The paper is focused on the surface wave field in functionally graded multi-layer transversely isotropic heterogeneous magneto-elastic reinforced media. The Geometry of the problem is formulated by considering the $(n-1)$ finite layer composite structure over a semi-infinite substance, occupying the domain: $-\infty <x,y<\infty ,$ $h_{i-1}\le z\le h_i,$ $i=1,2,\cdots n-1,$ $h_0=0$ and $h_{n-1}\le z\le \infty$. Mechanical properties of magneto-elastic heterogeneous reinforced media in wave scattering are an essential part of this study. A generalized Haskell’s [1] technique has been applied to obtain the wave scattering relation in multi-layer heterogeneous magneto-elastic media using suitable boundary conditions. Estimated wave scattering relation is in affirmation with the general Love-type surface wave relation in case of a single layered medium over a semi-infinite substance as well as multi-layered media over the semi-infinite substance. A finite difference technique is derived to obtain the group and phase velocities with shear deformation in the magneto-elastic heterogeneous reinforced media. To study the group and phase velocity in a square grid, stability conditions for introducing finite difference techniques have been derived. Using graphical representation, it has been examined that phase velocity, group velocity, and wave scattering in the layered media are affected by heterogeneity, reinforced, magneto-elastic coupling parameters, and stability ratio.

本文重点研究功能梯度多层横向各向同性非均质磁弹性增强介质中的表面波场。问题的几何是通过考虑$（ñ-\mathrm{1个}）$ 半无限物质上的有限层复合结构，占据以下领域： $-\infty <X，ÿ<\infty ，$ $H_{\mathrm{一世}-\mathrm{1个}}\le ž\le H_{\mathrm{一世}}，$ $\mathrm{一世}=\mathrm{1个}，2，\cdots ñ-\mathrm{1个}，$ $H_0=0$ 和 $H_{ñ-\mathrm{1个}}\le ž\le \infty$。磁弹性非均质增强介质在波散射中的力学性能是这项研究的重要组成部分。已应用通用的Haskell [1]技术使用合适的边界条件获得多层非均质磁弹性介质中的波散射关系。在半无限物质上的单层介质以及在半无限物质上的多层介质的情况下，估计的波散射关系与一般的Love型表面波关系是肯定的。推导了一种有限差分技术来获得磁弹性非均质增强介质中具有剪切变形的群速度和相速度。为了研究方格中的群速度和相速度，已经导出了引入有限差分技术的稳定性条件。