Gradient-Enhanced Kriging
My research topic was one theme throughout all thesis I had written at the university: prediction of a continuous but unknown characteristic of a natural parameter. Usually some surface in the underground, e.g. a coal seam. Whilst there are many mathematical models which existed back then, when I started in 1990, and today even more, the objetive was always to consider more available data rather than fine-tuning the mathematical models. In fact I had shown in may examples how these models can be twisted and abused in any way you want if you understand the basics.
Data cannot be created (by mathematical models). You measure it. And we measure a lot. The secret is to fuse everything in an intelligent way. That was the ultimate objetive. The vehicle I used was to include relative changes of the parameter of interest. For example the undulations of a coal seams detected by geophysics (the bare information: here it goes up, and there down by a certain gradient and within an uncertain range) within the good-old Kriging method. This method could only consider absolute measurements until the extension Prof. Menz proposed. I implemented the theory and researched the behavior of the method. It is known as:
Gradient-Enhanced Kriging
Finally the developed software contains many more methods and features, which I explain here. Some are untested and barely understood, others resulted in extended research, PhD thesis and publications (see extended research).
To achieve working and use case oriented software I had to dive into various areas:
- Geostatistics
- Numerical Mathematics
- Geophysics
- Geology
- Theoretical geodesy
- C software development on sparse resources researching fast and efficient algorithms
The subject of my PhD thesis was: Gradient Kriging – an integral geostatistical method for a joint evaluation of absolute and relative measurements