1.6 Constitutive Relations

The electromagnetic properties of rocks (σ, ε, and μ) are expressed by the constitutive relations from the previous section:

J = σE,

(1.6.1)

D = εE,

(1.6.2)

and

B = μH.

(1.6.3)

In the most general cases σ, ε, and μ are complex tensors which are functions of angular frequency ω=2πf, the field strengths, position r, temperature T, pressure P, and composition. For example,

σ = σ(ω, E, r, T, P).

(1.6.4)

In geophysics we usually normalize ε and μ by the free space values ε₀ and μ₀, and define the dielectric constant, K and relative magnetic permeability, K_m as

K = ε/ε0

(1.6.5)

and

Km = μ/μ0 ,

(1.6.6)

respectively. Furthermore, for purely traditional reasons in geophysics the conductivity is usually expressed by its reciprocal, the resistivity, ρ,

ρ = 1/σ.

(1.6.7)