Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these met...Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.展开更多
To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order vel...To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic （VTI） media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.展开更多
Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumb...Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.展开更多
The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and...The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.展开更多
This article provides the application of the high-order, staggered-grid, finite-difference scheme to model elastic wave propagation in 3-D isotropic media. Here, we use second-order, tempo- ral- and high-order spatial...This article provides the application of the high-order, staggered-grid, finite-difference scheme to model elastic wave propagation in 3-D isotropic media. Here, we use second-order, tempo- ral- and high-order spatial finite-difference formulations with a staggered grid for discretization of the 3-D elastic wave equations of motion. The set of absorbing boundary conditions based on paraxial approximations of 3-D elastic wave equations are applied to the numerical boundaries. The trial re- sults for the salt model show that the numerical dispersion is decreased to a minimum extent, the accuracy high and diffracted waves abundant. It also shows that this method can be used for modeling wave propagation in complex media with the lateral variation of velocity.展开更多
Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coeff...Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.展开更多
Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to ...Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.展开更多
There is usually source effect in the field work of controlled-source audio-frequency magnetotelluric method.Source effect is a thorny problem during field working,data processing and interpretation.Therefore,it is ve...There is usually source effect in the field work of controlled-source audio-frequency magnetotelluric method.Source effect is a thorny problem during field working,data processing and interpretation.Therefore,it is very important for the results of field prospecting to model source effect and summarize its influence rules.Based on the previous research,the authors use 3D finite difference method to simulate the electromagnetic field and set different anomaly situation to study the source effect in near-field measurement,then conclude the influence rules of source effect.Simulations provide the reference for the actual field work and data processing to correct the influence of source effect,so the information of the underground will be more approaching to the real.展开更多
The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the...The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its stag- gered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of nu- merical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.展开更多
In this paper, we firstly derive the stability conditions of high-order staggered-grid schemes for the three-dimensional (3D) elastic wave equation in heterogeneous media based on the energy method. Moreover, the plan...In this paper, we firstly derive the stability conditions of high-order staggered-grid schemes for the three-dimensional (3D) elastic wave equation in heterogeneous media based on the energy method. Moreover, the plane wave analysis yields a sufficient and necessary stability condition by the von Neumann criterion in homogeneous case. Numerical computations for 3D wave simulation with point source excitation are given.展开更多
Wave propagation in the viscoacoustic media is physically dispersive and dissipated.Completely excluding the numerical dispersion error from the physical dispersion in the viscoacoustic wave simu-lation is indispensab...Wave propagation in the viscoacoustic media is physically dispersive and dissipated.Completely excluding the numerical dispersion error from the physical dispersion in the viscoacoustic wave simu-lation is indispensable to understanding the intrinsic property of the wave propagation in attenuated media for the petroleum exploration geophysics.In recent years,a viscoacoustic wave equation char-acterized by fractional Laplacian gains wide attention in geophysical community.However,the first-order form of the viscoacoustic wave equation,often solved by the conventional staggered-grid pseu-dospectral method,suffers from the numerical dispersion error in time due to the low-order finite-difference approximation.It is challenging to completely eliminate the error because the viscoacoustic wave equation contains two temporal derivatives,which stem from the time stepping and the amplitude attenuation terms,respectively.To tackle the issue,we derive two exact first-order k-space viscoacoustic formulations that can fully exclude the numerical error from the physical dispersion.For the homoge-neous case,two formulations agree with the viscoacoustic analytical solution very well and have the same efficiency.For the heterogeneous case,our second k-space formulation is more efficient than the first one because the second formulation significantly reduces the number of the wavenumber-space mixed-domain operators,which are the expensive part of the viscoacoustic k-space simulation.Nu-merical cases validate that the two first-order k-space formulations are effective and efficient alternatives to the current staggered-grid pseudospectral formulation for the viscoacoustic wave simulation.展开更多
The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the dat...The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the data in the frequency domain, which is very suitable for parallel computation. With the advantage of MPI and based on an analysis of the flow of the 3D magnetotelluric serial forward algorithm, we suggest the idea of parallel computation and apply it. Three theoretical models are tested and the execution efficiency is compared in different situations. The results indicate that the parallel 3D forward modeling computation is correct and the efficiency is greatly improved. This method is suitable for large size geophysical computations.展开更多
Tensor controlled-source audio-frequency magnetotellurics （CSAMT） can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most...Tensor controlled-source audio-frequency magnetotellurics （CSAMT） can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional （3D） staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory Broyden- Fletcher-Goldfarb-Shanno （LBFGS） method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic, the isotropic inversion will introduce errors to the interpretation.展开更多
The elasticity, viscosity, and the relationships derived from rheology weakness properties are taken into account in mechanics. Comparing with the corresponding relationships derived from damage mechanics, we find the...The elasticity, viscosity, and the relationships derived from rheology weakness properties are taken into account in mechanics. Comparing with the corresponding relationships derived from damage mechanics, we find the weakness factor has the same significance as the damage factor. We simulate the wave field using a staggered-grid pseudospectral method to show the influence of the weakness factor qualitatively. Applying the analytical solution of plane waves, we give the velocity and attenuation coefficient of three body waves, which are affected by the wave frequency and the weakness factor of saturated discrete media. Our results show that velocity decreases with increasing weakness factor, the attenuation coefficient increases with an increase in the weakness factor, and that the influence of weakness depends on the mode of the body waves.展开更多
Based on Carcione-Leclaire model,the time-splitting high-order staggered-grid finite-difference algorithm is proposed and constructed for understanding wave propagation mechanisms in gas hydrate-bearing sediments.Thre...Based on Carcione-Leclaire model,the time-splitting high-order staggered-grid finite-difference algorithm is proposed and constructed for understanding wave propagation mechanisms in gas hydrate-bearing sediments.Three compressional waves and two shear waves,as well as their energy distributions are investigated in detail.In particular,the influences of the friction coefficient between solid grains and gas hydrate and the viscosity of pore fluid on wave propagation are analyzed.The results show that our proposed numerical simulation algorithm proposed in this paper can effectively solve the problem of stiffness in the velocity-stress equations and suppress the grid dispersion,resulting in higher accuracy compared with the result of the Fourier pseudospectral method used by Carcione.The excitation mechanisms of the five wave modes are clearly revealed by the results of simulations.Besides,it is pointed that,the wave diffusion of the second kind of compressional and shear waves is influenced by the friction coefficient between solid grains and gas hydrate,while the diffusion of the third compressional wave is controlled by the fluid viscosity.Finally,two fluid-solid(gas-hydrate formation)models are constructed to study the mode conversion of various waves.The results show that the reflection,transmission,and transformation of various waves occur on the interface,forming a very complicated wave field,and the energy distribution of various converted waves in different phases is different.It is demonstrated from our studies that,the unconventional waves,such as the second and third kinds of compressional waves may be converted into conventional waves on an interface.These propagation mechanisms provide a concrete wave attenuation explanation in inhomogeneous media.展开更多
In the process of accurate interpretation of multi-wave seismic data,we wanted to solve the problem of multi-wave information recognition.Based on techniques of elastic wave forwarding,targeting the geological model o...In the process of accurate interpretation of multi-wave seismic data,we wanted to solve the problem of multi-wave information recognition.Based on techniques of elastic wave forwarding,targeting the geological model of a reservoir of an oil field exploration area,we used a high-order staggered-grid difference technology to simulate many shots of seismic records of nonzero offset shots,implemented multi-wave seismic data processing to acquire the CMP of P waves and converted waves,NMO traces of CCP pre stacks,including AVA information and superposition profiles.Based on the AVA calculation of the model,the layer parameters of the model and the forwarding wave field relations of the P-S wave,we also compared and studied the correspondence between P waves and converted waves.The results of our analysis show that the results from simulation and from the AVO analysis are consistent.Significant wave field differences between P waves and converted waves in the same reservoir were found,which are helpful in recognizing and interpreting the multi-wave information in this area.We made use of the multi-wave data to provide the important guidelines for reservoir prediction.展开更多
Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-differ...Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.展开更多
The immersed boundary(IB)method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid.The IB formulation of such problems uses a Lagrangi...The immersed boundary(IB)method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid.The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid.It is well known that some versions of the IB method can suffer from poor volume conservation.Methods have been introduced to improve the volume-conservation properties of the IB method,but they either have been fairly specialized,or have used complex,nonstandard Eulerian finite-difference discretizations.In this paper,we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method.We consider both collocated and staggered-grid discretization methods.For the tests considered herein,the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods,and in many cases considered in this work,the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes.We also compare the performance of cell-centered schemes that use either exact or approximate projection methods.We find that the volumeconservation properties of approximate projection IB methods depend strongly on the formulation of the projection method.When used with the IB method,we find that pressure-free approximate projection methods can yield extremely poor volume conservation,whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.展开更多
基金This research is supported by the National Natural Science Foundation of China(NSFC)under contract no.42274147.
文摘Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.
基金supported by the National High-Tech Research and Development Program of China(Grant No.2006AA06Z202)the Open Fund of the Key Laboratory of Geophysical Exploration of CNPC(Grant No.GPKL0802)+1 种基金the Graduate Student Innovation Fund of China University of Petroleum(East China)(Grant No.S2008-1)the Program for New Century Excellent Talents in University(Grant No.NCET-07-0845)
文摘To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic （VTI） media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.
基金supported by the National Science Foundation of China(No.41174100)the Large-scale Oil and Gas Field and Coalbed Methane Development Major Projects(No.2011ZX05019-008-08)the China National Petroleum Corporation(No.2014A-3609)
文摘Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.
基金jointly supported by the NSF(No.41720104006)the Strategic Priority Research Program of the Chinese Academy of Sciences(A)(No.XDA14010303)+2 种基金the National Oil and Gas Project(Nos.2016ZX05002-005-007HZ and 2016ZX05014-001-008HZ)the Shandong Innovation Project(No.2017CXGC1602)the Qingdao Innovation Project(Nos.16-5-1-40-jch and 17CX05011)
文摘The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.
文摘This article provides the application of the high-order, staggered-grid, finite-difference scheme to model elastic wave propagation in 3-D isotropic media. Here, we use second-order, tempo- ral- and high-order spatial finite-difference formulations with a staggered grid for discretization of the 3-D elastic wave equations of motion. The set of absorbing boundary conditions based on paraxial approximations of 3-D elastic wave equations are applied to the numerical boundaries. The trial re- sults for the salt model show that the numerical dispersion is decreased to a minimum extent, the accuracy high and diffracted waves abundant. It also shows that this method can be used for modeling wave propagation in complex media with the lateral variation of velocity.
文摘Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.
文摘Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.
基金Supported by project of China Geological Survey(No.12120113098400)
文摘There is usually source effect in the field work of controlled-source audio-frequency magnetotelluric method.Source effect is a thorny problem during field working,data processing and interpretation.Therefore,it is very important for the results of field prospecting to model source effect and summarize its influence rules.Based on the previous research,the authors use 3D finite difference method to simulate the electromagnetic field and set different anomaly situation to study the source effect in near-field measurement,then conclude the influence rules of source effect.Simulations provide the reference for the actual field work and data processing to correct the influence of source effect,so the information of the underground will be more approaching to the real.
基金Fund Project of Key Lab of Geophysical Exploration of China National Petroleum Corporation (GPR0408).
文摘The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its stag- gered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of nu- merical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.
文摘In this paper, we firstly derive the stability conditions of high-order staggered-grid schemes for the three-dimensional (3D) elastic wave equation in heterogeneous media based on the energy method. Moreover, the plane wave analysis yields a sufficient and necessary stability condition by the von Neumann criterion in homogeneous case. Numerical computations for 3D wave simulation with point source excitation are given.
文摘Wave propagation in the viscoacoustic media is physically dispersive and dissipated.Completely excluding the numerical dispersion error from the physical dispersion in the viscoacoustic wave simu-lation is indispensable to understanding the intrinsic property of the wave propagation in attenuated media for the petroleum exploration geophysics.In recent years,a viscoacoustic wave equation char-acterized by fractional Laplacian gains wide attention in geophysical community.However,the first-order form of the viscoacoustic wave equation,often solved by the conventional staggered-grid pseu-dospectral method,suffers from the numerical dispersion error in time due to the low-order finite-difference approximation.It is challenging to completely eliminate the error because the viscoacoustic wave equation contains two temporal derivatives,which stem from the time stepping and the amplitude attenuation terms,respectively.To tackle the issue,we derive two exact first-order k-space viscoacoustic formulations that can fully exclude the numerical error from the physical dispersion.For the homoge-neous case,two formulations agree with the viscoacoustic analytical solution very well and have the same efficiency.For the heterogeneous case,our second k-space formulation is more efficient than the first one because the second formulation significantly reduces the number of the wavenumber-space mixed-domain operators,which are the expensive part of the viscoacoustic k-space simulation.Nu-merical cases validate that the two first-order k-space formulations are effective and efficient alternatives to the current staggered-grid pseudospectral formulation for the viscoacoustic wave simulation.
基金This research is sponsored by the National Natural Science Foundation of China （No. 40374024）.
文摘The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the data in the frequency domain, which is very suitable for parallel computation. With the advantage of MPI and based on an analysis of the flow of the 3D magnetotelluric serial forward algorithm, we suggest the idea of parallel computation and apply it. Three theoretical models are tested and the execution efficiency is compared in different situations. The results indicate that the parallel 3D forward modeling computation is correct and the efficiency is greatly improved. This method is suitable for large size geophysical computations.
基金sponsored by National Natural Science Foundation of China(No.41374078)
文摘Tensor controlled-source audio-frequency magnetotellurics （CSAMT） can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional （3D） staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory Broyden- Fletcher-Goldfarb-Shanno （LBFGS） method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic, the isotropic inversion will introduce errors to the interpretation.
基金0ur work is supported by the 0pen Fund of the CNPC Key Lab of Geophysical Exploration （GPKL0202）, the 0pen Fund of the State Key Laboratory of 0il and Gas Reservoir Geology and Exploitation （PLC200304）, and the Natural Science Foundation of Hubei Province （2002AB018）.
文摘The elasticity, viscosity, and the relationships derived from rheology weakness properties are taken into account in mechanics. Comparing with the corresponding relationships derived from damage mechanics, we find the weakness factor has the same significance as the damage factor. We simulate the wave field using a staggered-grid pseudospectral method to show the influence of the weakness factor qualitatively. Applying the analytical solution of plane waves, we give the velocity and attenuation coefficient of three body waves, which are affected by the wave frequency and the weakness factor of saturated discrete media. Our results show that velocity decreases with increasing weakness factor, the attenuation coefficient increases with an increase in the weakness factor, and that the influence of weakness depends on the mode of the body waves.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974018 and 11734017)the Strategic Pilot and Technology Special Fund of the Chinese Academy of Sciences,China(Grant No.XDA14020303)。
文摘Based on Carcione-Leclaire model,the time-splitting high-order staggered-grid finite-difference algorithm is proposed and constructed for understanding wave propagation mechanisms in gas hydrate-bearing sediments.Three compressional waves and two shear waves,as well as their energy distributions are investigated in detail.In particular,the influences of the friction coefficient between solid grains and gas hydrate and the viscosity of pore fluid on wave propagation are analyzed.The results show that our proposed numerical simulation algorithm proposed in this paper can effectively solve the problem of stiffness in the velocity-stress equations and suppress the grid dispersion,resulting in higher accuracy compared with the result of the Fourier pseudospectral method used by Carcione.The excitation mechanisms of the five wave modes are clearly revealed by the results of simulations.Besides,it is pointed that,the wave diffusion of the second kind of compressional and shear waves is influenced by the friction coefficient between solid grains and gas hydrate,while the diffusion of the third compressional wave is controlled by the fluid viscosity.Finally,two fluid-solid(gas-hydrate formation)models are constructed to study the mode conversion of various waves.The results show that the reflection,transmission,and transformation of various waves occur on the interface,forming a very complicated wave field,and the energy distribution of various converted waves in different phases is different.It is demonstrated from our studies that,the unconventional waves,such as the second and third kinds of compressional waves may be converted into conventional waves on an interface.These propagation mechanisms provide a concrete wave attenuation explanation in inhomogeneous media.
基金the Doctor Research Fund for Universities of China (No.20070616004)the National High Technology Research and Development Program of China (No.2007AA060505)
文摘In the process of accurate interpretation of multi-wave seismic data,we wanted to solve the problem of multi-wave information recognition.Based on techniques of elastic wave forwarding,targeting the geological model of a reservoir of an oil field exploration area,we used a high-order staggered-grid difference technology to simulate many shots of seismic records of nonzero offset shots,implemented multi-wave seismic data processing to acquire the CMP of P waves and converted waves,NMO traces of CCP pre stacks,including AVA information and superposition profiles.Based on the AVA calculation of the model,the layer parameters of the model and the forwarding wave field relations of the P-S wave,we also compared and studied the correspondence between P waves and converted waves.The results of our analysis show that the results from simulation and from the AVO analysis are consistent.Significant wave field differences between P waves and converted waves in the same reservoir were found,which are helpful in recognizing and interpreting the multi-wave information in this area.We made use of the multi-wave data to provide the important guidelines for reservoir prediction.
基金supported by the National Basic Research Program of China (No. 2013CB228604)the National Science and Technology Major Project (No. 2011ZX05030-004-002,2011ZX05019-003)the National Natural Science Foundation (No. 41004050)
文摘Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.
基金support from American Heart Association grant 10SDG4320049National Science Foundation grants DMS 1016554 and OCI 1047734.
文摘The immersed boundary(IB)method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid.The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid.It is well known that some versions of the IB method can suffer from poor volume conservation.Methods have been introduced to improve the volume-conservation properties of the IB method,but they either have been fairly specialized,or have used complex,nonstandard Eulerian finite-difference discretizations.In this paper,we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method.We consider both collocated and staggered-grid discretization methods.For the tests considered herein,the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods,and in many cases considered in this work,the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes.We also compare the performance of cell-centered schemes that use either exact or approximate projection methods.We find that the volumeconservation properties of approximate projection IB methods depend strongly on the formulation of the projection method.When used with the IB method,we find that pressure-free approximate projection methods can yield extremely poor volume conservation,whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.
