A new method for seismological investigation of the Earth's crust and the upper mantle, geodynamic processes and earthquake preparation zones has been developed using powerful vibrational sources of seismic waves. Since nuclear explosions have been prohibited, this method remains the only active method for deep seismic sounding of the Earth. Advances in the experimental research with powerful vibrators make it possible to consider the active seismology method as a new tool for studying the Earth, whose technology is similar to seismic prospecting methods. The paper considers experimental investigations with powerful vibrators and mathematical problems of geophysics connected with active seismology.