Although tsunamis generated by submarine mass failure are not as common as those induced by submarine earthquakes, sometimes the generated tsunamis are higher than a seismic tsunami in the area close to the tsunami source, and the forecast is much more difficult. In the present study, reciprocal Green's functions are proposed as a useful tool in the 10 forecast of submarine landslide tsunamis. The forcing of the continuity equation due to depth change in a landslide is represented by the temporal derivative of the water depth. After a convolution with the reciprocal Green's function, the tsunami waveform can be obtained promptly. Thus, various tsunami scenarios can be considered once a submarine landslide happens, and a useful forecast can be formulated. When a submarine landslide occurs, the various possibilities for tsunami generation can be analysed, and a useful forecast can be devised. 15
IntroductionA Tsunami is a serious hazard to coastal cities and its forecast is essential for hazard mitigation. Of all tsunami hazards, seismic tsunamis are easier to forecast because earthquake information can be retrieved and broadcast very quickly. With the aid of elasticity theories and regression formula for assessing the length scale of fault ruptures, the tsunami source can be estimated with satisfactory accuracy. Based on Green's function (GF; see, e.g. Wei et al., 2003), reciprocal Green's function 20 (RGF; see, e.g. Chen et al., 2012), or real-time direct simulation, the propagation of tsunami is calculated in a short time. The coastal inundation then can be obtained by real-time direct simulations, analytical solutions (see, e.g., Lin et al. 2014), orpre-calculated inundation maps (see, e.g., Chen et al., 2015). Some of the approaches mentioned above have been integrated and an economical forecast system has been developed to provide both offshore water surface elevation and an inundation map (Chen et al. 2015). The efficiency and robustness of these systematic analyses are superior to real-time equation-solving, 25 as has been shown in previous studies.Besides seismic tsunamis, a few recent events are believed to be closely related to submarine mass failure (SMF). For example, the 1998 Papua New Guinea Tsunami (Tappin et al., 2001), the 2007 Chilean Tsunami (Sepúlveda et al., 2010) and the 2018 Sulawesi Tsunami (Heidarzadeh et al., 2019) all occurred after submarine earthquakes. However, in each case the earthquake was not strong enough to generate a big tsunami. The devastating tsunamis following the earthquake were all 30