Download or read book Finite difference Modeling of 3D Seismic Wave Propagation in High contrast Media written by and published by . This book was released on 2008 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Finite difference Modeling of Seismic Wave Propagation in Fractured Media written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Finite Difference Modelling of Earthquake Motions written by Peter Moczo and published by Cambridge University Press. This book was released on 2014-04-24 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.

Download or read book A Two Dimensional Finite difference Simulation of Seismic Wave Propagation in Elastic Media written by Jeih-San Liow and published by . This book was released on 1988 with total page 404 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 The Finite Difference Modelling of Earthquake Motions written by Peter Moczo and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.

Download or read book Simulation of Seismic Real and Virtual Data Using the 3d Finite difference Technique and Representation Theorem written by Xiujun Yang and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic modeling is a technique for simulating wave propagation through the subsurface. For a given geological model, seismic modeling allows us to generate snapshots of wave propagation and synthetic data. In my dissertation, for real seismic events I have chosen to implement the finite-difference modeling technique. When adequate discretization in space and time is possible, the finite-difference technique is by far one of the most accurate tools for simulating elastic-wave propagation through complex geological models. In recent years, a significant amount of work has been done in our group using 2D finite-difference modeling. For complex salt structures which exploration and pro- duction industries meet today, 2D finite-difference modeling is not sufficient to study subsalt imaging or the demultiple of subsalt models. That is why I have developed a 3D finite-difference modeling code. One of the key challenges that I have met in developing the 3D finite-difference code is to adapt the absorbing boundary conditions. Absorbing boundary conditions are needed to describe the infinite geological models by limited computing domain. I have validated the 3D finite-difference code by comparing its results with analytic solutions. I have used 3D finite-difference program to generate data corresponding to 3D complex model which describes salt and subsalt structures of Gulf of Mexico. The resulting data include reflections, diffractions and other scattering phenomena. I have also used finite-difference program in anisotropic context to show that we can effectively predict shear-wave splitting and triplication in the data. There are new sets of events that are not directly recorded in seismic data, they have been called virtual events. These events are turning to be as important as real events in modern data processing. Therefore we also have to learn how to model them. Unfortunately, they cannot yet be modeled directly from finite-difference. Here I will describe how to model these events by using cross correlation type representation theorem. As illustration of how important of virtual events for seismic data process- ing, I also described an internal multiple attenuation technique which utilized virtual events.

Download or read book Introduction to Modeling Seismic Wave Propagation by the Finite Difference Methods written by P. Moczo and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modeling of the Effects of Wave induced Fluid Motion on Seismic Velocity and Attenuation in Porous Rocks written by Yang Zhang (Ph. D.) and published by . This book was released on 2010 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we use the X-ray CT images of Berea sandstones to carry out the numerical study of the effects of wave-induced fluid motion on seismic velocity and attenuation in porous rocks. In numerical modeling, it is possible to control the factors and inputs that are hard to accomplish in laboratory measurements and isolate those of interest that have significant impact on the seismic responses; this can help in understanding the fundamental physics of seismic waves propagating in saturated porous rocks. The ultimate goal of computational rock physics is to supplement the traditional laboratory measurements, that are time consuming and costly, with cheaper numerical experiments that allow the parameter space to be explored more thoroughly. For this purpose, in this thesis we develop a computational method for time domain simulation of wave propagation in poroelastic medium. The medium is composed of an elastic matrix saturated with a Newtonian fluid. The method operates on a digitized representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid finite-difference scheme which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is incorporated and can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers. When applying the linear solver to compute the effective elastic properties of 3D digitized porous rocks, we find discrepancies between the numerical results and the laboratory measurements. The reason for such a problem is the loss of small features, such as cracks and micro-pores, in the digitized matrix of rocks during the imaging process of aggregation. A hybrid approach, combining the numerical computation 3 and the effective media theories, is developed to deduce the lost cracks from a limited number of laboratory measurements. This approach can recover the lost cracks and is capable of predicting the effective elastic properties of the rock matrix. Compared to the traditional inversion schemes based only on the effective media theories, this hybrid scheme has the advantage of utilizing the complex micro-structures of 3D digitized porous rocks that are resolved in the imaging process, and it helps limit the inversion space for crack distribution. In the study of the dynamic and low-frequency responses of saturated porous rocks, we employ the stress-strain calculation in numerical modeling so as to compute the velocities and attenuations of rock samples, the sizes of which are much smaller than the seismic wavelength of interest. For these cases, transmission measurement cannot be used. Realizing the significant contribution of small cracks to the total attenuation, we extend the hybrid approach by incorporating the modified squirt-flow model where a fluid with frequency-dependent bulk modulus is introduced. Therefore, attenuation due to viscous fluid in stiff pores, that are resolved in the imaging process, can be computed numerically. Attenuation due to viscous fluid in compliant pores can be determined by the modified squirt-flow model since we know the crack distribution. In the inversion for crack distribution, besides using the velocities of P- and S-waves measured in laboratory for the dry and water-saturated cases, measured attenuation data of P-waves are also used so as to further constrain the inversion, and to improve the uniqueness of the inversion results. By using such an extended hybrid approach, we are able to predict both the velocities of saturated porous rocks and the attenuations. From numerical study with the linear solver, we can conclude that the linear solver is able to accurately couple elastic solid and viscous fluid and handle high material contrast and the complex micro-structures of 3D digitized porous rocks. The stress-strain calculation is capable of computing the velocities and attenuations of saturated porous rocks the sizes of which are much smaller than the wavelength of interest. The hybrid approach is a practical way to study the seismic properties of saturated porous rocks until high enough resolution digitized data and enough computational resources are available. From the computations, we observe that the small features, such as cracks lost in the imaging process, are critical for accurately predicting velocities and attenuations of saturated porous rocks. Generally, attenuation is more sensitive to the viscosity of the saturating fluid than velocity is, and attenuation due to viscous fluid in compliant pores is greater than that due to viscous fluid in stiff pores.

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 Finite difference Seismic Wave Modeling Including Surface Topography written by Stig Ottar Hestholm and published by . This book was released on 1999 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: I present synthetics of seismic wave propagation near free surface topography. The velocity-stress formulations of both the full elastic and viscoelastic wave equations are used, and I have derived exact boundary conditions for any arbitrary, smooth topography in terms of the particle velocities. Program codes are developed for 2 and 3 dimensions (2-D and 3-D) using finite-difference (F-D) methods for both spatial and temporal numerical discretizations. An 8th order F-D method is used inside the physical model space, and the spatial F-D order decreases gradually towards the free surface topography. The discretization of the medium equations along the side and bottom boundaries, the free surface topography boundary conditions, and the forward time stepping, are all by 2nd order F-D methods. The leap-frog technique is used for time stepping everywhere except for the memory variable equations in the viscoelastic cases, where an explicit version of the unconditionally stable Crank-Nicholson method is used. I show synthetics applying the schemes to isotropic 2-D and 3-D media covered by topographies that are either described by analytic expressions or by real elevation data. These data are taken from an area in South-Eastern Norway that contains the NORESS seismic receiver array. Domains up to 60 x 60 kilometers are used in 3-D simulations, and the applied sources are plane waves generated by a plane of Ricker type point sources. These sources represent earthquakes or teleseismic explosions. For 2-D simulations I have used both plane waves and point sources, since the larger models permissible in 2-D allow for point sources to represent earthquakes or teleseismic explosions quite well. For 2-D simulations I have also included examples using layered media with randomization by a 2-D von Karman function with and without apparent anisotropy. Synthetic snapshots and seismograms show Rayleigh (Rg)-waves emanating from areas of prominent topography as well as strong surface wa

Download or read book Seismic Wave Propagation in Non Homogeneous Elastic Media by Boundary Elements written by George D. Manolis and published by Springer. This book was released on 2016-09-23 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the mathematical potential and computational efficiency of the Boundary Element Method (BEM) for modeling seismic wave propagation in either continuous or discrete inhomogeneous elastic/viscoelastic, isotropic/anisotropic media containing multiple cavities, cracks, inclusions and surface topography. BEM models may take into account the entire seismic wave path from the seismic source through the geological deposits all the way up to the local site under consideration. The general presentation of the theoretical basis of elastodynamics for inhomogeneous and heterogeneous continua in the first part is followed by the analytical derivation of fundamental solutions and Green's functions for the governing field equations by the usage of Fourier and Radon transforms. The numerical implementation of the BEM is for antiplane in the second part as well as for plane strain boundary value problems in the third part. Verification studies and parametric analysis appear throughout the book, as do both recent references and seminal ones from the past. Since the background of the authors is in solid mechanics and mathematical physics, the presented BEM formulations are valid for many areas such as civil engineering, geophysics, material science and all others concerning elastic wave propagation through inhomogeneous and heterogeneous media. The material presented in this book is suitable for self-study. The book is written at a level suitable for advanced undergraduates or beginning graduate students in solid mechanics, computational mechanics and fracture mechanics.

Download or read book The Leading Edge written by and published by . This book was released on 2009 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Seismology written by Heiner Igel and published by Oxford University Press. This book was released on 2017 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering and many other fields. It looks under the hood of current simulation technology and provides guidelines on what to look out for when carrying out sophisticated simulation tasks.

Download or read book Seismic Full Waveform Modeling Imaging in Attenuating Media written by Peng Guo and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Seismic attenuation strongly affects seismic waveforms by amplitude loss and velocity dispersion. Without proper inclusion of Q parameters, errors can be introduced for seismic full waveform modeling and imaging. Three different (Carcione's, Robertsson's, and the generalized Robertsson's) isotropic viscoelastic wave equations based on the generalized standard linear solid (GSLS) are evaluated. The second-order displacement equations are derived, and used to demonstrate that, with the same stress relaxation times, these viscoelastic formulations are equivalent. By introducing separate memory variables for P and S relaxation functions, Robertsson's formulation is generalized to allow different P and S wave stress relaxation times, which improves the physical consistency of the Qp and Qs modelled in the seismograms.The three formulations have comparable computational cost. 3D seismic finite-difference forward modeling is applied to anisotropic viscoelastic media. The viscoelastic T-matrix (a dynamic effective medium theory) relates frequency-dependent anisotropic attenuation and velocity to reservoir properties in fractured HTI media, based on the meso-scale fluid flow attenuation mechanism. The seismic signatures resulting from changing viscoelastic reservoir properties are easily visible. Analysis of 3D viscoelastic seismograms suggests that anisotropic attenuation is a potential tool for reservoir characterization. To compensate the Q effects during reverse-time migration (RTM) in viscoacoustic and viscoelastic media, amplitudes need to be compensated during wave propagation; the propagation velocity of the Q-compensated wavefield needs to be the same as in the attenuating wavefield, to restore the phase information. Both amplitude and phase can be compensated when the velocity dispersion and the amplitude loss are decoupled. For wave equations based on the GSLS, because Q effects are coupled in the memory variables, Q-compensated wavefield propagates faster than the attenuating wavefield, and introduce unwanted phase shift. Numerical examples show that there are phase (depth) shifts in the Q-compensated RTM images from the GSLS equation. An adjoint-based least-squares reverse-time migration is proposed for viscoelastic media (Q-LSRTM), to compensate the attenuation losses in P and S images. The viscoelastic adjoint operator, and the P and S modulus perturbation imaging conditions are derived using the adjoint-state method and an augmented Lagrangian functional. Q-LSRTM solves the viscoelastic linearized modeling operator for synthetic data, and the adjoint operator is used for back propagating the data residual. Q-LSRTM is capable of iteratively updating the P and S modulus perturbations,in the direction of minimizing data residuals, and attenuation loss is iteratively compensated. A novel Q compensation approach is developed for adjoint seismic imaging by pseudodifferential scaling. With a correct Q model included in the migration algorithm, propagation effects, including the Q effects, can be compensated with the application of the inverse Hessian to the RTM image. Pseudodifferential scaling is used to efficiently approximate the action of the inverse Hessian. Numerical examples indicate that the adjoint RTM images with pseudodifferential scaling approximate the true model perturbation, and can be used as well-conditioned gradients for least-squares imaging.

Download or read book Finite difference Modeling of 2 5 D Wave Propagation in Variable Density Medium written by Hardoyo and published by . This book was released on 1993 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: