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虽然钻井中的声波传播理论已比较成熟，但在纵、横渡的激发机制方面仍存在着一些不同的观点。本文通过对纵、横波割线积分进行分析，导出了其远场近似解的表达式，并探讨了稳态情况下的共振和非共振纵、横波振幅的衰减问题，获得的主要结论如下：（1）共振纵、横波皆有几何扩散现象。其中，共振纵波的振幅按Z－1衰减；而共振横波的振幅则近似按衰减。（2）共振纵波的振幅与岩石、流体密度比P2／P1及纵、横波速度vP和vs有关；而共振横渡的幅度值除与上述几个因素有关外，还与共振频率、井半径α和流体速度vf有关。（3）非共振纵波的几何衰减介于z－1和［zln（z／α）］－1之间；而非共振横渡的几何衰减则介于z－2和之间。（4）在纵、横渡远场近似解中不存在奇点。
Although the sound wave propagation theory in drilling is relatively mature, there are still some different opinions on the excitation mechanism of vertical and horizontal crossing. Based on the analysis of the secant integrals of longitudinal and transverse waves, this paper derives the expressions of far-field approximate solutions and discusses the attenuation of resonance and non-resonant longitudinal and transverse wave amplitudes under steady-state conditions. The main conclusions are as follows: 1) resonant longitudinal and transverse waves all have geometric diffusion phenomenon. Among them, the amplitude of the resonant longitudinal wave attenuation Z-1; and the amplitude of the resonant shear wave is approximately attenuated. (2) The amplitude of resonant longitudinal wave is related to the density of rock and fluid, and the fluid density is related to P2 / P1 and the longitudinal and transverse wave velocities vP and vs. In addition to the above several factors, the amplitude of resonance crossover is related to the resonance frequency, Fluid velocity vf related. (3) The geometric attenuation of nonresonant longitudinal waves is between z-1 and [zln (z / α)] -1; the geometric attenuation of non-resonant transverse waves is between z-2 and. (4) There is no singularity in vertical and horizontal far-field approximations.