3-D modelling and analysis of superparamagnetic effects in ATEM based on the FDFD

Abstract

SUMMARY Superparamagnetic (SPM) effects lead to 1/t power-law delay approximately during the middle and late periods of transient electromagnetic responses. Ignoring SPM effects can produce large errors and cause incorrect data interpretation. Furthermore, because of the non-linearity of the Chikazumi magnetic susceptibility model, it is difficult to discretize the model in the time domain. Therefore, developing an algorithm for 3-D modelling of SPM effects in the time domain directly is difficult. In view of the above problems, we propose a 3-D modelling method of SPM effects for airborne transient electromagnetic (ATEM) data. We also introduce the widely used Chikazumi magnetic susceptibility model into the finite-difference frequency-domain (FDFD) method. According to the mapping relations between the magnetic field intensity and the magnetic permeability on the grid after discretization, we re-establish the scientific matrix of the magnetic permeability. And we adopt arithmetic averaging of the two adjacent cubes’ magnetic permeability as the magnetic permeability in boundary, which is a different setting method with the electrical conductivity. The 3-D modelling of SPM effects is successfully realized, and its maximum relative error is less than 7 per cent. We subsequently analyse the intrinsic properties of the abnormal magnetic medium, as well as the effect of the SPM unit's parameters, such as the depth, thickness, electrical conductivity, zero-frequency magnetic susceptibility, and the height of the receiver, on the response. Then, we calculate the SPM responses of 3-D magnetic bodies and analyse the influence of magnetic susceptibility and electrical conductivity on magnetite responses. The present study can provide theoretical guidance for ATEM detection in magnetic media and lay a foundation for 3-D inversion of SPM effects.