In this paper, we studied the propagation of Love waves in multilayered viscoelastic orthotropic medium in the presence of initial stress by using finite difference scheme. The closed form of dispersion relation is established and has found in the complex form for the case of $(n-1)$ layers lying over a half-space. Real part and imaginary part of the dispersion relation is derived for one layer lie over a half space correspond to dispersion curve and attenuation curve respectively. It has been shown that the acquired dispersion equation is in affirmation with the classical Love wave equation for both the cases when single and double layers lie over a half space. The stability criterion for the utilized finite difference technique and the expression for the phase and group velocity have been formed. The effect of viscoelastic parameter, initial stress on phase velocity and attenuation coefficient of Love wave has been studied. Moreover, phase and group velocity alteration for different values of Courant number has been illustrated by means of graphs.

在本文中，我们使用有限差分格式研究了初始应力存在下多层粘弹性正交各向异性介质中Love波的传播。色散关系的封闭形式成立，并在复形式中找到$(n-1)$层位于半空间上。分别对应色散曲线和衰减曲线的半个空间上的一层，导出色散关系的实部和虚部。已经证明，当单层和双层位于半个空间上时，所获得的色散方程与经典的 Love 波动方程是一致的。已经形成了所利用的有限差分技术的稳定性判据以及相速度和群速度的表达式。研究了粘弹性参数、初始应力对Love波相速度和衰减系数的影响。此外，还通过图表说明了不同库朗数值下的相位和群速度变化。