Anisotropy tensors in magnetotelluric interpretation

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Reilly, W.I. 1979 Anisotropy tensors in magnetotelluric interpretation. [s.l.]: [s.n.]. Report / Geophysics Division 136 16 p.

Abstract: In the magnetotelluric method, the relationship between an observed horizontal magnetic field vector B[i] and an observed horizontal elecric field vector E[j] can be expressed by the complex admittance tensor Y[ij], viz. B[i] = Y[ij] E[j]. For a signal of frequency w, the response of a uniform horizontally anisotropic half-space can be characterised by the complex tensor gamma[ij] = omega.mu(i.sigma[ij] + omega.epsilon[ij]), where mu is the scalar magnetic permeability, sigma[ij] is a real apparent conductivity tensor, and epsilon[ij] a real apparent permittivity tensor. The tensors sigma[ij] and epsilon[ij] can be derived from the observed admittance tensor Y[ij] by the relationship gamma[ij] = -omega.omega.a[rs].delta[ri][tu].Y[st].Y[uj], where a[rs] is the metric tensor and delta[ri][tu] a generalised Kronecker delta defined in the horizontal plane. Inversion of the conductivity tensor sigma[ij] yields an apparent resistivity tensor ro[ij] which is comparable with those derived from general DC dipole-dipole measurements