Modelling data from inside the Earth: local smoothing of mean and dispersion structure in deep drill data

The paper describes the analysis of data originating from the German Deep Drill Program. The amount of ‘cataclastic rocks’ is modelled with data resulting from a series of measurements taken from deep drill samples ranging from 1000 up to 5000 m depth. The measurements thereby describe the amount of strongly deformed rock particles and serve as indicator for the occurrence of cataclastic shear zones, which are areas of severely‘ground’ stones due to movements of different layers in the earth crust. The data represent a ‘depth series’ as analogue to a ‘time series’, with mean, dispersion and correlation structure varying in depth. The general smooth structure is thereby disturbed by peaks and outliers so that robust procedures have to be applied for estimation. In terms of statistical modelling technology three different peculiarities of the data have to be tackled simultaneously, that is estimation of the correlation structure, local bandwidth selection and robust smoothing. To do so, existing routines are adapted and combined in new ‘two-stage’ estimation procedures.