The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Peter Moczo - One of the best experts on this subject based on the ideXlab platform.
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stable discontinuous Staggered Grid in the finite difference modelling of seismic motion
Geophysical Journal International, 2010Co-Authors: Peter Moczo, Jozef Kristek, Martin GalisAbstract:SUMMARY We present an algorithm of the spatial discontinuous Grid for the 3-D fourth-order velocity–stress Staggered-Grid finite-difference modelling of seismic wave propagation and earthquake motion. The ratio between the Grid spacing of the coarser and finer Grids can be an arbitrary odd number. The algorithm allows for large numbers of time levels without inaccuracy and eventual instability due to numerical noise inevitably generated at the contact of two Grids with different spatial Grid spacings. The key feature of the algorithm is the application of the Lanczos downsampling filter. The algorithm of the discontinuous Grid is directly applicable also to the displacement-stress Staggered-Grid finite-difference scheme.
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seismic wave propagation in viscoelastic media with material discontinuities a 3d fourth order Staggered Grid finite difference modeling
Bulletin of the Seismological Society of America, 2003Co-Authors: Jozef Kristek, Peter MoczoAbstract:We address the basic theoretical and algorithmic aspects of memory-efficient implementation of realistic attenuation in the Staggered-Grid finite-difference modeling of seismic-wave propagation in media with material discontinuities. We show that if averaging is applied to viscoelastic moduli in the frequency domain, it is possible to determine anelastic coefficients of the averaged medium representing a material discontinuity. We define (1) the anelastic functions in a new way, as being independent of anelastic coefficients, and (2) a new coarse spatial distribution of the anelastic functions in order to properly account for material discontinuities and, at the same time, to have it memory efficient. Numerical tests demonstrate that our approach enables more accurate viscoelastic modeling than other approaches.
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3d heterogeneous Staggered Grid finite difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities
Bulletin of the Seismological Society of America, 2002Co-Authors: Peter Moczo, Jozef Kristek, Vaclav Vavrycuk, Ralph J Archuleta, Ladislav HaladaAbstract:We analyze the problem of a heterogeneous formulation of the equation of motion and propose a new 3D fourth-order Staggered-Grid finite-difference (FD) scheme for modeling seismic motion and seismic-wave propagation. We first consider a 1D problem for a welded planar interface of two half-spaces. A simple physical model of the contact of two media and mathematical considerations are shown to give an averaged medium representing the contact of two media. An exact heterogeneous formulation of the equation of motion is a basis for constructing the corresponding heterogeneous FD scheme. In a much more complicated 3D problem we analyze a planar-interface contact of two isotropic media (both with interface parallel to a coordinate plane and interface in general position in the Cartesian coordinate system) and a nonplanar-interface contact of two isotropic media. Because in the latter case 21 elastic coefficients at each point are necessary to describe the averaged medium, we consider simplified boundary conditions for which the averaged medium can be described by only two elastic coefficients. Based on the simplified approach we construct the explicit heterogeneous 3D fourth-order displacement-stress FD scheme on a Staggered Grid with the volume harmonic averaging of the shear modulus in Grid positions of the stress-tensor components, volume harmonic averaging of the bulk modulus in Grid positions of the normal stress-tensor components, and volume arithmetic averaging of density in Grid positions of the displacement components. Our displacement-stress FD scheme can be easily modified into the velocity-stress or displacement-velocity-stress FD schemes. The scheme allows for an arbitrary position of the material discontinuity in the spatial Grid. Numerical tests for 12 configurations in four types of models show that our scheme is more accurate than the Staggered-Grid schemes used so far. Numerical examples also show that differences in thickness of a soft surface or interior layer smaller than one Grid spacing can cause considerable changes in seismic motion. The results thus underline the importance of having a FD scheme with sufficient sensitivity to heterogeneity of the medium. Manuscript received 21 May 2001.
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efficient methods to simulate planar free surface in the 3d 4th order Staggered Grid finite difference schemes
Studia Geophysica Et Geodaetica, 2002Co-Authors: Jozef Kristek, Peter Moczo, Ralph J ArchuletaAbstract:We numerically tested accuracy of two formulations of Levander's (1988) stress-imaging technique for simulating a planar free surface in the 4th-order Staggered-Grid finite-difference schemes. We have found that both formulations (one with normal stress-tensor components at the surface, the other with shear stress-tensor components at the surface) require at least 10 Grid spacings per minimum wavelength (λ min÷h = 10) if Rayleigh waves are to be propagated without significant Grid dispersion in the range of epicentral distances up to 15λ dom S. Because interior 4th-order Staggered-Grid schemes usually do not require more than 6 Grid spacings per minimum wavelength, in the considered range of epicentral distances, it was desirable to find alternative techniques to simulate a planar free surface, which would not require denser spatial sampling than λ min÷h = 6. Therefore, we have developed and tested new techniques: 1. Combination of the stress imaging (with the shear stress-tensor components at the surface) with Rodrigues' (1993) vertically refined Grid near the free surface. 2. Application of the adjusted finite-difference approximations to the z-derivatives at the Grid points at and below the surface that uses no virtual values above the surface and no stress imaging. The normal stress-tensor components are at the surface in one formulation, while the shear stress-tensor components are at the surface in the other formulation. The three developed formulations give for the spatial sampling λ min÷h = 6 results very close to those obtained by the discrete-wavenumber method. Because, however, the technique with the vertically refined Grid near the free surface requires 3 times smaller time step (due to the refined Grid), the technique with adjusted finite-difference approximations is the most accurate and efficient technique from the examined formulations in the homogeneous halfspace.
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3d fourth order Staggered Grid finite difference schemes stability and Grid dispersion
Bulletin of the Seismological Society of America, 2000Co-Authors: Peter Moczo, Jozef Kristek, Ladislav HaladaAbstract:We investigated stability and Grid dispersion in the 3D fourth-order in space, second-order in time, displacement-stress Staggered-Grid finite-difference scheme. Though only displacement-stress scheme is explicitly treated, all results also apply to the velocity-stress and displacement-velocity-stress finite-difference schemes. We derived independent stability conditions for the P and S waves by exact separation of equations for the two types of waves. Since the S -wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5 (that is usually used in modeling), we recommend to sample a minimum S wavelength by six Grid spacings. Grid dispersion is strongest for a wave propagating in the direction of a coordinate axis and weakest for a wave propagating along a body diagonal. Grid dispersion in the fourth-order scheme for the sampling ratios s = 1/5 and s = 1/6 is smaller than Grid dispersion in the second-order scheme for s = 1/10 and s = 1/12, respectively.
Yang Liu - One of the best experts on this subject based on the ideXlab platform.
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prestack reverse time migration with a time space domain adaptive high order Staggered Grid finite difference method
Exploration Geophysics, 2013Co-Authors: Hongyong Yan, Yang Liu, Hao ZhangAbstract:With advanced computational power, prestack reverse-time migration (RTM) is being used increasingly in seismic imaging. The accuracy and efficiency of RTM strongly depends on the algorithms used for numerical solutions of wave equations. Hence, how to solve the wave equation accurately and rapidly is very important in the process of RTM. In this paper, in order to improve the accuracy of the numerical solution, we use a time-space domain Staggered-Grid finite-difference (SFD) method to solve the acoustic wave equation, and develop a new acoustic prestack RTM scheme based on this time-space domain high-order SFD. Synthetic and real data tests demonstrate that the RTM scheme improves the imaging quality significantly compared with the conventional SFD RTM. Meanwhile, in the process of wavefield extrapolation, we apply adaptive variable-length spatial operators to compute spatial derivatives to decrease computational costs effectively with little reduction of the accuracy of the numerical solutions.
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acoustic vti modeling and pre stack reverse time migration based on the time space domain Staggered Grid finite difference method
Journal of Applied Geophysics, 2013Co-Authors: Hongyong Yan, Yang LiuAbstract:Abstract Reverse-time migration (RTM) is based on seismic numerical modeling algorithms, and the accuracy and efficiency of RTM strongly depend on the algorithm used for numerical solution of wave equations. Finite-difference (FD) methods have been widely used to solve the wave equation in seismic numerical modeling and RTM. In this paper, we derive a series of time–space domain Staggered-Grid FD coefficients for acoustic vertical transversely isotropic (VTI) equations, and adopt these difference coefficients to solve the equations, then analyze the numerical dispersion and stability, and compare the time–space domain Staggered-Grid FD method with the conventional method. The numerical analysis results demonstrate that the time–space domain Staggered-Grid FD method has greater accuracy and better stability than the conventional method under the same discretizations. Moreover, we implement the pre-stack acoustic VTI RTM by the conventional and time–space domain high-order Staggered-Grid FD methods, respectively. The migration results reveal that the time–space domain Staggered-Grid FD method can provide clearer and more accurate image with little influence on computational efficiency, and the new FD method can adopt a larger time step to reduce the computation time and preserve the imaging accuracy as well in RTM. Meanwhile, when considering the anisotropy in RTM for the VTI model, the imaging quality of the acoustic VTI RTM is better than that of the acoustic isotropic RTM.
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elastic prestack reverse time migration using the time space domain high order Staggered Grid finite difference method
Seg Technical Program Expanded Abstracts, 2013Co-Authors: Hongyong Yan, Yang Liu, H. LiuAbstract:Summary Elastic prestack reverse-time migration (RTM) can fully reveal underground information. The accuracy and efficiency of elastic RTM is strongly dependent on the algorithms used for numerical solutions of wave equations. Staggered-Grid finite-difference (SFD) methods have been widely used to solve wave equations in RTM. Conventional SFD method derives spatial difference coefficients from space domain dispersion relation, but it is difficult to satisfy time-space domain dispersion relation of wave equations exactly. In this paper, we extend a time-space domain SFD method to elastic prestack RTM for improving image quality. We implement elastic prestack RTM using the conventional and the time-space domain high-order SFD methods, respectively. The modeling tests show that the elastic RTM using the time-space domain SFD method generates better images than that using the conventional SFD method. The application of the time-space domain SFD method to elastic RTM problems is preferable.
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a hybrid absorbing boundary condition for elastic Staggered Grid modelling
Geophysical Prospecting, 2012Co-Authors: Yang Liu, Mrinal K SenAbstract:We recently proposed an efficient hybrid scheme to absorb boundary reflections for acoustic wave modelling that could attain nearly perfect absorptions. This scheme uses weighted averaging of wavefields in a transition area, between the inner area and the model boundaries. In this paper we report on the extension of this scheme to 2D elastic wave modelling with displacement-stress formulations on Staggered Grids using explicit finite-difference, pseudo-implicit finite-difference and pseudo-spectral methods. Numerical modelling results of elastic wave equations with hybrid absorbing boundary conditions show great improvement for modelling stability and significant absorption for boundary reflections, compared with the conventional Higdon absorbing boundary conditions, demonstrating the effectiveness of this scheme for elastic wave modelling. The modelling results also show that the hybrid scheme works well in 2D rotated Staggered-Grid modelling for isotropic medium, 2D Staggered-Grid modelling for vertically transversely isotropic medium and 2D rotated Staggered-Grid modelling for tilted transversely isotropic medium.
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high order finite difference numerical modeling of wave propagation in viscoelastic tti media using rotated Staggered Grid
Chinese Journal of Geophysics, 2012Co-Authors: Hongyong Yan, Yang LiuAbstract:This study is based on the Carcione's theories of viscoelasticity and anisotropy. We present two-dimensional, three-component, first-order velocity-stress wave equations of viscoelastic tilted transversely isotropic (viscoelastic TTI) media and use an any-order finite-difference (FD) scheme to numerically solve the equations. The equations of the perfectly matched layer (PML) are also derived for the wave equations in viscoelastic TTI media and the any-order FD scheme with a rotated Staggered Grid is also used to solve these equations. The results of numerical modeling indicate that the modeling precision is high and the absorbing boundary condition attains good effect in the viscoelastic TTI media, and high precise snapshots of wave fields and synthetic seismograms can be obtained, which can reflect the characteristics of viscoelasticity and anisotropy of subsurface media.
Jozef Kristek - One of the best experts on this subject based on the ideXlab platform.
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stable discontinuous Staggered Grid in the finite difference modelling of seismic motion
Geophysical Journal International, 2010Co-Authors: Peter Moczo, Jozef Kristek, Martin GalisAbstract:SUMMARY We present an algorithm of the spatial discontinuous Grid for the 3-D fourth-order velocity–stress Staggered-Grid finite-difference modelling of seismic wave propagation and earthquake motion. The ratio between the Grid spacing of the coarser and finer Grids can be an arbitrary odd number. The algorithm allows for large numbers of time levels without inaccuracy and eventual instability due to numerical noise inevitably generated at the contact of two Grids with different spatial Grid spacings. The key feature of the algorithm is the application of the Lanczos downsampling filter. The algorithm of the discontinuous Grid is directly applicable also to the displacement-stress Staggered-Grid finite-difference scheme.
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seismic wave propagation in viscoelastic media with material discontinuities a 3d fourth order Staggered Grid finite difference modeling
Bulletin of the Seismological Society of America, 2003Co-Authors: Jozef Kristek, Peter MoczoAbstract:We address the basic theoretical and algorithmic aspects of memory-efficient implementation of realistic attenuation in the Staggered-Grid finite-difference modeling of seismic-wave propagation in media with material discontinuities. We show that if averaging is applied to viscoelastic moduli in the frequency domain, it is possible to determine anelastic coefficients of the averaged medium representing a material discontinuity. We define (1) the anelastic functions in a new way, as being independent of anelastic coefficients, and (2) a new coarse spatial distribution of the anelastic functions in order to properly account for material discontinuities and, at the same time, to have it memory efficient. Numerical tests demonstrate that our approach enables more accurate viscoelastic modeling than other approaches.
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3d heterogeneous Staggered Grid finite difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities
Bulletin of the Seismological Society of America, 2002Co-Authors: Peter Moczo, Jozef Kristek, Vaclav Vavrycuk, Ralph J Archuleta, Ladislav HaladaAbstract:We analyze the problem of a heterogeneous formulation of the equation of motion and propose a new 3D fourth-order Staggered-Grid finite-difference (FD) scheme for modeling seismic motion and seismic-wave propagation. We first consider a 1D problem for a welded planar interface of two half-spaces. A simple physical model of the contact of two media and mathematical considerations are shown to give an averaged medium representing the contact of two media. An exact heterogeneous formulation of the equation of motion is a basis for constructing the corresponding heterogeneous FD scheme. In a much more complicated 3D problem we analyze a planar-interface contact of two isotropic media (both with interface parallel to a coordinate plane and interface in general position in the Cartesian coordinate system) and a nonplanar-interface contact of two isotropic media. Because in the latter case 21 elastic coefficients at each point are necessary to describe the averaged medium, we consider simplified boundary conditions for which the averaged medium can be described by only two elastic coefficients. Based on the simplified approach we construct the explicit heterogeneous 3D fourth-order displacement-stress FD scheme on a Staggered Grid with the volume harmonic averaging of the shear modulus in Grid positions of the stress-tensor components, volume harmonic averaging of the bulk modulus in Grid positions of the normal stress-tensor components, and volume arithmetic averaging of density in Grid positions of the displacement components. Our displacement-stress FD scheme can be easily modified into the velocity-stress or displacement-velocity-stress FD schemes. The scheme allows for an arbitrary position of the material discontinuity in the spatial Grid. Numerical tests for 12 configurations in four types of models show that our scheme is more accurate than the Staggered-Grid schemes used so far. Numerical examples also show that differences in thickness of a soft surface or interior layer smaller than one Grid spacing can cause considerable changes in seismic motion. The results thus underline the importance of having a FD scheme with sufficient sensitivity to heterogeneity of the medium. Manuscript received 21 May 2001.
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efficient methods to simulate planar free surface in the 3d 4th order Staggered Grid finite difference schemes
Studia Geophysica Et Geodaetica, 2002Co-Authors: Jozef Kristek, Peter Moczo, Ralph J ArchuletaAbstract:We numerically tested accuracy of two formulations of Levander's (1988) stress-imaging technique for simulating a planar free surface in the 4th-order Staggered-Grid finite-difference schemes. We have found that both formulations (one with normal stress-tensor components at the surface, the other with shear stress-tensor components at the surface) require at least 10 Grid spacings per minimum wavelength (λ min÷h = 10) if Rayleigh waves are to be propagated without significant Grid dispersion in the range of epicentral distances up to 15λ dom S. Because interior 4th-order Staggered-Grid schemes usually do not require more than 6 Grid spacings per minimum wavelength, in the considered range of epicentral distances, it was desirable to find alternative techniques to simulate a planar free surface, which would not require denser spatial sampling than λ min÷h = 6. Therefore, we have developed and tested new techniques: 1. Combination of the stress imaging (with the shear stress-tensor components at the surface) with Rodrigues' (1993) vertically refined Grid near the free surface. 2. Application of the adjusted finite-difference approximations to the z-derivatives at the Grid points at and below the surface that uses no virtual values above the surface and no stress imaging. The normal stress-tensor components are at the surface in one formulation, while the shear stress-tensor components are at the surface in the other formulation. The three developed formulations give for the spatial sampling λ min÷h = 6 results very close to those obtained by the discrete-wavenumber method. Because, however, the technique with the vertically refined Grid near the free surface requires 3 times smaller time step (due to the refined Grid), the technique with adjusted finite-difference approximations is the most accurate and efficient technique from the examined formulations in the homogeneous halfspace.
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3d fourth order Staggered Grid finite difference schemes stability and Grid dispersion
Bulletin of the Seismological Society of America, 2000Co-Authors: Peter Moczo, Jozef Kristek, Ladislav HaladaAbstract:We investigated stability and Grid dispersion in the 3D fourth-order in space, second-order in time, displacement-stress Staggered-Grid finite-difference scheme. Though only displacement-stress scheme is explicitly treated, all results also apply to the velocity-stress and displacement-velocity-stress finite-difference schemes. We derived independent stability conditions for the P and S waves by exact separation of equations for the two types of waves. Since the S -wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5 (that is usually used in modeling), we recommend to sample a minimum S wavelength by six Grid spacings. Grid dispersion is strongest for a wave propagating in the direction of a coordinate axis and weakest for a wave propagating along a body diagonal. Grid dispersion in the fourth-order scheme for the sampling ratios s = 1/5 and s = 1/6 is smaller than Grid dispersion in the second-order scheme for s = 1/10 and s = 1/12, respectively.
David A Kopriva - One of the best experts on this subject based on the ideXlab platform.
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a Staggered Grid multidomain spectral method for the compressible navier stokes equations
Journal of Computational Physics, 1998Co-Authors: David A KoprivaAbstract:We present a flexible, non-conforming Staggered-Grid Chebyshev spectral multidomain method for the solution of the compressible Navier?Stokes equations. In this method, subdomain corners are not included in the approximation, thereby simplifying the subdomain connectivity. To allow for local refinement of the polynomial order or subdomain subdivision, non-conforming subdomains are treated by a mortar method. Spectral accuracy is shown in one- and two-dimensional linear and non-linear problems. Application is made to four compressible flow problems: the Couette flow, a steady boundary layer over a flat plate, steady transonic flow in a nozzle, and unsteady flow over a cylinder at a Reynolds number of 75.
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a conservative Staggered Grid chebyshev multidomain method for compressible flows ii a semi structured method
Journal of Computational Physics, 1996Co-Authors: David A KoprivaAbstract:We present a Chebyshev multidomain method that can solve systems of hyperbolic equations in conservation form on an unrestricted quadrilateral subdivision of a domain. Within each subdomain the solutions and fluxes are approximated by a Staggered-Grid Chebyshev method. Thus, the method is unstructured in terms of the subdomain decomposition, but strongly structured within the subdomains. Communication between subdomains is done by a mortar method in such a way that the method is globally conservative. The method is applied to both linear and nonlinear test problems and spectral accuracy is demonstrated.
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a conservative Staggered Grid chebyshev multidomain method for compressible flows
Journal of Computational Physics, 1995Co-Authors: David A Kopriva, John H KoliasAbstract:We present a new multidomain spectral collocation method that uses a Staggered Grid for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss?Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.
Mrinal K Sen - One of the best experts on this subject based on the ideXlab platform.
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a hybrid absorbing boundary condition for elastic Staggered Grid modelling
Geophysical Prospecting, 2012Co-Authors: Yang Liu, Mrinal K SenAbstract:We recently proposed an efficient hybrid scheme to absorb boundary reflections for acoustic wave modelling that could attain nearly perfect absorptions. This scheme uses weighted averaging of wavefields in a transition area, between the inner area and the model boundaries. In this paper we report on the extension of this scheme to 2D elastic wave modelling with displacement-stress formulations on Staggered Grids using explicit finite-difference, pseudo-implicit finite-difference and pseudo-spectral methods. Numerical modelling results of elastic wave equations with hybrid absorbing boundary conditions show great improvement for modelling stability and significant absorption for boundary reflections, compared with the conventional Higdon absorbing boundary conditions, demonstrating the effectiveness of this scheme for elastic wave modelling. The modelling results also show that the hybrid scheme works well in 2D rotated Staggered-Grid modelling for isotropic medium, 2D Staggered-Grid modelling for vertically transversely isotropic medium and 2D rotated Staggered-Grid modelling for tilted transversely isotropic medium.
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scalar wave equation modeling with time space domain dispersion relation based Staggered Grid finite difference schemes
Bulletin of the Seismological Society of America, 2011Co-Authors: Yang Liu, Mrinal K SenAbstract:The Staggered-Grid finite-difference (SFD) method is widely used in numerical modeling of wave equations. Conventional SFD stencils for spatial derivatives are usually designed in the space domain. However, when they are used to solve wave equations, it becomes difficult to satisfy the dispersion relations exactly. Liu and Sen (2009c) proposed a new SFD scheme for one-dimensional (1D) scalar wave equation based on the time–space domain dispersion relation and plane wave theory, which is made to satisfy the exact dispersion relation. This new SFD scheme has greater accuracy and better stability than a conventional scheme under the same discretizations. In this paper, we develop this new SFD scheme further for numerical solution of 2D and 3D scalar wave equations. We demonstrate that the modeling accuracy is second order when the conventional 2 M -th-order space-domain SFD and the second order time-domain finite-difference stencils are directly used to solve the scalar wave equation. However, under the same discretization, our 1D scheme can reach 2 M -th-order accuracy and is always stable; 2D and 3D schemes can reach 2 M -th-order accuracy along 8 and 48 directions, respectively, and have better stability. The advantages of the new schemes are also demonstrated with dispersion analysis, stability analysis, and numerical modeling.
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an implicit Staggered Grid finite difference method for seismic modelling
Geophysical Journal International, 2009Co-Authors: Yang Liu, Mrinal K SenAbstract:SUMMARY We derive explicit and new implicit Staggered-Grid finite-difference (FD) formulas for derivatives of first order with any order of accuracy by a plane wave theory and Taylor’s series expansion. Furthermore, we arrive at a practical algorithm such that the tridiagonal matrix equations are formed by the implicit FD formulas derived from the fractional expansion of derivatives. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to or greater than that of a (4N)th-order explicit formula. The new implicit method only involves solving tridiagonal matrix equations. We also demonstrate that a( 2N + 2)th-order implicit formulation requires nearly the same amount of memory and computation as those of a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (4N)th-order explicit formulation when additional cost of visiting arrays is not considered. Our analysis of efficiency and numerical modelling results for elastic wave propagation demonstrates that a high-order explicit Staggered-Grid method can be replaced by an implicit Staggered-Grid method of some order, which will increase the accuracy but not the computational cost.
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finite difference modelling of s wave splitting in anisotropic media
Geophysical Prospecting, 2008Co-Authors: Reeshidev Bansal, Mrinal K SenAbstract:We have implemented a 3D finite-difference scheme to simulate wave propagation in arbitrary anisotropic media. The anisotropic media up to orthorhombic symmetry were modelled using a standard Staggered Grid scheme and beyond (monoclinic and triclinic) using a rotated Staggered Grid scheme. The rationale of not using rotated Staggered Grid for all types of anisotropic media is that the rotated Staggered Grid schemes are more expensive than standard Staggered Grid schemes. For a 1D azimuthally anistropic medium, we show a comparison between the seismic data generated by our finite-difference code and by the reflectivity algorithm; they are in excellent agreement. We conducted a study on zero-offset shear-wave splitting using the finite-difference modelling algorithm using the rotated Staggered Grid scheme. Our S-wave splitting study is mainly focused on fractured media. On the scale of seismic wavelenghts, small aligned fractures behave as an equivalent anisotropic medium. We computed the equivalent elastic properties of the fractures and the background in which the fractures were embedded, using low-frequency equivalent media theories. Wave propagation was simulated for both rotationally invariant and corrugated fractures embedded in an isotropic background for one, or more than one, set of fluid-filled and dry fractures. S-wave splitting was studied for dipping fractures, two vertical non-orthogonal fractures and corrugated fractures. Our modelling results confirm that S-wave splitting can reveal the fracture infill in the case of dipping fractures. S-wave splitting has the potential to reveal the angle between the two vertical fractures. We also notice that in the case of vertical corrugated fractures, S-wave splitting is sensitive to the fracture infill.
