Plane wave decomposition is a convenient and effective method in the study of wave field. Various complex wave fields can be obtained by using plane wave composition. In this paper, the method of plane wave is used to...Plane wave decomposition is a convenient and effective method in the study of wave field. Various complex wave fields can be obtained by using plane wave composition. In this paper, the method of plane wave is used to study elastic wave propagation in inhomogeneous and anisotropic media. The f k transformation is applied to time space domain wave equation in inhomogeneous anisotropic media. As a result, the frequency wave number domain wave equation (Christoffel equation) can be obtained. Using the relation between elastic parameters or its spatial derivatives and Christoffel matrix elements, a method for solving the Christoffel matrix in inhomogeneous anisotropic media is formulated and applied to inhomogeneous TIV as well as inhomogeneous EDA media. The results obtained show that directional derivative of wave amplitude in continuum is negative, so amplitude is reduced, when propagating direction directs to velocity increasing direction; and directional derivative of wave amplitude is positive that means amplitude enhanced when propagating direction directs to velocity decreasing direction. Thus, wave amplitude depends on propagation direction (even in isotropic medium), but does not always attenuate. The conclusion that in continuum wave amplitude attenuates does not apply to all propagation direction.展开更多
During the seismic wave propagation process,as for the anisotropic lower medium,the speed is a function of the propagating direction.This article focuses on solving the problem how to get the transmittance angle and s...During the seismic wave propagation process,as for the anisotropic lower medium,the speed is a function of the propagating direction.This article focuses on solving the problem how to get the transmittance angle and speed,knowing the upper seismic wave propagation velocity and the angle of incidence conditions.The main theories used Snell law,Christoffel equation and speed characteristics.Taking the HTI medium as an example,the authors give the detailed solving process and draw the space velocity characteristic curve.展开更多
文摘Plane wave decomposition is a convenient and effective method in the study of wave field. Various complex wave fields can be obtained by using plane wave composition. In this paper, the method of plane wave is used to study elastic wave propagation in inhomogeneous and anisotropic media. The f k transformation is applied to time space domain wave equation in inhomogeneous anisotropic media. As a result, the frequency wave number domain wave equation (Christoffel equation) can be obtained. Using the relation between elastic parameters or its spatial derivatives and Christoffel matrix elements, a method for solving the Christoffel matrix in inhomogeneous anisotropic media is formulated and applied to inhomogeneous TIV as well as inhomogeneous EDA media. The results obtained show that directional derivative of wave amplitude in continuum is negative, so amplitude is reduced, when propagating direction directs to velocity increasing direction; and directional derivative of wave amplitude is positive that means amplitude enhanced when propagating direction directs to velocity decreasing direction. Thus, wave amplitude depends on propagation direction (even in isotropic medium), but does not always attenuate. The conclusion that in continuum wave amplitude attenuates does not apply to all propagation direction.
文摘During the seismic wave propagation process,as for the anisotropic lower medium,the speed is a function of the propagating direction.This article focuses on solving the problem how to get the transmittance angle and speed,knowing the upper seismic wave propagation velocity and the angle of incidence conditions.The main theories used Snell law,Christoffel equation and speed characteristics.Taking the HTI medium as an example,the authors give the detailed solving process and draw the space velocity characteristic curve.
