Analysis of geophysical signals by using hilbert space geometry

Abstract

The contribution presents some results achieved by the authors during several years of research of the process of rotary drilling of rocks by using metric spaces. The authors successfully apply this approach in the solution of specific problems in geophysics and also metallurgy. The authors use abstract structures – so called Hilbert spaces - for the implementation of process signals as algebraic vectors. The geometric structure of these spaces enables mutual metric comparisons of geophysical signals in relation to the rock type and the mode of drilling. Some space is also given to the visualization of the degree of divergence between geophysical or process signals being analyzed.

Keywords

• geophysical signal
• rocks disintegration
• rotary drilling
• the Hilbert space
• inner product operation
• visualization of process