Multifractional Brownian motions in geosciences
Multifractional Brownian motions in geosciences
Editor(s): S. Gaci, J. Lévy-Véhel, C. Keylock, J. Wanliss, and. D. Schertzer
Fractional Brownian motion (fBm) is one of the most popular stochastic fractal models. It is a non-stationary process with stationary increments. It is parametrized by an exponent, H, called the Hurst exponent, which measures its self-similarity degree and long-range dependence properties. Since this model has everywhere local regularity H, it does not allow to analyze signals having a regularity which varies in time or space, as are most geophysical signals. Multifractional Brownian motion (mBm) was introduced as a generalization of fBm to overcome this limitation.

Though no longer stationary nor self-similar, mBm offers the advantage to be very flexible since it can model phenomena whose sample paths display a time/space-dependent regularity. Multifractional Brownain motion has gained acceptance in many research areas: geophysics, signal and image processing, financial data series, network traffic phenomena, and biomedicine.

There is now a significant number of papers dealing with the application of mBm in geosciences, and one purpose of this special issue is to collect scientific researches related to this topic, and thus demonstrate the contribution of mBm in our field. More importantly, we think it is of interest to let a wider audience of researchers be aware of the potential benefits of this process to foster new applications. The issue will cover the following applications and other relevant topics:
  • Well logging;
  • Petrophysical characterization of oil/gas reservoir;
  • Analysis of the geomagnetic activity;
  • Signal and image processing analysis of geological/geophysical data;
  • Topographic modeling;
  • Probabilistic and statistical properties of mBm of interest in Geosciences;
  • Processes related to or generalizing mBm.

Download citations of all papers

03 Mar 2014
Latitudinal variation of stochastic properties of the geomagnetic field
J. A. Wanliss, K. Shiokawa, and K. Yumoto
Nonlin. Processes Geophys., 21, 347–356,,, 2014
11 Sep 2013
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
J. Lévy Véhel
Nonlin. Processes Geophys., 20, 643–655,,, 2013
23 Jul 2013
Multifractal analysis of vertical profiles of soil penetration resistance at the field scale
G. M. Siqueira, E. F. F. Silva, A. A. A. Montenegro, E. Vidal Vázquez, and J. Paz-Ferreiro
Nonlin. Processes Geophys., 20, 529–541,,, 2013
12 Jul 2013
Mapping local singularities using magnetic data to investigate the volcanic rocks of the Qikou depression, Dagang oilfield, eastern China
G. Chen, Q. Cheng, T. Liu, and Y. Yang
Nonlin. Processes Geophys., 20, 501–511,,, 2013
11 Jul 2013
Intermittency and multifractional Brownian character of geomagnetic time series
G. Consolini, R. De Marco, and P. De Michelis
Nonlin. Processes Geophys., 20, 455–466,,, 2013
06 Feb 2013
Characterization of turbulence stability through the identification of multifractional Brownian motions
K. C. Lee
Nonlin. Processes Geophys., 20, 97–106,,, 2013
23 Nov 2012
Multifractal model of magnetic susceptibility distributions in some igneous rocks
M. E. Gettings
Nonlin. Processes Geophys., 19, 635–642,,, 2012
CC BY 4.0