scholarly journals Hybrid High-Order Methods for the Acoustic Wave Equation in the Time Domain

2021 ◽  
Author(s):  
Erik Burman ◽  
Omar Duran ◽  
Alexandre Ern
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
High Order ◽  
Acoustic Wave Equation ◽  
High Order Methods ◽  
The Time Domain

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.

High-order implicit staggered-grid finite differences methods for the acoustic wave equation

2017 ◽  
Vol 34 (2) ◽  
pp. 602-625
Author(s):  
Miguel Uh Zapata ◽  
Reymundo Itzá Balam ◽  
Jonathan Montalvo-Urquizo
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Finite Differences ◽  
High Order ◽  
Staggered Grid ◽  
Acoustic Wave Equation

Solving the 3D acoustic wave equation on generalized structured meshes: A finite-difference time-domain approach

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. T363-T378 ◽  
Author(s):  
Jeffrey Shragge
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
3D Seismic ◽  
Acoustic Wave Equation ◽  
Structured Meshes ◽  
Cartesian Geometry ◽  
And Inversion ◽  
Difference Time

The key computational kernel of most advanced 3D seismic imaging and inversion algorithms used in exploration seismology involves calculating solutions of the 3D acoustic wave equation, most commonly with a finite-difference time-domain (FDTD) methodology. Although well suited for regularly sampled rectilinear computational domains, FDTD methods seemingly have limited applicability in scenarios involving irregular 3D domain boundary surfaces and mesh interiors best described by non-Cartesian geometry (e.g., surface topography). Using coordinate mapping relationships and differential geometry, an FDTD approach can be developed for generating solutions to the 3D acoustic wave equation that is applicable to generalized 3D coordinate systems and (quadrilateral-faced hexahedral) structured meshes. The developed numerical implementation is similar to the established Cartesian approaches, save for a necessary introduction of weighted first- and mixed second-order partial-derivative operators that account for spatially varying geometry. The approach was validated on three different types of computational meshes: (1) an “internal boundary” mesh conforming to a dipping water bottom layer, (2) analytic “semiorthogonal cylindrical” coordinates, and (3) analytic semiorthogonal and numerically specified “topographic” coordinate meshes. Impulse response tests and numerical analysis demonstrated the viability of the approach for kernel computations for 3D seismic imaging and inversion experiments for non-Cartesian geometry scenarios.

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