Mathematical principles of the integral kinematics of impulsive electromagnetic disturbances in absorbing media
© Shuman V.N., Reva N.V.
The mathematical aspects of the integral kinematics of impulsive electromagnetic disturbances in the quasitationary (diffusive) domain are analyzed. The novelty if the conception is that the integral kinematics in the diffusive approximation is defined by the "centers of gravity" and "centers of inertia" of excitations as "times" of their arrival at the electromagnetic echo registration points. Here the process description itself is accurate in the same sense in which the laws of mechanics describing the "center of masses" propagation in dynamics are accurate. The key element of the performed generalization consists in four mathematical theorems from which simple analytical dependents of the remote hodographs and their velocities on the geoelectrical section parameters have been obtained. A detailed scheme of their proofs is given. The mathematical results presented not only elucidate the physics of the process but also clarify the main phenomena appearing in the propagation of impulsive electromagnetic excitations in absorbing media. On the whole, the diffusive kinematics is not only seen to be an instrument of the qualitative study of the process but also an important element of the further improvement of the electromagnetic sounding systems.