Random Scattering and Uncertainty in Magnetotellurics
Wednesday, April 24, 2002 - 11:00am - 12:00pm
Benjamin White (ExxonMobil)
In magnetotelluric (MT) surveys, surface measurements of the earth's electrical impedance over a broad frequency range at a number of different sites are analyzed to produce maps of electrical resistivity in the subsurface. Naturally occurring ambient electromagnetic (EM) radiation is used as a source. In this work, we examine the effects of the earth's fine scale microstructure, which is well documented from well log resistivity measurements, on scattering of the EM waves. Using a locally plane stratified earth model, we show how MT data may be viewed as arising statistically from a smoothed effective medium version of the resistivity vs. depth profile. The difference between the data produced by the true medium and that produced by the effective medium is due to random scattering noise. This noise is fundamental to MT and other diffusive-wave EM exploration methods, since it arises from the very small spatial scales that are usually ignored. The noise has unique statistical properties, which we characterize from first principles, using a limit theorem for stochastic differential equations with a small parameter. We show that when scattering is the dominant noise source, a thin layer of increased resistivity at depth can be reliably detected only if the noise statistics are incorporated properly into the detection algorithm. This sets a new fundamental limit on the vertical detection capability of MT data. The theory agrees well with Monte Carlo simulations of MT responses from random resistivity microlayers.