# Modeling of geodetic displacement field caused by the activities of the volcano’s magma reservoir and sensitivity analysis of the parameters of the model

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Abstract

Volcanoes and their eruption indicate dynamic process of the inside of ground, which are often located along the boundaries of tectonic plates. Study of movements and surface deformation of the volcano is essential because surface deformation reflects changes in the subsurface. In the studies of crustal deformation, volcanic models provide valuable insights of the features of volcanoes and their behavior throughout time. These models have been adjusted based on geodetic and seismic geological data. According to the geometry of deformation source, various models have been proposed for volcanoes. One of the analytical geodetic displacement models is Mogi model, which assumes the volcano's magma reservoir with spherical geometry as a source of surface deformation. in the Mogi model, the Earth's crust has been described as a half-bound elastic body which is called an elastic half-space. Half-space is a planar surface, which is taken as surrounding an environment and extended indefinitely in all direction. Displacement field of the Mogi model is caused by hydrostatic pressure change in a finite spherical source with a radius smaller than its depth in an elastic half-space. Modeling of displacement field using the analytical models requires determination of rheological and geological parameters of the volcanic magma reservoir. Hence, by taking into account the assumptions about the properties of the crust in the desired area, one can obtaine displacement field from geodetic observations as the boundary value problem of the elastic models. Then geophysical and geological parameters can be obtained by solving the inverse problem. On the other hand, solving the inverse problem has many answers. Hence, optimization algorithms are used to solve this problem. Optimization algorithms gain the most likely answers. In this study, parameter extraction was performed by genetic optimization algorithm. In this algorithm mating probability 50% and mutation probability 5% was assumed for a population of 1,000 subjects. RMSE (Root Mean Square Error) of inversion was 0.006 mm. After determining the required parameters, the displacement field modeling was done by the Mogi model. Finally, The sensitivity analysis of the displacement field to changes of the model input parameters was evaluated. The purpose of sensitivity analysis is to discover changes in which the input parameters, most affected the model output. An important result that can be extracted from the sensitivity analysis is that a more sensitive parameter is a more one reliable in the parameter extraction process. By performing this analysis, the displacement field showed most sensitivity to the coordinate quantities of the source center and least sensitivity to the volume change of the quantity of magma reservoir. This analysis indicates that the Mogi model is more robust in determining the location parameters of the source, but is poor in determining the source volume change parameters. In order to extract the parameter, it can be possible to obtain the optimal value by changing the sensitive parameters and comparing the output with the observations. It is notable that the Mogi model is very sensitive to the shallow sources.

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