Modeling the dynamic process of tsunami earthquake by liquid-solid coupling model

Abstract

Tsunami induced by earthquake is an interaction problem between liquid and solid. Shallow-water wave equation is often used to modeling the tsunami, and the boundary or initial condition of the problem is determined by the displacement or velocity field from the earthquake under sea floor, usually no interaction between them is considered in pure liquid model. In this study, the potential flow theory and the finite element method with the interaction between liquid and solid are employed to model the dynamic processes of the earthquake and tsunami. For modeling the earthquake, firstly the initial stress field to generate the earthquake is set up, and then the occurrence of the earthquake is simulated by suddenly reducing the elastic material parameters inside the earthquake fault. It is different from seismic dislocation theory in which the relative slip on the fault is specified in advance. The modeling results reveal that P, SP and the surface wave can be found at the sea surface besides the tsunami wave. The surface wave arrives at the distance of 600 km from the epicenter earlier than the tsunami 48 minutes, and its maximum amplitude is 0.55 m, which is 2 times as large as that of the sea floor. Tsunami warning information can be taken from the surface wave on the sea surface, which is much earlier than that obtained from the seismograph stations on land. The tsunami speed on the open sea with 3 km depth is 175.8 m/s, which is a little greater than that predicted by long wave theory, (gh)1/2=171.5 m, and its wavelength and amplitude in average are 32 km and 2 m, respectively. After the tsunami propagates to the continental shelf, its speed and wavelength is reduced, but its amplitude become greater, especially, it can elevate up to 10 m and run 55 m forward in vertical and horizontal directions at sea shore, respectively. The maximum vertical accelerations at the epicenter on the sea surface and on the earthquake fault are 5.9 m/s2 and 16.5 m/s2, respectively, the later is 2.8 times the former, and therefore, sea water is a good shock absorber. The acceleration at the sea shore is about 1/10 as large as at the epicenter. The maximum vertical velocity at the epicenter is 1.4 times that on the fault. The maximum vertical displacement at the fault is less than that at the epicenter. The difference between them is the amplitude of the tsunami at the epicenter. The time of the maximum displacement to occur on the fault is not at the beginning of the fault slipping but retards 23 s.