Download or read book Seismic Modeling and Imaging with the Fourier Method written by Chunlei Chu and published by . This book was released on 2009 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Application of Fourier Finite Differences and Lowrank Approximation Method for Seismic Modeling and Subsalt Imaging written by Xiaolei Song and published by . This book was released on 2012 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, subsalt oil and gas exploration is drawing more and more attention from the hydrocarbon industry. Hydrocarbon exploitation requires detailed geolog- ical information beneath the surface. Seismic imaging is a powerful tool employed by the hydrocarbon industry to provide subsurface characterization and monitoring information. Traditional wave-equation migration algorithms are based on the one- way-in-depth propagation using the scalar wave equation. These algorithms focus on downward continuing the upcoming waves. However, it is still really difficult for con- ventional seismic imaging methods, which have dip limitations, to get a correct image for the edge and shape of the salt body and the corresponding subsalt structure. The dip limitation problem in seismic imaging can be solved completely by switching to Reverse-Time Migration (RTM). Unlike old methods, which deal with the one-way wave equation, RTM propagator is two-way and, as a result, it no longer imposes dip limitations on the image. It can also handle complex waveforms, including pris-matic waves. Therefore it is a powerful tool for subsalt imaging. RTM involves wave extrapolation forward and backward in time. In order to accurately and efficiently extrapolate the wavefield in heterogeneous media, I develop three novel methods for seismic wave modeling in both isotropic and tilted transversely isotropic (TTI) me- dia. These methods overcome the space-wavenumber mixed-domain problem when solving the acoustic two-way wave equation. The first method involves cascading a Fourier Transform operator and a finite difference (FD) operator to form a chain operator: Fourier Finite Differences (FFD). The second method is lowrank finite dif- ferences (LFD), whose FD schemes are derived from the lowrank approximation of the mixed-domain operator and are represented using adapted coefficients. The third method is lowrank Fourier finite differences (LFFD), which use LFD to improve the accuracy of TTI FFD mothod. The first method, FFD, may have an advantage in efficiency, because it uses only one pair of multidimensional forward and inverse FFTs (fast Fourier transforms) per time step. The second method, LFD, as an accurate FD method, is free of FFTs and in return more suitable for massively parallel computing. It can also be applied to the FFD method to reduce the dispersion in TTI case, which results in the third method, LFFD. LFD and LFFD are based on lowrank approx- imation which is a general method to handle mixed-domain operators and can be easily applied to more complicated mixed-domain operators. I show pseudo-acoustic modeling in orthorhombic media by lowrank approximation as an example.

Download or read book Seismic Migration Imaging of Acoustic Energy by Wave Field Extrapolation written by A. J. Berkhout and published by Elsevier. This book was released on 2012-12-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic Migration: Imaging of Acoustic Energy by Wave Field Extrapolation, Second Edition, Volume A: Theoretical Aspects covers the theoretical aspects of seismic migration techniques. This volume is divided into 11 chapters that consider the concept of propagation and scattering matrices. This book begins with a presentation of a selection of concepts and properties of seismic migration from vector analysis. These topics are followed by considerable chapters on the mathematical aspects of migration, including discrete spectral analysis, two-dimensional Fourier transforms, and wave theory. The subsequent chapters describe the derivation of the Kirchhoff integral for upward traveling wave field and wave field extrapolation for downward traveling source waves and upward traveling reflected waves. These chapters also propose a matrix formulation to represent single seismic record and multi-record data sets, along with different modeling algorithms. A chapter examines inverse wave field extrapolation, in which the medium must be horizontally layered, the layers being homogeneous. The book ends with a summary and comparison of different approaches to seismic migration.

Download or read book Seismic Modeling and Imaging with the Complete Wave Equation written by Ralph Phillip Bording and published by SEG Books. This book was released on 1997 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic modelling and imaging of the earth's subsurface are complex and difficult computational tasks. The authors of this volume present general numerical methods based on the complete wave equation for solving these important seismic exploration problems.

Download or read book Seismic Migration written by A. J. Berkhout and published by Elsevier. This book was released on 2012-12-02 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic Migration: Imaging of Acoustic Energy by Wave Field Extrapolation derives the migration theory from first principles. This book also obtains a formulated forward modeling and migration theory by introducing the propagation matrices and the scattering matrix. The book starts by presenting the basic results from vector analysis, such as the scalar product, gradient, curl, and divergence. It also describes the theorem of Stokes, theorem of Gause and the Green’s theorem. The book also deals with discrete spectral analysis, two-dimensional Fourier theory and plane wave analysis. It also describes the wave theory, including the plane waves and k-f diagram, spherical waves, and cylindrical waves. This book explores the forward problem and the inward problem of the wave field extrapolation, as well as the modeling by wave field extrapolation. Furthermore, the book explains the migration in the wave number-frequency domain. It also includes the summation approach and finite-difference approach to migration, as well as a comparison between the different approaches to migration. Finally, the book offers the limits of lateral resolution as the last chapter.

Download or read book Seismic Modeling Imaging and Inversion in Viscoacoustic Media written by Jidong Yang and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: During wave propagation, seismic energy is dissipated by the geometrical spreading, heterogeneity scattering and lattice internal friction. The energy decay related to internal friction is known as intrinsic attenuation, which reflects the viscosity (anelastic) property of subsurface minerals and rocks. Particularly, the saturations of gas give rise to strong seismic intrinsic attenuation. Incorporating attenuation into seismic modeling, imaging and inversion enables accurate detection of hydrocarbon reservoir and characterization of fluid properties. To date, a number of wave equations have been developed to describe the intrinsic attenuation effects. For example, in the frequency-domain, the viscous behavior can be described using a complex-valued velocity. It explicitly incorporates the quality factor (Q) into the wave equation and therefore is easy to utilize to compensate attenuation effects in reverse-time migration (RTM) and full-waveform inversion (FWI). But its requirements for solving the Helmholtz equation include large computer memory cost, which is still challenging for largescale 3D models. On the other hand, the attenuation can be incorporated in the time-domain wave equation based upon the standard linear solid (SLS) theory. Since the dispersion and dissipation are coupled in the SLS, and the quality factor Q has to be transformed to stress and strain relaxation times, it is difficult to use in seismic imaging and inversion. Another popular time-domain wave equation is formulated based on constant-Q theory. Although this approach has the advantage that the dispersion and dissipation terms are decoupled, it is necessary to calculate a mixed-domain operator using complicated numerical solvers, such as the low-rank approximation. In this study, starting from the frequency-domain viscoacoustic wave equation, I first use a second-order polynomial to approximate the dispersion term, followed by a pseudo-differential operator to approximate the dissipation term. These two approximations make it possible to transform the frequency-domain equation into the time domain, and derive a new complexvalued viscoacoustic wave equation. The advantages of the new wave equation include: (1) the dispersion and dissipation effects are naturally separated, which can be used to compensate amplitude loss in seismic migration by reversing the sign of the dissipation term; (2) Q is explicitly incorporated into the wave equation, which makes it easy to directly derive the misfit gradient with respect to Q and estimate subsurface attenuation models using Q-FWI; and (3) this new viscoacoustic wave equation can be numerically solved using finite-difference time marching and a Fourier transform, which does not require mixed-domain solvers as required in the constant-Q method, and has lower memory cost than the frequency-domain approach. Based on the new complex-valued wave equation, I develop a viscoacoustic RTM workflow to correct the attenuation-associated dispersion and dissipation effects. A time-reversed wave equation is derived to extrapolate receiver-side wavefields, in which the sign of the dissipation term is reversed while the dispersion term remains unchanged. In wavefield extrapolation, both source and receiver wavefields are complex-valued and their real and imaginary parts satisfy the Hilbert transform. This analytic property helps to explicitly decompose up- and down-going waves. Then, a causal imaging condition, which crosscorrelates the down-going source-side wavefield and the up-going receiver-side wavefield, is utilized to suppress lowwavenumber artifacts in migrated images. Furthermore, with limited recording apertures, finite-frequency source functions, irregular subsurface illuminations, viscoacoustic RTM is still insufficient to produce satisfactory reflectivity images with high resolution and amplitude fidelity. By incorporating the complexvalued wave equation into a linear waveform inversion scheme, I develop a viscoacoustic least-squares reverse-time migration (LSRTM) scheme. Based on the Born approximation, I first linearize the wave equation and derive a viscoacoustic demigration operator. Then, using the Lagrange multiplier method, I derive the adjoint viscoacoustic wave equation and the corresponding sensitivity kernels. With the forward and adjoint operators, a linear inverse problem is formulated to estimate the subsurface reflectivity model. A total-variation regularization is introduced to enhance the robustness of the proposed viscoacoustic LSRTM, and a diagonal Hessian is used as a preconditioner to accelerate convergence. Traditional waveform inversion for attenuation is commonly based on the SLS wave equation, in which case the quality factor Q has to be converted to the stress and strain relaxation times. When using multiple attenuation mechanisms in the SLS method, it is difficult to directly estimate these relaxation time parameters. Based on the new time-domain complex-valued viscoacoustic wave equation, I present an FWI framework for simultaneously estimating subsurface P-wave velocity and attenuation distributions. Since Q is explicitly incorporated into the wave equation, I directly derive sensitivity kernels for P-wave velocity and attenuation using the adjoint-state method, and simultaneously estimate their distributions. By analyzing the Gauss-Newton Hessian, I observe strong inter-parameter crosstalk artifacts, especially the leakage from velocity to Q. I approximate the Hessian inverse using a preconditioned L-BFGS method in FWI, which significantly reduces inter-parameter crosstalk, and produces accurate velocity and attenuation models.

Download or read book Digital Imaging and Deconvolution written by Enders A. Robinson and published by SEG Books. This book was released on 2008 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering ideas and methods while concentrating on fundamentals, this book includes wave motion; digital imaging; digital filtering; visualization aspects of the seismic reflection method; sampling theory; the frequency spectrum; synthetic seismograms; wavelet processing; deconvolution; seismic attributes; phase rotation; and seismic attenuation.

Download or read book Practical Seismic Data Analysis written by Hua-Wei Zhou and published by Cambridge University Press. This book was released on 2014-01-23 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern introduction to seismic data processing in both exploration and global geophysics demonstrates practical applications through real data and tutorial examples. The underlying physics and mathematics of the various seismic analysis methods are presented, giving students an appreciation of their limitations and potential for creating models of the sub-surface. Designed for a one-semester course, this textbook discusses key techniques within the context of the world's ever increasing need for petroleum and mineral resources - equipping upper undergraduate and graduate students with the tools they need for a career in industry. Examples presented throughout the text allow students to compare different methods and can be demonstrated using the instructor's software of choice. Exercises at the end of sections enable students to check their understanding and put the theory into practice and are complemented by solutions for instructors and additional case study examples online to complete the learning package.

Download or read book Mathematics of Multidimensional Seismic Imaging Migration and Inversion written by N. Bleistein and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. This book presents the different seismic data processing methods, also known as seismic "migration," in a unified mathematical way. The book serves as a bridge between the applied math and geophysics communities by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophisticated geophysicist.

Download or read book Acoustical Imaging written by A.J. Berkhout and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Seismic Imaging Methods and Applications for Oil and Gas Exploration written by Yasir Bashir and published by Elsevier. This book was released on 2022-03-16 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic Imaging Methods and Application for Oil and Gas Exploration connects the legacy of field data processing and imaging with new research methods using diffractions and anisotropy in the field of geophysics. Topics covered include seismic data acquisition, seismic data processing, seismic wave modeling, high-resolution imaging, and anisotropic modeling and imaging. This book is a necessary resource for geophysicist working in the oil and gas and mineral exploration industries, as well as for students and academics in exploration geophysics. Provides detailed methods that are used in the industry, including advice on which methods to use in specific situations Compares classical methods with the latest technologies to improve practice and application in the real world Includes case studies for further explanation of methods described in the book

Download or read book Depth Imaging of Foothills Seismic Data written by Canadian Society of Exploration Geophysicists and published by [Calgary] : Canadian Society of Exploration Geophysicists. This book was released on 1999 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing exploration problems in complex overthrust environments and then developing practical solutions in terms of migration methods and applications, this book conveys heuristic descriptions of mathematical algorithms and provides case history applications from overthrust belts. Examples derived from model and real data sets are provided. This book evolved from a project of the Canadian Society of Exploration Geophysicists Superfund, a fund designed to support exploration geophysics research at Canadian universities. The project's purpose was to study the seismic depth imaging of complex geologic structures in the Canadian Foothills. This book is intended for seismic processors, interpreters, and researchers. It begins with a description of exploration problems in complex overthrust environments and then develops practical solutions in terms of migration methods and applications. The book conveys heuristic descriptions of mathematical algorithms and provides case-history applications from overthrust belts. In addition to conventional poststack and prestack depth-migration approaches, the book examines migration from topography and anisotropic migration methods while providing examples derived from model and real data sets. Because of the increasing interest in Foothills oil and gas exploration, the book should provide valuable information for practitioner and theoretician alike.

Download or read book Seismic Interferometry written by Gerard Thomas Schuster and published by Cambridge University Press. This book was released on 2009-05-14 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the theory and practice of seismic interferometry for academic researchers, oil industry professionals and advanced students.

Download or read book Theory of Seismic Imaging written by John A. Scales and published by Springer. This book was released on 1995-05-17 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic imaging methods are currently used to produce images of the Earth's subsurface properties at diverse length scales, from high-resolution, near-surface environmental studies for oil and gas exploration to long-period images of the entire planet. This book presents the physical and mathematical basis of imaging algorithms in the context of controlled-source reflection seismology. The approach taken is motivated by physical optics and theoretical seismology. The theory is constantly put into practice via a graded sequence of computer exercises using the widely available SU (Seismic Unix) software package.

Download or read book Fast Fourier Transform and Wavefront Approach for Seismic Modeling written by Dennis Chuan Ching Ling and published by . This book was released on 2008 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Modeling of Seismic Wave Propagation written by K. R. Kelly and published by SEG Books. This book was released on 1990 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Seismic Modeling and Imaging in Complex Media Using Low rank Approximation written by Junzhe Sun and published by . This book was released on 2016 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic 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.