Abstract The problem of estimating seismic ground deformation is central to state-of-practice procedures of designing and maintaining infrastructure in earthquake-prone areas. Particularly, the problem of estimating the displacement field in a soft shallow layer overlying rigid bedrock induced by simple shear wave excitation has been favored by engineers due to its simplicity combined with inherent relevance for practical scenarios. We here derive analytical estimates for both the fundamental frequency and the amplitude of the first resonant mode of such systems by applying an intuitive argument based on resonance of single-degree-of-freedom systems. Our estimates do not presuppose a continuous velocity distribution, and can be used for fast assessment of site response in seismic hazard assessment and engineering design. On the basis of the said estimates of fundamental frequency and amplitude, we next propose a novel definition of “equivalent homogeneous shear modulus” of the inhomogeneous deposit, and we show that the response of the fundamental mode is controlled primarily by the properties of the layers contiguous to the bedrock. We finally discuss the validity of our argument, and evaluate the accuracy of our results by comparison with analytical and numerical solutions.

中文翻译：

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非均质土壤沉积的基本共振模式

摘要 估计地震地面变形的问题是地震多发地区基础设施设计和维护实践程序的核心。特别是，估计由简单剪切波激发引起的覆盖刚性基岩的软浅层中的位移场的问题因其简单性和与实际场景的内在相关性而受到工程师的青睐。我们在这里通过应用基于单自由度系统共振的直观论证来推导出此类系统的基频和第一共振模式的振幅的分析估计。我们的估计不以连续的速度分布为前提，可用于地震灾害评估和工程设计中现场响应的快速评估。基于对基频和振幅的上述估计，我们接下来提出了非均质沉积物的“等效均质剪切模量”的新定义，并且我们表明基模的响应主要受层的特性控制与基岩相邻。我们最后讨论了我们论证的有效性，并通过与解析解和数值解的比较来评估我们结果的准确性。