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针对圆弧状沉积谷地对平面SH波的二维散射问题,曾有学者提出一种闭合形式的解析解,将波的散射问题转化为一无穷维代数方程组求解,但较高的入射波频率会导致该方程组的系数矩阵病态,从而限制了该解析解适用的频带范围。沿用这种闭合式的解析解的求解思路,并通过选择坐标系避免了线性方程组的求解,散射波函数的待定系数具有明确的解析表达式,因此在一个非常宽的频带范围内给出了该散射问题的解析解,并探讨了入射波与谷地特性对地面运动的影响。
Aiming at the two-dimensional scattering problem of plane SH waves in arc-like sedimentary valleys, some scholars have proposed a closed form analytical solution that transforms the wave scattering problems into an infinite-dimensional algebraic equations, but the higher incident wave frequency Which leads to the ill-posed coefficient matrix of the system of equations, thus limiting the applicable frequency range of the analytical solution. Following the idea of solving this closed analytic solution and solving the system of linear equations by choosing a coordinate system, the undetermined coefficients of the scattering wave function have explicit analytic expressions, thus giving a very wide frequency range The analytical solution to this scattering problem and the effect of incident wave and valley properties on ground motion are discussed.