Depth profiles of electrical conductivity from linear combinations of electromagnetic induction measurements

Within the past 10 yr, frequency‐domain electromagnetic (FEM) induction techniques have become more and more widely used in soil science and hydrology. Each measurement of apparent electrical conductivity represents a depth‐weighted average of soil electrical conductivity. However, the depth weighting corresponding to each measurement may be very different from that required by the user. The simultaneous use of multiple measurements (with different depth weightings) should allow some aspects of the depth distribution of electrical conductivity to be inferred. We illustrate a method for obtaining linear combinations of FEM measurements to estimate the soil electrical conductivity within the depth interval of interest. The method relies on the simple fact that the measurement‐system response is linear, so that a linear combination of apparent‐conductivity readings corresponds to a linear combination of response functions. One can seek a linear combination of response functions that has desirable characteristics. This sets up an optimization problem that can be solved by standard methods, which avoids difficulties encountered with layered inversions to resolve nonlayered systems. The approach was applied to GEONICS EM31, EM34, and EM38 instruments in three examples: (i) single frequency measurements at vertical and horizontal dipole configurations, (ii) frequency measurements using the EM34 at all six possible configurations, and (iii) frequency measurements using the EM38 held at varying heights above the ground. The derived linear combinations were applied to field data from southern Australia. Soil conductivity profiles predicted using linear combinations showed good agreement with profiles measured with a conductivity probe.