井孔声波频散方程伪瑞利波的近似解析公式

Approximate Solutions for Pseudo-Rayleigh Modes in a Fluid-filled Borehole

对于相速度介于井内流体声速和地层横波速度之间的井孔伪瑞利波模式,给出了一个近似解析公式。其解类似于无限固体夹水平流体层中的伪瑞利波模式。近似公式对所有高阶模式都给出很好的近似。

For cf < c < cs,an approximate equation for pseudo-Rayleigh modes in a fluid-filled borehole is obtained,which can be solved to obtain the dimensionless wave number explicitly as function of the phase velocity.The equation is similar to the corresponding equation for the pseudo-Rayleigh modes in a plane geometry model involving a layer of fluid between two elastic half spaces.The approximation is valid for almost all pseudo-Rayleigh higher modes.