Geophysicists had already cognizance of that the pervasive velocity anisotropy with varying degree in the mantle or the sedimentary rock of upper crust is an important physical property . almost all existed research works fasten on those transversely isotropic media with vertical or horizontal axis of symmetry ( ti ) . , 地球物理学者已认识到从地幔到地壳上部的沉积岩存在着不同程度的各向异性，且对具有垂直或水平对称轴的横向各向同性介质( ti )有很多的研究。
As the oil exploration aimed at anisotropy inhomogeneous porous reservoir presently , it is important to study the acoustic theory and borehole acoustic field distribution with numerical simulating so as to invent new logging methods and equipments to obtain enough information to evaluate the complex reservoir characters quantificationally and identify the hydrocarbon zone accurately 随著陆上油气勘探目标趋向孔隙结构复杂、非均质性强的油气储集层，基于地层各向同性介质的测井理论显露弊端；因此研究复杂地质条件下的井筒声场分布特徵、为储层解释和发展刚井新方法提供理论依据成为必然。
The amplitude characteristic equations of p wave and s wave in transverse isotropic media have been deduced by using the method of aki and richards , that is use the border conditions in elastic interface to solve the elastic wave equation and to decide the energy distribution of different types of wave 本文针对横向各向同性介质( ti - transverseisotropy ) ，利用aki和richards的方法，即根据弹性分界面上的边界条件求解弹性波动方程，确定各种波之间的能量分配关系，建立了横向各向同性介质中p波和sv波入射时的振幅特征方程。
By using the method of separation of variables , a recursive formula was derived for the electromagnetic fields in a circular coaxial cable with a radial conductor plate and filled with multilayered homogeneous isotropic media , and the relationship between the first and the nth layers of the electromagnetic fields was determined 摘要采用分离变量方法，推导了有径向导体板、填充均匀的多层各向同性介质的同轴线各层电磁场之间的递推关系，得到了第1层与第n层介质中电磁场的关系方程。
The software development for the studied methods is completed in the fortran and c language . after applying these new methods to the real data inversion , the better geology effect was obtained . it shows that the inversion based on the amplitude characteristic equation has better utility and wide development prospects 本文用fortran和c语言完成了所述方法的应用软件研制工作，并结合实际资料进行了参数反演，取得了较好的效果，说明了用本文建立的振幅特征方程进行横向各向同性介质多波ava参数反演是可行的，且具有广阔的发展前景。
