Аннотация:In volcanic and seismically active areas, it is very important to assess land surface displacements, which can be detected by a variety of modern methods, both ground-based and satellite-based, including satellite radar interferometry. Displacements observed on volcanic slopes are often induced by internal and external processes related in one way or another to the movement of magma in the Earth's crust. For example, landslides and rockfalls caused by volcanic earthquakes, lava and pyroclastic flows forming new relief on the surface, or slope uplift/sedimentation as magma advances to the surface or, conversely, retreats from the magma source. Data on the registration of such displacements can be used to study volcanic activity in general and magmatic systems in particular. One of the approaches to the study of processes related to volcanic activity is the interpretation of measured displacements of the volcanic surface by means of building mathematical models and solving inverse problems, which is reduced to the determination of model parameters, at which the best agreement of the numerical solution with the observed data is achieved. Depending on the object of study, the model parameters make it possible to estimate the velocities of magma movement, scale, depth of occurrence and physical characteristics of the magma centre, etc. The paper presents some results of studies of volcanoes of the Kuril-Kamchatka subduction zone on the basis of data on earth surface displacements calculated by PCA interferometry methods. The recorded displacements allowed us to study in detail with the help of mathematical models the causes of anomalously rapid subsidence of the upper part of the lava field of Tolbachik in 2012-2013, eight times higher than average values, to obtain quantitative estimates of porosity, glass content and lava temperature 7 years after the volcanic eruption. We will also present estimates of the contribution of various processes to the shrinkage of the pyroclastic flow on 29.08.2019 at Shiveluch volcano, and a model of the intrusive body emplacement that formed the uplift on the western slope of Shiveluch volcano in the post-paroxysmal phase of the eruption on 11.04.2023. The research was funded by the Russian Science Foundation grant No. 23-17-00064 (https://rscf.ru/project/23-17-00064).