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.