## Abstract

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 L_{α}(v) can be expressed as a function of frequency v by L_{α}(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.

Original language | English |
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Pages (from-to) | 258-264+6 |

Journal | IEEJ Transactions on Fundamentals and Materials |

Volume | 130 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 |

## Keywords

- Conductive/dielectric matrix
- Electromagnetic wave
- Fractal
- Frequency dependence
- Seismo-EM radiation
- Skin depth

## ASJC Scopus subject areas

- Electrical and Electronic Engineering