Assessment of the amplitude of seiches generated by remote earthquakes in small inland water bodies

The process of formation of seiche level oscillations initiated by remote earthquakes in small inland bodies of water is analyzed, and a method for estimating the amplitude of such oscillations is proposed. It is shown that to estimate the amplitude, a reservoir can be described by two parameters: horizontal extent and maximum period of natural oscillations. The method is based on an exact analytical solution of a one-dimensional problem within the framework of the linear theory of long waves. The method assumes knowledge of the horizontal components of seismic ground motions. For numerical calculations, the work used a record of the catastrophic earthquake in Turkey on February 6, 2023, obtained by a seismometer of the Department of Physics of the Earth, Faculty of Physics, Lomonosov Moscow State University (Moscow) at a distance of 2050 km from the epicenter. The efficiency of the method is confirmed by comparing analytical estimates with the results of two-dimensional numerical modeling conducted for a set of model basins of cylindrical shape and constant depth, as well as for reservoirs with bathymetry corresponding to real lakes. It has been shown that the earthquake in question in the water bodies of the Moscow region could have caused fluctuations in the water level with a range of up to 0.5 m.