Magnetometric resistivity (MMR) anomalies of two‐dimensional structures

Abstract

An inexpensive, rapid method has been developed for computing all three components of the magnetic field due to galvanic current flow from a point electrode in the vicinity of a conductive subsurface structure of infinite strike‐length and arbitrary cross‐section. For any three‐dimensional (3-D) structure, the magnetic field may be written as a sum of surface integrals over boundaries defining changes in conductivity by a direct modification of the Biot‐Savart law. The integrand of each surface integral includes the components of the electric field tangential to the boundary, which may be evaluated on the boundary using a standard integral equation technique. In the case of a two‐dimensional (2-D) structure, a reformulation of the theory by taking a one‐dimensional Fourier transform along the strike results in the reduction of both the surface integrals necessary to solve the integral equation for the electric field, and the integrals used in computing the magnetic field, to line integrals in wavenumber domain. We evaluate the integrals numerically and solve the integral equation for each of about ten wavenumbers; finally, we obtain the magnetic field in space domain through a concluding one‐dimensional inverse Fourier transform. Type curves and characteristic curves for the simple model of a buried horizontal cylinder beneath a thin layer of conductive overburden are constructed. In the absence of overburden, the half‐width of the anomaly is linearly related to the depth of the cylinder. In the presence of overburden, the form of the anomaly may be predicted in a simple manner from the corresponding anomaly in the absence of overburden, provided the distance from the current source is sufficiently large for most of the available current to have penetrated the overburden.