Petrophysical causes of electromagnetic dispersion

An electromagnetic pulse propagating through air or vacuum does not change shape, but one propagating through material may significantly alter shape with distance of propagatIOn. The change in shape is most often caused by frequency dependent material properties. All frequency dependences in material properties anse from energy loss mechanisms. Geometric spreading loss does not cause frequency dependence as the energy is not lost, but spread over the surface area of an expanding sphere about the antenna. Electrical energy loss mechanisms include intrinsic conduction thermal loss, orientational relaxation of the water molecule mechanical loss, and clay-mineral electrochemical loss. These result in complex frequency dependent dielectric permittivity. Magnetic energy loss includes magnetic domain and superparamagnetic relaxation losses, and others not well understood. These result in complex frequency dependent magnetic permeability. Frequency dependence may also result from heterogeneous distributions of these properties on spatial scales comparable to the electromagnetic wavelength in the material. The velocity of electromagnetic propagation in a material is determined by the speed of light in vacuum divided by the square root of the product of permittivity and permeability. Thus, the velocity of propagation is frequency dependent. In wet soils, this usually results in higher frequency components of a pulse attenuating and propagating faster than the lower frequency components, resulting in pulse broadening. A consequence of such changing shape in the propagating pulse is increased difficulty in performing pulse deconvolution and migration (phase coherent image reconstruction) as the pulse waveform is not everywhere the same shape and phase.