  The objective of the current study is to utilize an innovative method called
'change probabilities' for describing fracture roughness. In order to detect
and visualize anisotropy of rock joint surfaces, the roughness of
one-dimensional profiles taken in different directions is quantified. The
central quantifiers, 'change probabilities', are based on counting monotone
changes in discretizations of a profile. These probabilities, which are usually
varying with the scale, can be reinterpreted as scale-dependent Hurst
exponents. For a large class of Gaussian stochastic processes change
probabilities are shown to be directly related to the classical Hurst exponent,
which generalizes a relationship known for fractional Brownian motion. While
being related to this classical roughness measure, the proposed method is more
generally applicable, increasing therefore the flexibility of modeling and
investigating surface profiles. In particular, it allows a quick and efficient
visualization and detection of roughness anisotropy and scale dependence of
roughness.
