Implications of the Born approximation for the magnetotelluric problem in three‐dimensional environments

Abstract

A first‐order Born approximation is obtained for the integral equations governing the surface magnetotelluric response over a three‐dimensional earth. Although accurate only in cases of low resistivity contrasts, the resulting expressions: (1) exhibit a linear relationship between a spatial perturbation in subsurface resistivity and the ensuing perturbation on the surface field response, and, more importantly, (2) allow arbitrary degrees of complexity in the geometrical characteristics of the subsurface. The linear system solutions derived from the Born approximation are studied by examining the properties of their associated kernels. These kernels may be thought of as a suite of horizontal magnetotelluric “wavelets” weighting the subsurface resistivity distribution at different depth levels. Analytical expressions for the wavelets are obtained in the wavenumber domain, thus generating a suite of magnetotelluric “transfer functions.” Expressions for the latter are particularized to the cases of one‐ and two‐dimensional geolectric media yielding results consistent with the characteristics of the magnetotelluric fields known to hold in these low‐order environments. Inspection of the electric transfer functions reveals severe sensitivity to near‐surface lateral variations of resistivity, which persists even at deep sensing frequencies. This near‐surface sensitivity is the result of an additive term in the electric field transfer functions, the static component, acting as a spatial highpass filter of the lateral variations of surface resistivity. A second additive component in the electric transfer functions, the induction component, functions as a spatial lowpass filter of the lateral variations in subsurface resistivity, and is primarily responsible for the inductive part of the surface electric field response. A common problem in magnetotelluric interpretation, the electric static effect can be reduced by inverting the role of the static component, i.e., by spatially low‐pass filtering the surface electric field. The suggested low‐pass filter for such an operation is one for which the cutoff wavenumber increases with frequency and is therefore insensitive to the response from the induction component. Low‐pass filtering of the surface electric field is best implemented in the field if the electric dipoles are deployed end‐to‐end continuously along a survey path. The magnetic field transfer functions, on the other hand, exhibit a single induction term with band‐pass filter properties which may actually lead to some amount of local distortion on the measured surface magnetic field. We propose to reduce this distortion by referring all electric field measurements to the primary magnetic field within the survey area. The primary magnetic field components, in turn, can be estimated by the spatial average of the magnetic measurements acquired at an array of magnetic stations. The suggested procedures for both the acquisition and processing of natural electric and magnetic field data encompass altogether a novel adaptation of the magnetotelluric method.