Download or read book Seismic Modeling and Imaging with the Complete Wave Equation written by Ralph Phillip Bording and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Seismic Modeling and Imaging with the Complete Wave Equation written by Ralph Phillip Bording and published by . This book was released on 1997 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic modeling and imaging of the earth's subsurface are complex and difficult computational tasks. The authors present general numerical methods based on the complete wave equation for solving these important seismic exploration problems.

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 Numerical Modeling of Seismic Wave Propagation written by Johan O. A. Robertsson and published by SEG Books. This book was released on 2012 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: The decades following SEG's 1990 volume on numerical modeling showed a step change in the application and use of full wave equation modeling methods enabled by the increase in computational power. Full waveform inversion, reverse time migration, and 3D elastic finite-difference synthetic data generation are examples. A searchable CD is included.

Download or read book Seismic Modeling and Imaging of Realistic Earth Models Using New Full wave Phase shift Approach written by Nelka Chithrani Wijesinghe and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic modeling is a valuable tool for seismic interpretation of oil and gas reservoirs and is an essential part of seismic inversion algorithms. In this thesis, we have developed and verified the new full-wave phase-shift (FWPS) approach for solving seismic modeling and imaging problems. FWPS approach is based on a new way to generalize the "one-way" acoustic wave equation using a phase-shift structure. Our approach solves the full acoustic wave equation by separating the problem into an equation consisting of two coupled first-order partial differential equations for wave propagation in depth, in which the initial waves are purely one-way, but solving the equations for downgoing initial waves and then for upgoing initial waves, retaining the full two-way nature of the Helmholtz equation. This produces a complete set of linearly independent solutions, that is used to construct the correct, causal full wave solution that includes waves propagating both up and down. The initial conditions for the modeling problem are generated by solving the Lippmann-Schwinger integral equation formally, in a non-iterative fashion and converting the problem into a Volterra integral equation of the second kind. Reflection and wraparound from boundaries are effectively dealt with employing correct absorbing boundary conditions. We validate the new FWPS method by applying it to forward modeling and inversion. Time snapshot results are given for standard velocity models, as well as a realistic earth velocity model. We compare the realistic earth velocity model results from new FWPS approach to those obtained by finite differences (FD), with correct scattering boundary conditions imposed. We have stabilized our results by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing evanescent waves, while retaining all of the propagating waves and exponentially decaying evanescent waves. Our approach is easily parallelized to achieve approximate N2 scaling, where N is the number of coupled equations. We discuss the parallelization techniques used to optimize the algorithm and improve the computational cost. We show the presence of evanescent waves in a realistic earth velocity model by comparing the reflection matrix both with and without decaying evanescent waves.

Download or read book Full Seismic Waveform Modelling and Inversion written by Andreas Fichtner and published by Springer Science & Business Media. This book was released on 2010-11-16 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent progress in numerical methods and computer science allows us today to simulate the propagation of seismic waves through realistically heterogeneous Earth models with unprecedented accuracy. Full waveform tomography is a tomographic technique that takes advantage of numerical solutions of the elastic wave equation. The accuracy of the numerical solutions and the exploitation of complete waveform information result in tomographic images that are both more realistic and better resolved. This book develops and describes state of the art methodologies covering all aspects of full waveform tomography including methods for the numerical solution of the elastic wave equation, the adjoint method, the design of objective functionals and optimisation schemes. It provides a variety of case studies on all scales from local to global based on a large number of examples involving real data. It is a comprehensive reference on full waveform tomography for advanced students, researchers and professionals.

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.

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 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 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 Full Wave equation Based Passive Seismic Imaging and Multispectral Seismic Geometric Attributes written by Bin Lyu and published by . This book was released on 2020 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 True amplitude Imaging written by Jörg Schleicher and published by SEG Books. This book was released on 2007 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a pictorial presentation of the basic principles of Kirchhoff-type imaging and proceeding to a comprehensive treatment of its kinematic and dynamic aspects, this book is a valuable addition for anyone interested in the theory and practices of seismic data processing for imaging and parameter estimation with all its attendant processes.

Download or read book Seismic Waves written by Masaki Kanao and published by BoD – Books on Demand. This book was released on 2012-01-25 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni.

Download or read book Seismic Modeling Inversion and Imaging in Attenuating Media written by Tieyuan Zhu and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate seismic exploration demands sophisticated seismic techniques that can be applied to any complex geological setting, for example, attenuative and anisotropic media. This dissertation addresses attenuation problems in seismic exploration: how to model wave propagation in attenuating media, how to invert attenuation property of subsurface reliably, and how to mitigate attenuation effects in seismic images. The key innovations are (1) developing a novel viscoacoustic/elastic constant-Q wave equation that is practically efficient and accurately simulates the constant-Q attenuation behavior, (2) an iterative joint inversion framework for different geophysical datasets (e.g., attenuation data) to reduce the uncertainties of independent inversion results, (3) developing an Q-compensated reverse-time migration approach to compensate for attenuation effects (dispersion and amplitude loss) in seismic images. In the first part, I derive a novel viscoacoustic wave equation based on constant-Q theory. I investigate the accuracy of this wave equation. I show its application in a heterogeneous medium. Testing shows this model to be more computationally efficient than the most efficient single standard linear solid modeling. More importantly, this viscoacoustic equation separates attenuation and dispersion operators that allow us to mitigate both amplitude attenuation and phase dispersion effects in seismic imaging. This equation is the key modeling engine for seismic migration. Due to the data quality of the seismic waveform and the strong nonlinearity of the attenuation problem, I choose a joint inversion algorithm to invert for the attenuation coefficient. I develop an iterative joint inversion approach where one model domain acts as a constraint for inversion of the other, and the roles of the two domains are iteratively switched. This joint inversion stabilizes the inversion and ensures that results are geologically plausible. I apply the method to estimate Vp and the attenuation coefficient in field data examples. In the third part, I present a method to improve the image resolution by mitigating attenuation effects. I discuss the feasibility of time-reverse modeling in attenuating media using numerical experiments for 1D and 2D situations. I develop a Q-compensated reverse-time migration imaging approach (referred as Q-RTM). I illustrate this approach using different synthetic models. Numerical results further verify that this Q-RTM approach can effectively improve the resolution and quality of image, particularly beneath high-attenuation zones. To demonstrate the suitability, I apply the Q-RTM method to field data from the King Mountain site in west Texas. In the future, this method could readily be applied to other field datasets to improve the image resolution in high attenuation areas.

Download or read book Modeling and Imaging Elastic Waves in Heterogeneous Media written by Kuang He and published by . This book was released on 2010 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Resolution High Fidelity Seismic Imaging and Parameter Estimation for Geological Structure and Material Characterization written by Xiao-Bi Xie Ru-Shan Wu (Thorne Lay) and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this project, we develop new theories and methods for multi-domain one-way wave-equation based propagators, and apply these techniques to seismic modeling, seismic imaging, seismic illumination and model parameter estimation in 3D complex environments. The major progress of this project includes: (1) The development of the dual-domain wave propagators. We continue to improve the one-way wave-equation based propagators. Our target is making propagators capable of handling more realistic velocity models. A wide-angle propagator for transversely isotropic media with vertically symmetric axis (VTI) has been developed for P-wave modeling and imaging. The resulting propagator is accurate for large velocity perturbations and wide propagation angles. The thin-slab propagator for one-way elastic-wave propagation is further improved. With the introduction of complex velocities, the quality factors Qp and Qs have been incorporated into the thin-slab propagator. The resulting viscoelastic thin-slab propagator can handle elastic-wave propagation in models with intrinsic attenuations. We apply this method to complex models for AVO modeling, random media characterization and frequency-dependent reflectivity simulation. (2) Exploring the Information in the Local Angle Domain. Traditionally, the local angle information can only be extracted using the ray-based method. We develop a wave-equation based technique to process the local angle domain information. The approach can avoid the singularity problem usually linked to the high-frequency asymptotic method. We successfully apply this technique to seismic illumination and the resulting method provides a practical tool for three-dimensional full-volume illumination analysis in complex structures. The directional illumination also provides information for angle-domain imaging corrections. (3) Elastic-Wave Imaging. We develop a multicomponent elastic migration method. The application of the multicomponent one-way elastic propagator and the wide-angle correction preserve more dynamic information carried by the elastic waves. The vector imaging condition solves the polarization problem of converted wave imaging. Both P-P and P-S images can be calculated. We also use converted waves to improve the image of steep sub-salt structures. The synthetic data for the SEG/EAGE salt model are migrated with a generalized screen algorithm and for the converted PSS-wave path. All the sub-salt faults are properly imaged.