Effect of Water Compressibility, Sea-floor Elasticity, and Field Gravitational Potential on Tsunami Phase Speed Scientific Reports

Tsunamis can propagate thousands of kilometres across the ocean. Precise calculations of arrival times are essential for reliable early warning systems, determination of source and earth properties using the inverse problem, and time series modulation due to frequency dependency of phase speed. Far field observatories show a systematic discrepancy between observed and calculated arrival times. Models in present use and based on incompressible hydrodynamics and interaction with a rigid ocean floor overestimate the phase speed of tsunamis, leading to arrival time differences exceeding tens of minutes. These models neglect the simultaneous effects of the slight compressibility of water, sea-bed elasticity, and static compression of the ocean under gravity, hereinafter gravity. Here, we show that taking these effects into account results in more accurate phase speeds and travel times that agree with observations. Moreover, the semi-analytical model that we propose can be employed near real-time, which is essential for early warning inverse models and mitigation systems that rely on accurate phase speed calculations.

海啸（tsunami）可在大洋中传播数千公里。精准的到达时间计算，对于构建可靠的早期预警系统、通过反问题（inverse problem）确定震源与地球属性，以及校正因相速度（phase speed）频率依赖性引发的时间序列调制，均具有关键意义。远场观测台站的实测数据与计算得到的到达时间之间，存在系统性偏差。当前通用的基于不可压缩流体动力学（incompressible hydrodynamics）与刚性海底相互作用的海啸模型，会高估海啸的相速度，由此引发的到达时间偏差可达数十分钟。此类模型忽略了三项同时存在的物理效应：海水的微弱可压缩性、海底弹性（sea-bed elasticity），以及重力作用下海洋的静态压缩（下文简称重力效应）。本研究证实，将上述效应纳入模型考量后，可得到更精准的相速度与传播时间，且与实测结果一致。此外，我们提出的半解析模型（semi-analytical model）可实现准实时（near real-time）运算，这对于依赖精准相速度计算的早期预警反演模型与减灾系统而言，是不可或缺的。