Electromagnetic emission caused by fracturing of piezoelectric and piezomagnetic crystals in plates and its application for remote sensing of explosions and natural seismic and volcanic phenomena were studied theoretically. The difference of emission from piezoelectric and piezomagnetic plates in cases of explosions versus seismic and volcanic phenomena enables use of this analysis method for phenomenon identification. The analysis herein is based on a model of a plate of finite size with a uniformly moving crack. It has been demonstrated that time-dependent mechanical stresses, which exist in the vicinity of the crack apex, are sources of an alternating electromagnetic field. The nonstationary mechanical stresses in the vicinity of the moving crack cause nonstationary polarization currents, which include both potential and vortical components in the case of a piezoelectric crystal but only the vortical component in the case of a piezomagnetic crystal. In both cases, it is possible to observe the nonstationary magnetic dipole which is the source of the excited magnetic field in the near zone. Such a dipole is created due to the motion of the crack apex and depends on the specific crystalline symmetry. Comparison of the two types of crystal (piezoelectric and piezomagnetic) shows that emission from the piezomagnetic crystal is more effective. A very important result is that it is possible to observe the difference between seismic and volcanic versus industrial phenomena through analysis of the unloading wave, which is absent in the case of industrial phenomena. This opens the possibility to identify the type of disaster and take the correct decision.