## 1 Introduction  
Tsunamis are one of the most destructive coastal hazards in the world [1]. According to the March 2016 Japanese National Police Agency, the 2011 Tohoku earthquake (Mw 9.0) was the fourth largest measured earthquake in history and generated a tsunami resulting in massive casualties and property damage (15,894 deaths, 6152 injuries, 2562 missing). Even areas where no floods were predicted were damaged [2]. To better anticipate tsunamis, several tsunami observation networks are now in operation throughout the world. For instance, the Deep-ocean Assessment and Reporting of Tsunamis (DART) system is a global tsunami observation network (Pacific Ocean = 47 stations, Atlantic Ocean = 7 stations, and Indian Ocean = 6 stations) that has successfully forecasted and warned of transoceanic tsunamis [3]. The DONET system operated by Japan is another tsunami observation network, consisting of 150 offshore ocean bottom-mounted sensors with seismometers and ocean bottom pressure gauges spaced 30-60 km apart along the Japan Trench. They are connected by 5800 km of fiber optic cables [3]. Japan also operates tsunami observation instruments based on Global Positioning System (GPS) buoys along the coast of Japan [4]. All of these networks observe real-time tsunamis and contribute to increased tsunami forecasting accuracy [5; 6].  
Earthquakes located on the west coast of Japan, where the 1983 Akita and Okushiri tsunami of 1993 earthquakes occurred, generate tsunamis that damage coastal cities on the east coast of Korea [7]. The Korea Meteorological Administration operates a tsunami warning system using a network of coastal surge gauges and tidal gauges. Since these instruments are located in coastal areas, it is difficult to issue advance tsunami warnings for the coastal areas in the Korean peninsula. In addition, the coastal tsunami observation instruments record strongly distorted tsunami waves due to, for example, the effects of resonances in bays and bottom bathymetry. It means that the tsunami wave loses the properties of the source that generated it when it is approaching the coast. Therefore, coastal tsunami observation instruments are not proper for tsunami source inversion, while the tsunami source inversion plays a crucial role in tsunami forecasting [8]. Tsunami source inversion is a method to estimate the tsunami source location based on seismic information and tsunami waveforms recorded by offshore instruments. This method increases the accuracy of tsunami forecasting, including tsunami height at coastal communities [5,6]. Therefore, installing offshore tsunami observation instruments in terms of both tsunamis early warning and forecasting reduce damage by the tsunami.  
This study aims to identify optimal offshore regions for tsunami observation instrument deployment that will contribute to the tsunami early warning systems and increase the probability of tsunami detection based on numerical results from a number of potential tsunami scenarios and probability theory. This study also assumes that the offshore tsunami observation instruments will meet minimum specifications similar to the instruments used in the DART, DONET, and GPS buoy systems.