (pseudospectral method). The pseudo-analytical method offers an accurate solution and easy implementation, but it is restricted to the Fourier domain.
Using Mie scattering theory to debubble seismic airguns [SRC]
Joseph Jennings and Shuki Ronen
Airgun signatures contain a main pulse and then a few bubble oscliations. A process called designature or debubble such signatures into a broad band pulse. We prefer to do as much as possible with deterministic designature and leave as little as possible to statistical deconvolution. Air gun manufacturers provide a library of signatures under various conditions. However, the conditions are not well known. Near field hyderophones record the airguns. However, the near field hydrophones record all airguns in the array, and their data are contaminated by waves that do not radiate to the far field. Current methods that estimate the contribution of each airgun to the far field require inverting for a large number of parameters. In this report, we propose another a deterministic deconvolution method based on theory from Mie scattering. Our method is less sensitive to near field noise and requires only seven parameters. Instead of a linear inversion with thousands of unknowns, we have a non linear inversion with a small number of unknowns. We have encouraging results that demonstrate the potential of using Mie scattering theory for deterministic debubbling.

Velocity estimation

Balancing amplitude and phase in TFWI [SRC]
Ali Almomin and Biondo Biondi
Tomographic Full Waveform Inversion (TFWI) provides a robust and accurate method to invert the seismic data by simultaneously inverting all scales of the model using both amplitude and phase information. However, one shortcoming of TFWI is the large number of iteration required to achieve accurate results due to its slow convergence. In this report, I analyze the source of its slow convergence and propose two modifications to mitigate the problem. First by modifying the formulation of the regularization term to focus more on the phase information, and second by using an alternative enhancing operator that is less sensitive to the amplitudes in the extended model. Then, I test the modified TFWI on the marmousi 2 synthetic model. The results show a significant improvement in the convergence rate.
Full-waveform inversion based on nonlinear conjugate gradient method, Gauss-Newton method and full Newton method [SRC]
Yinbin Ma, Musa Maharramov, Biondo Biondi
Full-waveform inversion (FWI) generates a high-resolution subsurface model. Robust local minimization algorithms are required for FWI because the objective function is highly nonlinear. In this paper we compare the nonlinear conjugate gradient method, Gauss-Newton method and full Newton method for FWI. These methods use the gradient of objective function and application of Hessian on a model perturbation vector, which can be calculated efficiently with the adjoint-state methods. Numerical results suggest Newton-type methods resolve fine structure faster than the nonlinear conjugate gradient method in terms of number of wave propagation.

Case studies

Processing of continuous data at Apache Forties for seismic interferometry [SRC]
Jason P. Chang
I process continuous data from the Apache Forties data set for use in studies relating to passive seismic imaging. Spectrograms from multiple nodes indicate the presence of strong, naturally-occurring seismic energy at frequencies below 1 Hz, as well as the presence of seismic energy above 4 Hz that originates from the oil platform. After ignoring times of active seismic shooting, I perform passive seismic interferometry on over 2 days of hydrophone and vertical geophone data. For frequencies between 1.00 and 1.25 Hz, there are indications of Scholte-wave energy. However, the expected wavelengths (approximately 150 m/s) at these frequencies are likely comparable to the aperture of the array (approximately 400 m), which compromises the reliability of the arrivals. For frequencies between 3.00 and 7.00 Hz, there are no clear indications of interface waves. Asymmetry of seismic energy in the virtual source gathers suggests that platform vibrations dominate the ambient noise field at high frequencies.
Overview of the Apache Forties data set [SRC]
Gustavo Alves
I present a dataset acquired in 2010 by Apache North Sea and made available to the Stanford Exploration Project (SEP). The dataset is composed of three surveys acquired with four-component ocean-bottom nodes placed under production platforms in a close pattern. Active shooting was performed in a spiral geometry around the platforms at short offsets. The goal of this acquisition was to identify gas pockets at shallow depths and possible geo-hazards. This acquistion configuration can be advantageous for multi- component data processing such as elastic Reverse Time Migration (RTM).

Signal processing

Industrial scale high-performance adaptive filtering with PEF applications [SRC]
Kaixi Ruan, Joseph Jennings, Ettore Biondi, Robert G. Clapp, Stewart A. Levin, and Jon Claerbout
In most areas of SEP research, neither data nor models are truly stationary. As a consequence, global fitting, regridding, and inversion rarely approach the ideal of independent, identically-distributed residuals. Here we design and develop parallel multidimensional adaptive filter routines parsimonious in both memory and computation, suitable for industrial scale applications. We applied them to examples of three classes of time and space variable adaptive Prediction Error Filters (PEF) applications: (1) blind decon, (2) filling gaps in data, and (3) making random realizations of data; and then, outline other areas where these tools will have a wide application.
Stable reorientation for the Forties dataset [SRC]
Stewart A. Levin and Jason P. Chang
Traces from the nodal receivers used in the Forties platform undershoot require rotation to provide consistent multicomponent orientation. A quick quality control check on input data that were within just a few degrees of the desired North-East-Vertical orientation found vector magnitude changes approaching 25%. Inspecting the code in the existing module that applied nodal reorientation, the presence of an IF test against an arbitrary choice of epsilon, explicit unit vector renormalization, and angle transformations that their author questioned spurred us to derive and apply a stable and robust alternative that avoided those issues.
Fortran calling C: Clock drift correction [SRC]
Stewart A. Levin
Seafloor nodal clock drift is a skew that is taken as distributed linearly across the time between GPS synchronizations. When it came time to correct such skew in a nodal field dataset, I wanted to use the well-tested, accurate 8 point sinc resampler in the Colorado Schools of Mines Seismic Unix (SU) package while staying within the existing Fortran 2003 code I was modifying. In this short note I illustrate how I used the BIND features of modern Fortran to accomplish this.
Anatomy of a header sort [SRC]
Stewart A. Levin and Yinbin Ma
Routine trace sorting at SEP is basically a grid sort. When faced with spiral shooting around sea-bottom nodes, defining an offset grid was nonintuitive. Leveraging the venerable Unix disk-based sort program, we were able to complement our Sort3d with a gridless header SortByHdrs program capable of handling a couple billion traces if needed. Here we highlight some important subtleties in this approach.

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