Fourth‐Order Staggered‐Grid Finite‐Difference Seismic Wavefield Estimation Using a Discontinuous Mesh Interface (WEDMI)

2017 ◽  
Vol 107 (5) ◽  
pp. 2183-2193 ◽  
Author(s):  
Shiying Nie ◽  
Yongfei Wang ◽  
Kim B. Olsen ◽  
Steven M. Day
Keyword(s):  
Finite Difference ◽  
Fourth Order ◽  
Staggered Grid ◽  
Seismic Wavefield

Fourth‐order finite‐difference P-SV seismograms

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1425-1436 ◽  
Author(s):  
Alan R. Levander
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Dispersion Analysis ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Order System ◽  
Surface Boundary ◽  
Lamb’S Problem

I describe the properties of a fourth‐order accurate space, second‐order accurate time, two‐dimensional P-SV finite‐difference scheme based on the Madariaga‐Virieux staggered‐grid formulation. The numerical scheme is developed from the first‐order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses. The Madariaga‐Virieux staggered‐grid scheme has the desirable quality that it can correctly model any variation in material properties, including both large and small Poisson’s ratio materials, with minimal numerical dispersion and numerical anisotropy. Dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints/wavelength. The scheme can be used to accurately simulate wave propagation in mixed acoustic‐elastic media, making it ideal for modeling marine problems. Explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free‐surface or within a layer and to satisfy free‐surface boundary conditions. Benchmark comparisons of finite‐difference and analytical solutions to Lamb’s problem are almost identical, as are comparisons of finite‐difference and reflectivity solutions for elastic‐elastic and acoustic‐elastic layered models.

3D finite-difference modeling of elastic wave propagation in the Laplace-Fourier domain

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. T137-T155 ◽  
Author(s):  
Petr V. Petrov ◽  
Gregory A. Newman
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Fourth Order ◽  
Order Approximation ◽  
Staggered Grid ◽  
Order System ◽  
Finite Difference Schemes ◽  
Fourier Domain ◽  
Krylov Methods ◽  
Complex Objects

With the recent interest in the Laplace-Fourier domain full waveform inversion, we have developed new heterogeneous 3D fourth- and second-order staggered-grid finite-difference schemes for modeling seismic wave propagation in the Laplace-Fourier domain. Our approach is based on the integro-interpolation technique for the velocity-stress formulation in the Cartesian coordinate system. Five averaging elastic coefficients and three averaging densities are necessary to describe the heterogeneous medium, with harmonic averaging of the bulk and shear moduli, and arithmetic averaging of density. In the fourth-order approximation, we improved the accuracy of the scheme using a combination of integral identities for two elementary volumes — “small” and “large” around spatial gridpoints where the wave variables are defined. Two solution approaches are provided, both of which are solved with iterative Krylov methods. In the first approach, the stress variables are eliminated and a linear system for the velocity components is solved. In the second approach, we worked directly with the first-order system of velocity and stress variables. This reduced the computer memory required to store the complex matrix, along with reducing (by 30%) the number of arithmetic operations needed for the solution compared to the fourth-order scheme for velocity only. Numerical examples show that our finite-difference formulations for elastic wavefield simulations can achieve more accurate solutions with fewer grid points than those from previously published second and fourth-order frequency-domain schemes. We applied our simulator to the investigation of wavefields from the SEG/EAGE model in the Laplace-Fourier domain. The calculation is sensitive to the heterogeneity of the medium and capable of describing the structures of complex objects. Our technique can also be extended to 3D elastic modeling within the time domain.

scholarly journals Analysis of Seismic Wavefield Characteristics in 3D Tunnel Models Based on the 3D Staggered-Grid Finite-Difference Scheme in the Cylindrical Coordinate System

2021 ◽  
Vol 11 (13) ◽  
pp. 5854
Author(s):  
Zhiwu Zuo ◽  
Duo Li ◽  
Pengfei Zhou ◽  
Chunjin Lin ◽  
Zhichao Yang ◽  
...  
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Coordinate System ◽  
Finite Difference Scheme ◽  
Forward Modeling ◽  
Cylindrical Coordinate System ◽  
Staggered Grid ◽  
Geological Conditions ◽  
Cylindrical Coordinate ◽  
Seismic Wavefield

The accurate prediction of the geological conditions ahead of a tunnel plays an important role in tunnel construction. Among all forward geological prospecting methods, the seismic detection method is widely applied. However, due to the characteristics of the tunnel and the complexity of the geological conditions, the seismic wavefield is complicated. Carrying out a more realistic forward modeling method is vital for fully understanding the law of seismic wave propagation and the characteristics of seismic wavefield in the tunnel. In this paper, the 3D staggered-grid finite-difference scheme in the cylindrical coordinate system based on the decoupled nonconversion elastic wave equation is used to carry out the numerical simulation. This method can avoid the diffraction interferences produced at the edges of the tunnel face in the Cartesian coordinate system. Based on this forward modeling method, the characteristics of wavefield and propagation laws of seismic waves under three kinds of common typical unfavorable geological models were explored, which can provide theoretical guidance to seismic data interpretation of tunnel seismic forward prospecting in practice.

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