描述硬弹性下卧层上的软弹性层对SH平面脉冲地震波时间响应的三种方法
Three methods for the description of the temporal response to a SH plane impulsive seismic wave in a soft elastic layer overlying a hard elastic substratum
摘要：
我们处理平坦无应力表面的情况（即，地震学应用中的地面）将空气与均匀的、各向同性的、固体下层分离，所述固体下层由入射在下层中的SH平面体波引起的均匀的、各向同性的、固体层（与地面接触）覆盖。首先在频域中进行分析，然后在时域中进行分析。频域响应是{ \it normal}，因为没有激发共振（共振在这里被理解为在没有耗散的情况下响应是无限的情况）。这在时域中的转换是散射脉冲具有相对短的持续时间。的脉冲的持续时间被示出在很大程度上是由辐射阻尼显示在虚部的配置的复杂的本征频率。阐述了三种方法的时间历程的计算，并产生了相同的数值解的各种各样的配置感兴趣的非耗散，dispersionless介质的假设下，在地球物理环境。呼吁复杂的本征频率表示的方法被证明是最简单和最物理明确的方式获得的时间历程（在相同的假设下）。此外，它是特别适合的情况下，其中模式可以被激发时发生的入射波是不是平面或边界条件是不是无应力的变化，所有的横向坐标在地平面上。
英文摘要：
We treat the case of a flat stress-free surface (i.e., the ground in seismological applications) separating air from a homogeneous, isotropic, solid substratum overlain by a homogeneous, isotropic, solid layer (in contact with the ground) solicited by a SH plane body wave incident in the substratum. The analysis is first carried out in the frequency domain and subsequently in the time domain. The frequency domain response is {\it normal} in that no resonances are excited (a resonance is here understood to be a situation in which the response is infinite in the absence of dissipation). The translation of this in the time domain is that the scattered pulse is of relatively-short duration. The duration of the pulse is shown to be largely governed by radiation damping which shows up in the imaginary parts of the complex eigenfrequencies of the configuration. Three methods are elaborated for the computation of the time history and give rise to the same numerical solutions for a large variety of configurations of interest in the geophysical setting under the hypothesis of non-dissipative, dispersionless media. The method appealing to the complex eigenfrequency representation is shown to be the simplest and most physically-explicit way of obtaining the time history (under the same hypothesis). Moreover, it is particularly suited for the case in which modes can be excited as occurs when the incident wave is not plane or the boundary condition is not of the stress-free variety for all transverse coordinates on the ground plane.
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