This paper discusses the use of robust geostatistical methods on a multivariate data set of sediments in the Lake Geneva in Switzerland. Each variable is detrended via nonparametric estimation penalized with a smoothing parameter. The optimal trend is computed with a smoothing parameter based on cross-validation. Then, variograms are estimated by a highly robust estimator of scale. The parametric variogram models are fitted by generalized least squares, thus taking account ofthe variance-covariance structure of the variogram estimates. Kriging has been performed inside the Lake Geneva boundaries, and results are in close agreements with the geographical surroundings. The comparison of the kriging results with and without detrending the data relieved the importance of the trend detection and trend removing, and that a simple model with constant trend for this data set is not satisfactory. All these computations are done with the software S+SpatialStats, extended with new functions in Splus that are made available.