Modelling Data from Inside of Earth: Local Smoothing of Mean and Dispersion Structure in Deep Drill Data Mathematik, Informatik und Statistik - Open Access LMU - Teil 01/03

In this paper we analyse data originating from the German Deep Drill Program. We model the amount of 'cataclastic rocks' in a series of measurements taken from deep drill samples ranging from 1000 up to 5000 meters 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 easily speaking 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 we have to tackle three different peculiarities of the data 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.