In a series of papers by Smirnova and Hayakawa, fractal analyses of the ULF emissions in the frequency range of f = 0.001–0.3 Hz have been performed based on the geomagnetic data obtained in seismic active regions including Guam Island and Izu Peninsula. A certain dynamics of the spectrum slopes and the corresponding first-order fractal dimensions have been revealed in relation to the preparation phase of some strong earthquakes (EQs). In order to advance such a fractal approach which seems to be very promising for development of the EQ forecasting methods, we consider multifractal aspects in the analysis of geophysical data dynamics. First, as a case study, the seismicity distribution in the Kobe area of Japan is concerned in relation to the powerful Kobe EQ on 17 January 1995. Applying a multifractal approach, we have revealed that there is a gradual decrease in the certain high-order fractal dimensions which were obtained from the spectrum of singularities (multifractal spectrum) of the local seismicity