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Influence of timescales on the generation of seismic tsunamis

机译：时间尺度对地震海啸产生的影响

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摘要

A new semi-analytical solution is derived in a linear potential framework for simulating tsunami-like water waves caused by a dynamic sea ground deformation. The movement generating the tsunami is represented by a simplified model of the sea-floor displacement caused by a schematic seismic event. This displacement generalises the earlier work of Hammack (1973) and Todorovska and Trifunac (2001), in the sense that both the rise time (t(r)) in the vertical direction and the rupture propagation velocity (v(p)) in the horizontal direction are simultaneously included in the model. The influence of both parameters is investigated by applying the linear solution to a large range of parameter values. An analysis of the maximum amplitude of generated waves allows the identification of a resonance for no rise time (t(r) approximate to 0) and a rupture propagation velocity close to the long wave celerity (v(p) approximate to root gh), corroborating the resonance mechanism identified by Todorovska and Trifunac (2001). An empirical relationship is proposed to estimate the amplification factor as a function of the fault length. In a second step, an energetic ratio is defined representing the quantity of potential energy that is not taken into account properly when using the shallow water equations. The energetic ratio is estimated as the fraction of potential energy associated with wavelengths shorter than the long wave limit. This ratio is largest for rapid vertical motions, in particular in the vicinity of the resonant condition, suggesting that models based on the shallow water equations should not be used for these conditions. Numerical simulations using a nonlinear and dispersive wave propagation model are also performed, showing that the resonance effect still exists when nonlinear effects are included. Finally, the tsunami event of 1947 near New Zealand is analysed and shown to be close to the resonant condition, with seismic activity generating a free surface wave that could be much larger than the amplitude of the ground motion. (C) 2017 Elsevier Masson SAS. All rights reserved.
机译：一种新的半分析解决方案是在线性电位框架中来模拟由动态海面变形引起的海啸样水波。产生海啸的运动由由示意性地震事件引起的海地位移的简化模型表示。这种位移概述了哈默（1973）和Todorovska和Trifunac（2001）的早期工作，即垂直方向上的上升时间（T（r））和破裂传播速度（v（p））水平方向同时包括在模型中。通过将线性解决方案应用于大范围的参数值来研究两个参数的影响。对产生波的最大幅度的分析允许识别不上升时间的共振（T（R）近似为0），并且接近长波Celerity的破裂传播速度（V（P）近似于根GH），证实托杜罗夫斯卡和三瓣（2001）鉴定的共振机制。提出了一种经验关系来估计作为故障长度的函数的放大因子。在第二步骤中，定义能量比率表示在使用浅水方程时不适当地考虑的电位能量。估计能量比例是与长波极限短的波长相关的潜在能量的分数。对于快速垂直运动，该比率最大，特别是在谐振条件附近，表明基于浅水方程的模型不应用于这些条件。还执行使用非线性和色散波传播模型的数值模拟，示出在包括非线性效应时仍然存在谐振效果。最后，分析了1947年近新西兰的海啸事件，并被证明接近共振条件，地震活动产生的自由表面波可以远远大于地面运动的幅度。 （c）2017年Elsevier Masson SAS。版权所有。

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