##### Magnetotelluric response on vertically inhomogeneous earth having conductivity varying linearly with depth

Author:
D. Kao

Journal name: Geophysical Prospecting

Issue: Vol 30, No 6, December 1982 pp. 866 - 878

DOI: 10.1111/j.1365-2478.1982.tb01344.x

Organisations:
Wiley

Language: English

Info: Article, PDF ( 525.75Kb )

Summary:

Magnetotelluric response is studied for an inhomogeneous medium having conductivity varying linearly with depth as σ(*z*) =σ_{1}+α*z*. For a medium having conductivity increasing linearly with depth, the phase of the impedance approaches 60° at long periods and the apparent resistivity becomes log (ρ_{a}) = 2 log (1.36/α^{1/3}) — 1/3 log (*T*'). The asymptote of log (ρ_{a}, *T*'→∞) when plotted against log (*T*') has a constant gradient —1/3 and has an intercept on the log (*T*') axis, which equals 6 log (1.36/α^{1/3}). When a homogeneous layer with a moderate thickness overlies an inhomogeneous half-space, this layer does not affect the asymptote, but it affects the cut-off period and pushes this toward the long period direction. For a medium having conductivity decreasing linearly with depth, the impedance is equivalent to that of a Cagniard two-layer model; the intercept period related to the thickness is *T*'_{0}=σ_{1}(*h*_{2}/2)^{2}. Homogeneous multilayer approximations to an inhomogeneous layer are also investigated, and it is shown that the fit to the model variation depends on the number of layers and the layer parameters chosen.

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