## 1 Introduction  
It is generally believed that tsunamis can be divided into landslide-induced tsunamis and earthquake-induced tsunamis according to their causes. Due to the long duration and large spread distance of the earthquake-induced tsunami, it causes massive disasters, such as the Indian Oceant tsunami on 26 December 2004 and the Indonesian tsunami on 17 July 2006. Some large-volume landslide-induced tsunami has the same magnitude of long run-out as earthquake-induced tsunami and also causes substantial regional impact [1,2]. By contrast, landslide-induced tsunamis have three distinctive characteristics: larger run-ups locally, delayed time of arrival and the focusing of inundation along a narrow coastline, which means that it can cause locally larger disasters than the earthquake-induced tsunamis [3,4]. For example, the Lituya Bay tsunami (9 July 1958), the largest tsunami ever recorded, produced a run-up in excess of 400 m. In fact, after the Lituya Bay tsunami, there was another tsunami that caused great damage locally. It was the Papua New Guinea (PNG) tsunami, which was caused by an underwater landslide of a total volume of 6.4 km\({}^{3}\) and resulted in a 15 m run-up and 2000 deaths [5]. These two landslides-induced tsunamis have attracted the attention of the international tsunami organization and a large number of researchers. Until today, some research results and understandings related to the generation and propagation of tsunami waves have been obtained. The relevant information and the damage of the Lituya Bay tsunami and the PNG tsunami are in Figure 1.  
The tsunami caused by landslides can be divided into three types according to the initial submerged status of the slide block (submarine, subaerial, partial subaerial). The submarine landslides, which have less moving material in total but 100 times in vertically moving distance compared to the earthquakes, have caused the same comparable and damaging tsunami [6]. For example, the 1998 Papua New Guinea [4,7], the 1992 Flores Island [8]. In general, landslides in deep water areas are subcritical. Tsunamis caused by such landslides usually do not accumulate heavily, but run away from the landslide center. [PERSON] et al. 2005 further studied the wave patterns caused by subcritical landslides and found that a free surface drop would occur where the slider enters the water, followed by a symmetric sickle-shaped free surface [1]. [PERSON] et al. 2005 also studied the tsunami characteristics caused by subcritical landslides, and found that, under strong subcritical conditions, the maximum free surface elevation increased with the increase in landslide volume and slide acceleration, and decreased with  
Figure 1: The relevant information and the damage of the Lituya Bay tsunami and the Papua New Guinea tsunami: **(a)** Lituya Bay tsunami; and **(b)** Papua New Guinea tsunami. the increase in slide velocity, while the uplifted water volume was in direct proportion to the landslide volume and Froude number [9]. For the submarine landslide-induced tsunami in the shallow water area, higher and sharper waves are usually formed due to the slower wave velocity and higher Froude number. Tsunami spread caused by the submarine landslides with rapid acceleration or deceleration has a common characteristic which is the frequency dispersion; for example, the Tsunami generated by the Papua New Guinea Landslide in 1998 [7,10]. The importance of dispersion was also demonstrated in some studies [11,12], which found that there was at least a 50% relative error of a non-dispersion model in the maximum free surface elevation simulation compared with the dispersion model. Subaerial landslide-induced tsunami is also a research hotspot [13,14]. [PERSON] et al., 2005 gives a detailed description of the initial stage of landslide tsunami, and mainly discovering that, when the sliding block enters the water, it will squeeze the water and push the water forward, forming an offshore wave that spreads attenuating to the far field.