Three-dimensional geomagnetic response functions for global and semi-global scale induction problems

Abstract

SUMMARY Features of the geomagnetic response functions due to a 1000 km scale isolated conductivity anomaly embedded in a radially symmetric Earth with a surface heterogeneous layer were studied by three-dimensional (3-D) global forward modelling in order to understand the fundamental characteristics of the response functions for period of about 1–100 d and to examine the validity of 1-D like treatment for some of the responses. The geomagnetic deep sounding (GDS) response function has dipolar sensitivity to the lateral electrical conductivity contrast, while the D response (ratio of the eastward to northward component of geomagnetic field variation) shows the 3-D effect as a quadrupole-like distribution having peaks outside of heterogeneity. Although GDS and D responses were used in global induction studies in the past, we examined if the horizontal transfer function (HTF), the ratios of the geomagnetic north components at a station to those at other reference station, has enough sensitivity to the mantle heterogeneity and if it is worth to be included in global conductivity soundings. Modelling result shows that the spatial distribution of anomalous HTF is somewhat similar to the projection of heterogeneity on the surface so that the information different from those due to the GDS and D responses can be obtained by the HTF. The signatures of the conductivity heterogeneity in the GDS, D and HTF are detectable if the conductivity of the 1000-kmscale heterogeneous block is more than twice as conductive or five times as resistive as the surrounding medium. Both cases have an induction number of about 0.8. The anomalous parts of the response functions due to multiple heterogeneous bodies can be represented very well by the sum of those due to each isolated heterogeneity, if an induction number of each anomalous scattering body is less than about 2. Although the linearity breaks down when the induction number is larger, the difference between them is not significant compared with typical observational error of corresponding response functions. This implies that the sensitivity to an isolated block can be applied to discuss the resolution of multiple blocks, such as conductivity distribution having checkerboard pattern, and vise versa, in 3-D inversions. The distribution of 3-D GDS response implies that 1-D like treatment of the GDS response, such as compiling single station 1-D conductivity profiles to discuss regional differences of conductivity and correcting the static shift of magnetotelluric responses with converted GDS response, may cause serious problem if lateral heterogeneity is not negligible. This shows the necessity of modelling and analyses, which are compatible with 3-D structure.