Random Scattering and the Detection Capability of the Magnetotelluric Method

  • Benjamin S. White
  • Werner Kohler
  • Leonard J. Srnka
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 91)


Typical well logs show that formation electrical resistivity varies substantially as a function of depth in the earth. These variations consist typically of slow-scale macroscopic changes or trends, modulated by rapid variations due to fine scale layering. The rapidly varying resistivity fluctuations are significant in amplitude and occur over small spatial scales, down to the resolution of the logging tool. Using a plane stratified earth model, we examine the effects of this fine scale microstructure on the scattering of the naturally occurring electromagnetic waves used in magnetotellurics (MT). We show theoretically how MT data are influenced by the multiscale nature of the formation resistivity. MT data may be viewed as arising largely from a smoothed “effective medium” version of the resistivity vs. depth profile. The difference between the data produced by the actual medium and that produced by the effective medium is due to scattering noise arising from the layering microstructure. We model this fine scale layering as a rapidly varying stochastic process. This scattering noise component of MT data is fundamental since it arises from the very structure of the medium being probed. This noise is substantial at frequencies above ≈0.1Hz and has unique statistical properties, which we characterize. We assess the impact of this noise upon the detectability of a thin layer of increased resistivity at depth. We show that the theory agrees well with Monte Carlo simulations.


Half Space Effective Medium Apparent Resistivity Surface Impedance Effective Medium Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Vozoff, K., The magnetotelluric method, 1991, Electromagnetic Methods in Applied Geophysics-Applications, Chapter 8, edited by Nabighian, M. N., Society of Exploration Geophysicists.Google Scholar
  2. [2]
    Zhdanov, M. S. and Keller, G. V, 1994, The Geoelectrical Methods in Geophysical Exploration, Elsevier.Google Scholar
  3. [3]
    Kaufman, A. A. and Keller, G. V., 1981, The Magnetotelluric Sounding Method, Elsevier.Google Scholar
  4. [4]
    White, B. S., Kohler, W. E. and Srnka, L. J., Random Scattering in Magnetotellurics, to appear in Geophysics.Google Scholar
  5. [5]
    O’Doherty, R. E and Anstey, N. A., 1971, Reflections on Amplitudes, Geophysical Prospecting, 11, 430–458.Google Scholar
  6. [6]
    Khasminskii, R. Z., 1966, On stochastic processes defined by differential equations with a small parameter, Theory of Probability and its Applications, 11, 211–228.Google Scholar
  7. [7]
    Parker, R. L., 1994, Geophysical Inverse Theory, Princeton University Press.Google Scholar
  8. [8]
    Melsa, J. A. and Cohn, D. L., 1978, Decision and Estimation Theory, McGraw-Hill.Google Scholar
  9. [9]
    Srnka, L. J. and Crutchfield, W. Y. II, 1987, Riccati inversion of magnetotelluric data, Geophysical Journal of the Royal Astronomical Society, 91, 211–228.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Benjamin S. White
    • 1
  • Werner Kohler
    • 2
  • Leonard J. Srnka
    • 3
  1. 1.ExxonMobil Research and Engineering CompanyAnnandale
  2. 2.Department of MathematicsVirginia TechBlacksburg
  3. 3.ExxonMobil Upstream Research CompanyHouston

Personalised recommendations