Generalised relative and cumulative response functions for electromagnetic induction conductivity meters operating at low induction numbers

Relative and cumulative analytical response functions have been widely used as a powerful tool for forward modelling and interpretation of measurements obtained by electromagnetic induction conductivity meters operating at low induction numbers for one-dimensional layered earth models. These well-known functions were derived and should be used for the instruments laid on the surface of the earth. In this paper, we extended the response functions and obtained new generalised analytical expressions, which can be used for instruments carried at any height from the surface. The proposed new equations were compared with numerically constructed functions, obtained using the full solution of Maxwell's equations, and proved to be in very good agreement at low induction numbers. Quantitative analyses of the behaviour of the relative response and the depth of investigation of electromagnetic induction instruments, when raised from the ground, could also be done using the generalised functions.