Dynamic Analysis for a Shallow Isosceles Trapezoid Depression Impacted by SH Waves

Abstract

This paper presents a series solution of shear horizontal (SH) wave scattering by a shallow isosceles trapezoid depression in half-space. An appropriate multiregion-matching technique was adopted to divide the analytical model into three parts, which is necessary to meet the conditions of applying the wave function expansion method. Based on the complex function method, the wave field expressions, satisfying stress-free boundary conditions, were constructed. In addition, introducing complex variables avoided the redundant formula derivation for the implementation of coordinate transformation. The unknown coefficients in the wave field expressions were solved by Fourier series expansion in a complex field, and the convergence analysis was carried out to determine the number of traction terms of the series solution. Frequency-domain and time-domain results were presented to analyze the wave motion amplification and propagation process. The proposed method not only provides a benchmark for numerical simulation results but also makes up for the limitations of the theoretical research method of trapezoidal depression topography.