P. Schmoldt, PhD - MTNet - DIAS

3. Mathematical description of electromagnetic relations
yields for the skin depth:
MT station
d s
Earth surface
Fig. 3.1.: Induction depth δs for an MT station over a conductive half-space.
δs =
2
. (3.44)
ωµσ
When applying ω = 2π/T, σ = 1/ρ, and the assumption that µ = µ0 = 4π10 −7 Vs/Am,
one derives an estimate for the skin depth that depends on period and subsurface resistivity,
i.e.
δs ≈ 0.5 ρT [km]. (3.45)
This approximation, however, is only valid for the case of a subsurface with homogeneous
electric resistivity, as attenuation will change accordingly, when the penetrating wave
enters an area with different electric parameters (Sec. 3.4).
For the halfspace case the lateral extent of the MT study region is roughly equivalent to
its vertical counterpart [Jones, 1983a]. The surface of a body, describing the area sensed
by an MT station for a wave of a certain period, can be approximated by a hemisphere
with its flat face coinciding with the Earth’s surface (Fig. 3.1). This circumstance enables
the investigator to plan the positioning of MT recording stations in a fieldwork campaign
by calculating the overlap of station sensitivity areas to be expected at a certain depth and
the necessary station spacing required to ensure the desired redundancy of measurements
obtained (cf. Sec. 6.1.2).
In case of a heterogeneous subsurface, δs can be approximated using the apparent resistivity
ρa (Eq. 3.60):
δs ≈ 0.5 ρaT [km]. (3.46)
For the case of a layered subsurface, the skin depth is controlled by subsequent absorption
of all layers relevant for a given period. If the energy of the penetrating wave is reduced to
1/e of the original value within the n-th layer of a known subsurface model, the respective
skin depth can be calculated as the sum of depth to the bottom of the layer n-1, i.e. dn−1,
and the skin depth in the layer n, i.e. t ′ n, (cf. Fig. 3.2):
δs = dn−1 + t ′ n. (3.47)
Whereas dn−1 is a priori known for a given model, t ′ n can be calculated using Equation
38