In the present paper, a study is performed in an irregular earth crust, layered over a semi-infinite half-space under the effect of gravity. The irregularities at the interface are possible combinations of geometric shapes such as rectangular, paraboic and triangular notches. The aim of the study is to come up with the influence of these irregularities on the phase velocity of shear horizontal waves. The current work also explores how inhomogeneities affect SH-wave propagation. The medium is assumed to exhibit inhomogeneities as a function of depth. These functions are the product of a linear algebraic function and an exponential function of depth. By means of separation of variables and the substitution method, the equation of motion is reduced to the hypergeometric equation. Suitable boundary conditions are employed to derive a closed form of the dispersion equation. Numerical computations are performed to visualize the impact of irregularity and inhomogeneity. It is observed that the irregular interfaces and the inhomogeneity involved in the medium have a significant effect on SH-wave propagation.

中文翻译：

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不规则地质和不均匀性对 SH 波传播的影响

在本文中，一项研究是在不规则的地壳中进行的，地壳在重力作用下分层在半无限的半空间上。界面处的不规则性可能是几何形状的组合，例如矩形、抛物面和三角形凹口。研究的目的是找出这些不规则性对水平横波相速度的影响。目前的工作还探讨了不均匀性如何影响 SH 波的传播。假定介质表现出作为深度函数的不均匀性。这些函数是线性代数函数和深度指数函数的乘积。通过变量分离和代换法，将运动方程简化为超几何方程。使用合适的边界条件来导出色散方程的封闭形式。执行数值计算以可视化不规则和不均匀性的影响。据观察，介质中的不规则界面和不均匀性对 SH 波传播有显着影响。