The 2015 Illapel Tsunami Source Recovery by Inversion of DART Tsunami Waveforms Using the R-Solution Method TATYANA A. VORONINA, 1 VLADISLAV V. VORONIN, 2 and VLADIMIR A. CHEVERDA 3 Abstract—An approach to recovering an initial tsunami waveform with its application to the 16 September 2015 Illapel tsunami is proposed. The approach is based on inverting the remote measurements of water-level data from the deep-ocean DART buoys without a priori information on a source except for the common information about its spatial localization. The ill-posed inverse problem in question is regularized by means of a least- squares inversion using the truncated singular value decomposition method and the r-solution method. The method proposed sup- presses the instability of the numerical solution of the ill-posed problem under consideration. The computational algorithm allows one to find the way to improve the inversion by selecting the most informative set of available observation stations. The method proposed was successfully applied to the 16 September 2015 Illapel tsunami. Key words: Tsunami numerical simulation, tsunami wave- form inversion, ill-posed inverse problem, singular value decomposition, r-solution. 1. Introduction According to the United States Geological Sur- vey, the 2015 Illapel earthquake occurred on 16 September, at 22:54:32 (UT), at 31:573  S, 72:674  W and at 22.4-km depth. This earthquake (Mw 8.3, Global CMT) generated local and trans-Pacific tsu- namis that caused economic losses, fatalities and devastation along the Pacific coast of Chile. The Peru–Chile subduction zone has been historically characterized by high seismic activities due to the collision of the two plates along tectonic boundaries: the Nazca plate subducts beneath the South American plate. In the last decade, there were numerous earthquakes (Mw [8) located in this region and there is a high probability of new similar events in the same area. Thus, the common objective of all studies is to understand the characteristics of the tsunamis trig- gered along the Peru–Chile Trench. One of such characteristic features of these earthquakes and tsu- namis is that their sources are in proximity to the coast which, in turn, causes an essential decrease in the time of identifying the regions at risk and of taking decisions on evacuation. There are two important aspects of assessing the tsunami hazard in the coastal areas: the initial waves generated in the source area and their subsequent propagation. This study deals with the first of these challenges. The sources of the earthquake and of the associ- ated tsunami of the 16 September 2015 Illapel Chile event have been studied by many researches from various viewpoints using different observation data (Heidarzadeh et al. 2016; Li et al. 2016; Ruiz et al. 2016; Tilmann et al. 2016; Melgar et al. 2016; Lee et al. 2016; Calisto et al. 2016; Fuentes et al. 2016; Tang et al. 2016). An overview of these studies on tsunami source and slip distribution was presented by Satake and Heidarzadeh (2017). As a result, they have summarized the following: the largest slip is located near 31  S, 72:31  W and it is displaced, approximately, 70 km to the NW of the epicenter; the slip amount varies from 5 to 16 m in different studies. According to this review, the tsunami source zone is centered around the 31  S. This zone is assumed to be limited by a travel time curve (Heidarzadeh et al. 2016) and is extending west to 73  W, while the main 1 Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Science, Pr. Ac. Lavrentieva, 6, 630090 Novosibirsk, Russia. E-mail: tanvor@bk.ru 2 Novosibirsk State University, Novosibirsk, Russia. 3 A.A.Trofimuk Institute of Petroleum Geology and Geo- physics of Siberian Branch of Russian Academy of Science, Novosibirsk, Russia. Pure Appl. Geophys. Ó 2019 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-019-02100-y Pure and Applied Geophysics