Offshore electrical exploration of sedimentary basins: The effects of anisotropy in horizontally isotropic, layered media

Abstract

Our electrical method for exploring beneath the sea consists of a long, vertical, bipolar ac source, extending downward from the sea surface to the bottom of the sea and a remote, encapsulated, microprocessor‐controlled magnetometer located on the sea floor. The amplitude and phase of the magnetic field are measured over a range of suitable frequencies and transmitter‐magnetometer separations. At the low‐frequency static limit, apparent resistivity curves, similar to standard Schlumberger resistivity sounding curves, are constructed as an aid in the direct interpretation of isotropic crustal resistivity. An intermediate relatively resistive or relatively conductive zone is detectable when the transmitter‐receiver separation exceeds the order of twice the depth to the zone. The physical property resolved by the method in an anisotropic crust, which has different horizontal and vertical resistivities, is the geometric mean of the two independent resistivities. The thickness of a layer is indeterminate. A layer with a coefficient of anisotropy f responds like an isotropic layer f times thicker. At higher frequencies, when induction in the sea water is significant, the apparent resistivity curves remain valid provided locally induced current flow does not dominate the galvanic flow in the crustal material beneath the sea. The presence of some locally induced current, at the electromagnetic resistive limit, is advantageous. It enables the coefficient of anisotropy f of an anisotropic zone to be determined jointly with the mean resistivity. An approximate direct scheme involves the calculation of the apparent anisotropy, a formula which, like the apparent resistivity formula, is a function only of field observations, in particular the phase difference between the measured magnetic field and the transmitted current. The depth of penetration and the resolution of mean resistivity and anisotropy are presented in terms of Fréchet kernels and resolving kernels. The kernels are analytic for the special case of a uniform crust. The shape of the Fréchet kernels for resistivity and anisotropy are different. At low frequency, this reflects the different behaviours of the galvanic in‐phase current flow and quadrature locally induced current flow. The sensitivity function for anisotropy vanishes identically at zero frequency. The inclusion of the complication of anisotropy for the interpretation of data collected over sedimentary basins is mainly for numerical convenience. The sediments themselves are unlikely to be anisotropic on a small scale. The anisotropic behavior is due to macro‐anisotropy, the grouping together of thin isotropic layers of different isotropic resistivities. Such a grouping is introduced into both forward and inverse computer algorithms when the resolving kernels about a given depth are wider than the thickness of a typical layer.