Browsing by Subject "Seismic modeling"
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Item High-order finite element methods for seismic wave propagation(2009-05) De Basabe Delgado, Jonás de Dios, 1975-; Sen, Mrinal K.; Wheeler, Mary F. (Mary Fanett)Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves in geophysical models. These methods o er a better control on the accuracy and more geometrical exibility than the Finite Di erence methods that have been traditionally used for the generation of synthetic seismograms. However, the success of these methods has outpaced their analytic validation. The accuracy of the FEMs used for seismic wave propagation is unknown in most cases and therefore the simulation parameters in numerical experiments are determined by empirical rules. I focus on two methods that are particularly suited for seismic modeling: the Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin Method (IP-DGM). The goals of this research are to investigate the grid dispersion and stability of SEM and IP-DGM, to implement these methods and to apply them to subsurface models to obtain synthetic seismograms. In order to analyze the grid dispersion and stability, I use the von Neumann method (plane wave analysis) to obtain a generalized eigenvalue problem. I show that the eigenvalues are related to the grid dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to the number of degrees of freedom inside one element. The grid dispersion results indicate that SEM of degree greater than 4 is isotropic and has a very low dispersion. Similar dispersion properties are observed for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes per wavelength to be used. On the other hand, the stability analysis shows that, in the elastic case, the size of the time step required in IP-DGM is approximately 6 times smaller than that of SEM. The results from the analysis are con rmed by numerical experiments performed using an implementation of these methods. The methods are tested using two benchmarks: Lamb's problems and the SEG/EAGE salt dome model.Item Seismic modeling and imaging in complex media using low-rank approximation(2016-12) Sun, Junzhe; Fomel, Sergey B.; Biros, George; Ghattas, Omar; Sen, Mrinal K.; Zhang, YuSeismic imaging in geologically complex areas, such as sub-salt or attenuating areas, has been one of the greatest challenges in hydrocarbon exploration. Increasing the fidelity and resolution of subsurface images will lead to a better understanding of geological and geomechanical properties in these areas of interest. Wavefield time extrapolation is the kernel of wave-equation-based seismic imaging algorithms, known as reverse-time migration. In exploration seismology, traditional ways for solving wave equations mainly include finite-difference and pseudo-spectral methods, which in turn involve finite-difference approximation of spatial or temporal derivatives. These approximations may lead to dispersion artifacts as well as numerical instability, therefore imposing a strict limit on the sampling intervals in space or time. This dissertation aims at developing a general framework for wave extrapolation based on fast application of Fourier integral operators (FIOs) derived from the analytical solutions to wave equations. The proposed methods are theoretically immune to dispersion artifacts and numerical instability, and are therefore desirable for applications to seismic imaging. First, I derive a one-step acoustic wave extrapolation operator based on the analytical solution to the acoustic wave equation. The proposed operator can incorporate anisotropic phase velocity, angle-dependent absorbing boundary conditions and further improvements in phase accuracy. I also investigate the numerical stability of the method using both theoretical derivations and numerical tests. Second, to model wave propagation in attenuating media, I use a visco-acoustic dispersion relation based on a constant-Q wave equation with decoupled fractional Laplacians, which allows for separable control of amplitude loss and velocity dispersion. The proposed formulation enables accurate reverse-time migration with attenuation compensation. Third, to further improve numerical stability of Q-compensation, I introduce stable Q-compensation operators based on amplitude spectrum scaling and smooth division. Next, for applications to least-squares RTM (LSRTM) and full-waveform inversion, I derive the adjoint operator of the low-rank one-step wave extrapolation method using the theory of non-stationary filtering. To improve the convergence rate of LSRTM in attenuating media, I propose Q-compensated LSRTM by replacing the adjoint operator in LSRTM with Q-compensated RTM. Finally, I extend the low-rank one-step wave extrapolation method to general elastic anisotropic media. Using the idea of eigenvalue decomposition and matrix exponential, I study the relationship between wave propagation and wave-mode decomposition. To handle the case of strong heterogeneity, I incorporate gradients of stiffnesses in wave extrapolation. Numerous synthetic examples in both 2D and 3D are used to test the practical application and accuracy of the proposed approaches.Item Seismic modeling and imaging with Fourier method : numerical analyses and parallel implementation strategies(2009-12) Chu, Chunlei, 1977-; Stoffa, Paul L., 1948-Our knowledge of elastic wave propagation in general heterogeneous media with complex geological structures comes principally from numerical simulations. In this dissertation, I demonstrate through rigorous theoretical analyses and comprehensive numerical experiments that the Fourier method is a suitable method of choice for large scale 3D seismic modeling and imaging problems, due to its high accuracy and computational efficiency. The most attractive feature of the Fourier method is its ability to produce highly accurate solutions on relatively coarser grids, compared with other numerical methods for solving wave equations. To further advance the Fourier method, I identify two aspects of the method to focus on in this work, i.e., its implementation on modern clusters of computers and efficient high-order time stepping schemes. I propose two new parallel algorithms to improve the efficiency of the Fourier method on distributed memory systems using MPI. The first algorithm employs non-blocking all-to-all communications to optimize the conventional parallel Fourier modeling workflows by overlapping communication with computation. With a carefully designed communication-computation overlapping mechanism, a large amount of communication overhead can be concealed when implementing different kinds of wave equations. The second algorithm combines the advantages of both the Fourier method and the finite difference method by using convolutional high-order finite difference operators to evaluate the spatial derivatives in the decomposed direction. The high-order convolutional finite difference method guarantees a satisfactory accuracy and provides the flexibility of using non-blocking point-to-point communications for efficient interprocessor data exchange and the possibility of overlapping communication and computation. As a result, this hybrid method achieves an optimized balance between numerical accuracy and computational efficiency. To improve the overall accuracy of time domain Fourier simulations, I propose a family of new high-order time stepping schemes, based on a novel algorithm for designing time integration operators, to reduce temporal derivative discretization errors in a cost-effective fashion. I explore the pseudo-analytical method and propose high-order formulations to further improve its accuracy and ability to deal with spatial heterogeneities. I also extend the pseudo-analytical method to solve the variable-density acoustic and elastic wave equations. I thoroughly examine the finite difference method by conducting complete numerical dispersion and stability analyses. I comprehensively compare the finite difference method with the Fourier method and provide a series of detailed benchmarking tests of these two methods under a number of different simulation configurations. The Fourier method outperforms the finite difference method, in terms of both accuracy and efficiency, for both the theoretical studies and the numerical experiments, which provides solid evidence that the Fourier method is a superior scheme for large scale seismic modeling and imaging problems.Item Sensitivity of seismic response to variations in the Woodford Shale, Delaware Basin, West Texas(2010-12) Shan, Na; Tatham, R. H. (Robert H.), 1943-; Sen, Mrinal K.; Spikes, Kyle T.; Ruppel, Stephen C.; Ogiesoba, Osareni C.The Woodford Shale is an important unconventional oil and gas resource. It can act as a source rock, seal and reservoir, and may have significant elastic anisotropy, which would greatly affect seismic response. Understanding how anisotropy may affect the seismic response of the Woodford Shale is important in processing and interpreting surface reflection seismic data. The objective of this study is to identify the differences between isotropic and anisotropic seismic responses in the Woodford Shale, and to understand how these anisotropy parameters and physical properties influence the resultant synthetic seismograms. I divide the Woodford Shale into three different units based on the data from the Pioneer Reliance Triple Crown #1 (RTC #1) borehole, which includes density, gamma ray, resistivity, sonic, dipole sonic logs, part of imaging (FMI) logs, elemental capture spectroscopy (ECS) and X-ray diffraction (XRD) data from core samples. Different elastic parameters based on the well log data are used as input models to generate synthetic seismograms. I use a vertical impulsive source, which generates P-P, P-SV and SV-SV waves, and three component receivers for synthetic modeling. Sensitivity study is performed by assuming different anisotropic scenarios in the Woodford Shale, including vertical transverse isotropy (VTI), horizontal transverse isotropy (HTI) and orthorhombic anisotropy. Through the simulation, I demonstrate that there are notable differences in the seismic response between isotropic and anisotropic models. Three different types of elastic waves, i.e., P-P, P-SV and SV-SV waves respond differently to anisotropy parameter changes. Results suggest that multicomponent data might be useful in analyzing the anisotropy for the surface seismic data. Results also indicate the sensitivity offset range might be helpful in determining the location for prestack seismic amplitude analysis. All these findings demonstrate the potentially useful sensitivity parameters to the seismic data. The paucity of data resources limits the evaluation of the anisotropy in the Woodford. However, the seismic modeling with different type of anisotropy assumptions leads to understand what type of anisotropy and how this anisotropy affects the change of seismic data.