Skin depth of electromagnetic (EM) wave depends on frequency of EM wave v and electrical properties of rocks and minerals. Previous studies have theoretically assumed that the skin depth Lα(v) can be expressed as a function of frequency v by Lα(v) ∝ v -φ and φ= 1 at high frequency or φ= 1/2 at low frequency. Based on fractal theory of rocks, we point out that the frequency exponent φ reflects internal fractal structures (i.e., occupancy, distribution and connectivity) of dielectric/conductive matrices of rocks such as pores, cracks, grain boundaries, inclusions and various fluids. Laboratory measurements of dielectric constant and conductivity of granite and previous studies on various rocks as a function of frequency show that p is an exponent ranging from 1/4 to 1. By extrapolation of the skin depth by laboratory measurements at a given frequency into at other frequencies, the skin depth with variation in φ becomes longer or shorter than that by previous studies. Moreover, at a given frequency, the skin depth decreases with increasing a fractal dimension of fracture systems (decreasing φ). Thus, the skin depth of EM wave through the crust for detecting seismo-EM radiations and through rock salt domes for detecting ultra-high energy neutrinos depends on fractal structures of dielectric/conductive matrices in heterogeneous crust.
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