Journal ArticleDOI
An acoustic wave equation for anisotropic media
TLDR
In this paper, a wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media.Abstract:
A wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves, which significantly reduces the computation time compared to the elastic wavefield solutions for exploding‐reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a TI medium are derived. These equations, based on the acoustic assumption (shear wave velocity = 0), are much simpler than their elastic counterparts, yet they yield an accurate description of traveltimes and geometrical amplitudes. Numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex TI models.read more
Citations
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Journal ArticleDOI
Anisotropic 3D full-waveform inversion
Michael Warner,Andrew Ratcliffe,Tenice Nangoo,Joanna Morgan,Adrian Umpleby,Nikhil Koolesh Shah,Vetle Vinje,I. Stekl,Lluís Guasch,Caroline Win,Graham Conroy,A. Bertrand +11 more
TL;DR: In this article, a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI) was developed and implemented on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea.
Journal ArticleDOI
An overview of depth imaging in exploration geophysics
TL;DR: In this paper, the authors describe the progress made in depth migration to the present and the most significant barriers to attaining its inversion goals in the future, and discuss some of the obstacles to reaching the point where seismic images can provide quantitatively accurate descriptions of rocks and fluids.
Journal ArticleDOI
Seismic wave extrapolation using lowrank symbol approximation
TL;DR: In this paper, a low-rank approximation of the space-wavenumber wave propagation matrix is proposed for wave propagation in 3D heterogeneous isotropic or anisotropic media.
Journal ArticleDOI
Reverse time migration in tilted transversely isotropic (TTI) media
TL;DR: In this article, a wave equation for P-waves is proposed in tilted transversely isotropic (TTI) media that can be solved as part of an acoustic anisotropic RTM algorithm, using standard explicit finite differencing.
Journal ArticleDOI
A stable TTI reverse time migration and its implementation
TL;DR: In this article, a vertical transversely isotropic wave system of equations that is equivalent to their elastic counterpart is derived and introduced to stabilize the TTI acoustic wave equations, and a stable solution can be found by either a pseudospectral method or a high-order explicit finite difference scheme.
References
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Book
Quantitative seismology : theory and methods
Keiiti Aki,Paul Richards +1 more
TL;DR: This work has here attempted to give a unified treatment of those methods of seismology that are currently used in interpreting actual data and develops the theory of seismic-wave propagation in realistic Earth models.
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Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Journal ArticleDOI
Weak elastic anisotropy
TL;DR: The equations governing weak anisotropy are much simpler than those governing strong anisotropic, and they are much easier to grasp intuitively as discussed by the authors, which is why they are easier to understand intuitively.
Journal ArticleDOI
Über die partiellen Differenzengleichungen der mathematischen Physik
TL;DR: In this paper, the authors present a Gebrauch bestimmt ausschließlich für den persönlichen, nicht kommerziellen Gebrauchs, which is a rechtschutzbestimmter gebrauch, and gilt vorbehaltlich der folgenden Einschränkungen.
Journal ArticleDOI
Velocity analysis for transversely isotropic media
Tariq Alkhalifah,Ilya Tsvankin +1 more
TL;DR: In this paper, a velocity analysis for transversely isotropic (TI) media was carried out by inverting the dependence of P•wave moveout velocities on the ray parameter.