Computational methods for large-scale 3D acoustic finite-difference modeling: A tutorial

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM223-SM230 ◽  
Author(s):  
John T. Etgen ◽  
Michael J. O’Brien
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Large Scale ◽  
Data Flow ◽  
Three Dimensions ◽  
Acoustic Medium ◽  
Ocean Bottom ◽  
Acoustic Wave Equation ◽  
P Waves ◽  
Core Method

We present a set of methods for modeling wavefields in three dimensions with the acoustic-wave equation. The primary applications of these modeling methods are the study of acquisition design, multiple suppression, and subsalt imaging for surface-streamer and ocean-bottom recording geometries. We show how to model the acoustic wave equation in three dimensions using limited computer memory, typically using a single workstation, leading to run times on the order of a few CPU hours to a CPU day. The structure of the out-of-core method presented is also used to improve the efficiency of in-core modeling, where memory-to-cache-to-memory data flow is essentially the same as the data flow for an out-of-core method. Starting from the elastic-wave equation, we develop a vector-acoustic algorithm capable of efficiently modeling multicomponent data in an acoustic medium. We show that data from this vector-acoustic algorithm can be used to test upgoing/downgoing separation of P-waves recorded by ocean-bottom seismic acquisition.

scholarly journals An acoustic wave equation for orthorhombic anisotropy

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1169-1172 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Transversely Isotropic ◽  
Order Equation ◽  
Sixth Order ◽  
Acoustic Medium ◽  
Complex Conjugate ◽  
Acoustic Wave Equation ◽  
P Waves ◽  
Isotropic Media

Using a dispersion relation derived under the acoustic medium assumption, I obtain an acoustic wave equation for orthorhombic media. Although an acoustic wave equation does not strictly describe a wave in anisotropic media, it accurately describes the kinematics of P‐waves. The orthorhombic acoustic wave equation, unlike the transversely isotropic one, is a sixth‐order equation with three sets of complex conjugate solutions. Only one set of these solutions are perturbations of the familiar acoustic wavefield solution for isotropic media for incoming and outgoing P‐waves and, thus, are of interest here. The other two sets of solutions are simply the result of this artificially derived sixth‐order equation.

An acoustic wave equation for anisotropic media

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1239-1250 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Computation Time ◽  
Transversely Isotropic ◽  
Acoustic Medium ◽  
Acoustic Wave Equation ◽  
P Waves ◽  
Kinematic Approximation ◽  
Vti Media

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.

Simulation of acoustic wavefields in heterogeneous media: A robust method for automatic suppression of numerical dispersion

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. T99-T110 ◽  
Author(s):  
Dinghui Yang ◽  
Guojie Song ◽  
Biaolong Hua ◽  
Henri Calandra
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Large Scale ◽  
Heterogeneous Media ◽  
Numerical Dispersion ◽  
Acoustic Wave Equation ◽  
Discrete Method ◽  
Computational Costs ◽  
Refined Method

Numerical dispersion limits the application of numerical simulation methods for solving the acoustic wave equation in large-scale computation. The nearly analytic discrete method (NADM) and its improved version for suppressing numerical dispersion were developed recently. This new method is a refinement of two previous methods and further increases the ability of suppressing numerical dispersion for modeling acoustic wave propagation in 2D heterogeneous media, which uses acoustic wave displacement, particle velocity, and their gradients to restructure the acoustic wavefield via the truncated Taylor expansion and the high-order interpolation approximate method. For the method proposed, we investigate its implementation and compare it with the higher-order Lax-Wendroff correction (LWC) scheme, the original nearly analytic discrete method (NADM) and its im-proved version with regard to numerical dispersion, computational costs, and computer storage requirements. The numerical dispersion relations provided by the refined algorithm for 1D and 2D cases are analyzed, as well as the numerical results obtained by this method against the exact solution for the 2D acoustic case. Numerical results show that the refined method gives no visible numerical dispersion for very large spatial grid increments. It can simulate high-frequency wave propagation for a given grid interval and automatically suppress the numerical dispersion when the acoustic wave equation is discretized, when too few samples per wavelength are used, or when models have large velocity contrasts. Unlike the high-order LWC methods, our present method can save substantial computational costs and memory requirements because very large grid increments can be used. The refined method can be used for the simulation of large-scale wavefields.

An analytic signal based accurate time-domain visco-acoustic wave equation from the Constant-Q theory

Geophysics ◽  
2021 ◽  
pp. 1-58
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Relaxation Property ◽  
Analytic Signal ◽  
Acoustic Wave Equation ◽  
Real Component ◽  
Frequency Components

We present a concise time-domain wave equation to accurately simulate wave propagation in visco-acoustic media. The central idea behind this work is to dismiss the negative frequency components from a time-domain signal by converting the signal to its analytic format. The negative frequency components of any analytic signal are always zero, meaning we can construct the visco-acoustic wave equation to honor the relaxation property of the media for positive frequencies only. The newly proposed complex-valued wave equation (CWE) represents the wavefield with its analytic signal, whose real part is the desired physical wavefield, while the imaginary part is the Hilbert transform of the real component. Specifically, this CWE is accurate for both weak and strong attenuating media in terms of both dissipation and dispersion and the attenuation is precisely linear with respect to the frequencies. Besides, the CWE is easy and flexible to model dispersion-only, dissipation-only or dispersion-plus-dissipation seismic waves. We have verified these CWEs by comparing the results with analytical solutions, and achieved nearly perfect matching. Except for the homogeneous Q media, we have also extended the CWEs to heterogeneous media. The results of the CWEs for heterogeneous Q media are consistent with those computed from the nonstationary operator based Fourier Integral method and from the Standard Linear Solid (SLS) equations.

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