Modelling Data from Inside of Earth: Local Smoothing of Mean and Dispersion Structure in Deep Drill Data

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.