GROUND-STATE CONDUCTIVITY PROFILE OF THE CORE-MANTLE SYSTEM OF THE EARTH

The ground state of the core-mantle conductivity system is defined as a step function transition from the constant non-zero conductivity of the core to zero conductivity in the mantle. This ground state is reached by letting the thickness of a transition region Δ → 0, where Δ appears as a parameter in the model conductivity of the system. By a transformation of the equation governing the behavior of the electrostatic potential φ, it is shown that the function V(x) = (1/σ 1 2)(d2σ 1 2/dx2) acts as a potential barrier in the quantum mechanical sense, and that for certain conductivity profiles σ(x), where x is the usual Cartesian coordinate, the electrostatic potential is screened out in regions where σ(x) → 0 as Δ → 0. Consequently, E = -∇φ also vanishes in these regions. The results generalize to the time-dependent case. Conditions that the conductivity function σ(x) must satisfy to qualify as the ground-state conductivity are defined and an example is provided. © 1979.