Skip to main content


We’d like to understand how you use our websites in order to improve them. Register your interest.

Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part I: Plane wave field model


In the 1-D magnetotelluric theory, a Riccati equation governs the depth variation of the impedance, or admittance, for a given distribution of the electrical conductivity. This equation can be used to compute the surface magnetotelluric functions for generally piecewise continuous conductivity profiles. In case of a simple layered medium, it provides the classical formulae for recalculating recursively the impedances between the individual layer boundaries. We present an extended version of the Riccati differential equations for generally anisotropic 1-D structures for the case of a plane wave incident field. Relation between the standard matrix propagation procedure for a layered medium and the Riccati equation approach, as a limiting case of the former, is demonstrated. In the anisotropic case, all elements of the 2 × 2 impedance tensor are present and, consequently, a system of four coupled Riccati equations has to be considered. Standard methods for the numerical solution of systems of ordinary differential equations are applied to the Riccati system, which gives an efficient alternative to the current matrix propagation procedures for the numerical evaluation of 1-D magnetotelluric impedances in anisotropic media. As an application, a synthetic study on the influence of a depth-variable regional strike on magnetotelluric decomposition results is presented, with the variable strike simulated by a variable anisotropy within the 1-D section.


  1. Abramovici, F., The forward magnetotelluric problem for an inhomogeneous and anisotropic structure, Geophysics, 39, 56–68, 1974.

  2. Bahr, K., Geological noise in magnetotelluric data—a classification of distortion types, Phys. Earth Planet. Int., 66, 24–38, 1991.

  3. Dekker, D. L. and L. M. Hastie, Magnetotelluric impedances of an anisotropic layered Earth model, Geophys. J. R. astr. Soc., 61, 11–20, 1980.

  4. Dmitriev, V. I. and M. N. Berdichevsky, The fundamental model of magnetotelluric sounding, Proc. IEEE, 67, 1034–1044, 1979.

  5. Groom, R. W. and R. C. Bailey, Decomposition of magnetotelluric impedance tensors in the presence of local 3-dimensional galvanic distortion, J. Geophys. Res.—Solid Earth and Planets, 94, 1913–1925, 1989.

  6. Hindmarsh, A. C., ODEPACK, a systematized collection of ODE solvers, in Scientific Computing, edited by R. S. Stepleman et al., pp. 55–64, North-Holland, Amsterdam, 1983.

  7. Jones, A. G. and R. W. Groom, Strike angle determination from the magnetotelluric impedance tensor in the presence of noise and local distortion: rotate at your peril!, Geophys. J. Int., 113, 524–534, 1993.

  8. Loewenthal, D. and M. Landisman, Theory for magnetotelluric observations on the surface of a layered anisotropic halfspace, Geophys. J. R. astr. Soc., 35, 195–214, 1973.

  9. O’Brien, D. P. and H. F. Morrison, Electromagnetic fields in an N-layered anisotropic half-space, Geophysics, 32, 668–677, 1967.

  10. Petzold, L. R., Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations, SIAMJ. Sci. Stat. Comput., 4, 136–148, 1983.

  11. Ralston, A., A First Course in Numerical Analysis, McGraw-Hill, New York, 578 pp., 1965.

  12. Reddy, I. K. and D. Rankin, Magnetotelluric effect of dipping anisotropies, Geophys. Prosp., 19, 84–97, 1971.

  13. Santos, F. A. M. and L. A. Mendes-Victor, 1D anisotropic versus 2D isotropic media in magnetotellurics, Acta Geod. Geoph Hung., 35, 49–61, 2000.

  14. Singh, R. P. and Y. Kant, Sensivity analysis of EM measurements over exponential varying conductivity earth models, Geophys. J. Int., 121, 111–116, 1995.

  15. Smith, J. T., Estimating galvanic distortion magnetic fields in magnetotellurics, Geophys. J. Int., 130, 65–72, 1997.

Download references

Author information



Corresponding author

Correspondence to Světlana Kováčiková.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kováčiková, S., Pek, J. Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part I: Plane wave field model. Earth Planet Sp 54, 473–482 (2002).

Download citation


  • Riccati Equation
  • Anisotropic Medium
  • Impedance Tensor
  • Anisotropic Layer
  • Decomposition Parameter