The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and ...The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and attenuation of elastic waves in the porous medium are widely investigated in recent years. However, we have not read any reports on numerical simulation based on the BISQ equation. In this paper, following the BISQ equation, elastic wave propagation in the transversely isotropic porous medium filled with fluids is simulated by the stag-gered grid method for different frequency and phase boundary cases and the two-layer medium. And propagating characteristics of seismic and acoustic waves and various phenomena occured in the propagating process are in-vestigated when the two mechanisms are considered simultaneously.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
The uniqueness theorem of time-harmonic electromagnetic fields, which is the theoretical basis of boundary value problem (BVP) of electromagnetic fields, is reviewed. So far there are many versions of the statements a...The uniqueness theorem of time-harmonic electromagnetic fields, which is the theoretical basis of boundary value problem (BVP) of electromagnetic fields, is reviewed. So far there are many versions of the statements and proofs on the theorem. However, there exist some limitations and lack of strictness in these versions, for instance, the discussion of the uniqueness of solution without considering the existence of solution and the lack of strictness in the case of loss-less medium. In contrast with the traditional statements and proofs, this paper introduces some important conclusions on operator equation from modern theory of partial differential equation (PDE) and attempts to solve the problems on the existence and uniqueness of the solution to operator equation which is derived from Maxwell’s equations of time-harmonic electromagnetic fields. This method provides a novel and rigorous approach to discuss and solve the existence and uniqueness of the solution to time- harmonic fields in the new mathematical framework. Some important conclusions are presented.展开更多
基金State Natural Sciences Foundation of China (No. 40174012) and the Key Laboratory Foundation of the CNPC (No. GPKL0104).
文摘The Biot and Squirt-flow are the two most important mechanisms of fluid flow in the porous medium with fluids. Based on the BISQ (Biot-Squirt) model where the two mechanisms are treated simultaneously, dispersion and attenuation of elastic waves in the porous medium are widely investigated in recent years. However, we have not read any reports on numerical simulation based on the BISQ equation. In this paper, following the BISQ equation, elastic wave propagation in the transversely isotropic porous medium filled with fluids is simulated by the stag-gered grid method for different frequency and phase boundary cases and the two-layer medium. And propagating characteristics of seismic and acoustic waves and various phenomena occured in the propagating process are in-vestigated when the two mechanisms are considered simultaneously.
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.
文摘The uniqueness theorem of time-harmonic electromagnetic fields, which is the theoretical basis of boundary value problem (BVP) of electromagnetic fields, is reviewed. So far there are many versions of the statements and proofs on the theorem. However, there exist some limitations and lack of strictness in these versions, for instance, the discussion of the uniqueness of solution without considering the existence of solution and the lack of strictness in the case of loss-less medium. In contrast with the traditional statements and proofs, this paper introduces some important conclusions on operator equation from modern theory of partial differential equation (PDE) and attempts to solve the problems on the existence and uniqueness of the solution to operator equation which is derived from Maxwell’s equations of time-harmonic electromagnetic fields. This method provides a novel and rigorous approach to discuss and solve the existence and uniqueness of the solution to time- harmonic fields in the new mathematical framework. Some important conclusions are presented.
