Continuum mechanics with asymmetric stress field and with dense dislocation distribution;

Theoretical modeling and numerical simulations of physical processes in earthquake foci and seismic activity along faults in various time scales (single earthquakes, seismic cycles and long-term activity);

Physical interpretation of seismic source parameters (including seismic moment and energy) and statistical relations among them, for natural and induces earthquakes;

Stochastic modeling and analysis of macroscopic relations in geophysical phenomena, nonlinear stochastic time series analysis, origins of long-tail distributions and multifractal patterns;

Algorithms and methods of computer simulations including time reversal, molecular dynamic and Markov Chain Monte Carlo techniques;

Probabilistic inverse theory and its application to seismology;

Analysis and modeling of macroscopic properties of geomaterials; porous reservoirs saturated by fluids; multi-phase flows through porous media; influence on microstructure upon the macroscopic relations;

Monitoring and analysis of rotational effects generated by earthquakes and icequakes;

Theoretical and numerical analysis of earthquake premonitory processes, relations with electric and electromagnetic fields;

Cellular automata and other complex system models of geophysical phenomena;

Discrete dynamical systems and analysis of their mathematical properties.