Geostatistical simulations are used to perform a global sensitivity analysis on a model Y = f(X1 ... Xk) where one of the model inputs Xi is a continuous 2D-field. Geostatistics allow specifying uncertainty on Xi with a spatial covariance model and generating random realizations of Xi. These random realizations are used to propagate uncertainty through model f and estimate global sensitivity indices. Focusing on variance-based global sensitivity analysis (GSA), we assess in this paper how sensitivity indices vary with covariance parameters (range, sill, nugget). Results give a better understanding on how and when to use geostatistical simulations for sensitivity analysis of spatially distributed models.