Derivation and implementation of the boundary integral formula for the convective acoustic wave equation in time domain

2014 ◽  
Vol 136 (6) ◽  
pp. 2959-2967 ◽  
Author(s):  
Yong Woo Lee ◽  
Duck Joo Lee
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Integral Formula ◽  
Boundary Integral ◽  
Acoustic Wave Equation ◽  
Boundary Integral Formula

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.

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.

Solving the tensorial 3D acoustic wave equation: A mimetic finite-difference time-domain approach

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. T183-T196 ◽  
Author(s):  
Jeffrey Shragge ◽  
Benjamin Tapley
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Internal Boundary ◽  
Laplacian Operator ◽  
Acoustic Wave Equation ◽  
Coordinate Systems ◽  
Difference Time

Generating accurate numerical solutions of the acoustic wave equation (AWE) is a key computational kernel for many seismic imaging and inversion problems. Although finite-difference time-domain (FDTD) approaches for generating full-wavefield solutions are well-developed for Cartesian computational domains, several challenges remain when applying FDTD approaches to scenarios arguably best described by more generalized geometry. In particular, how best to generate accurate and stable FDTD solutions for scenarios involving grids conforming to complex topography or internal surfaces. We address these issues by developing a mimetic FDTD (MFDTD) approach that combines four key components: a tensorial 3D AWE, mimetic finite-difference (MFD) operators, fully staggered grids (FSGs), and MFD Robin boundary conditions (RBC). The tensorial formulation of the 3D AWE permits wave propagation to be specified on (semi-) analytically defined coordinate meshes designed to conform to complex domain boundaries. MFD operators allow for higher order FD stencils to be applied throughout the model domain, including the boundary region where implementing centered FD stencils can be problematic. The FSG approach combines wavefield information propagated on four complementary subgrids to ensure the existence of all wavefield gradients required for computing the tensorial Laplacian operator, and thereby avoids interpolation approximations. The RBCs are implemented with a flux-preserving mimetic boundary operator that forestalls introduction of nonphysical energy into the grid by enforcing underlying flux-conservation laws. After validating the 3D MFDTD scheme on a sheared Cartesian mesh, we generate 3D wavefield simulation examples for internal boundary (IB) and topographic coordinate systems. The numerical examples demonstrate that the MFDTD scheme is capable of providing accurate and low-dispersion impulse responses for scenarios involving distorted IB meshes conforming to water-bottom surfaces and topographic coordinate systems exhibiting 2.5 km of topographic relief and including steep (65°) slope angles.

scholarly journals An efficient GPU-based time domain solver for the acoustic wave equation

2012 ◽  
Vol 73 (2) ◽  
pp. 83-94 ◽  
Author(s):  
Ravish Mehra ◽  
Nikunj Raghuvanshi ◽  
Lauri Savioja ◽  
Ming C. Lin ◽  
Dinesh Manocha
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Acoustic Wave Equation

scholarly journals An efficient time domain solver for the acoustic wave equation

2012 ◽  
Vol 131 (4) ◽  
pp. 3333-3333
Author(s):  
Ravish Mehra ◽  
Nikunj Raghuvanshi ◽  
Lauri Savioja ◽  
Ming Lin ◽  
Dinesh Manocha
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Acoustic Wave Equation
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