Impulsive moments at work

Abstract

The moments of the impulse response are a new tool for the interpretation of transient electromagnetic data. The nth moment is the integral of the impulse response weighted by time to the nth power. The zeroth- and first-order moment are equivalent to the inductive and resistive limits and the higher-order moments place emphasis on the late time data. A good approximation to the moments can be calculated relatively easily from the measured data. Also, for some simple models, the formulae for the moments are relatively simple expressions. Hence, it is comparatively easy to invert these expressions to derive source parameters from the measured moments. For example, the conductance of a thin sheet or the conductivity of a halfspace can be derived from the low-order moments. There are no analytic expressions for the high-order moments of a half-space, so the concept of realizable moments has been introduced to allow the higher-order realizable moments to be converted to a conductivity or conductance estimate. The moment data have been shown numerically to be additive. This has two ramifications. 1) The earth can be approximated by a multiplicity of small spheres and the properties of these spheres can be inverted for. A prototype-imaging scheme which does this gives promising results. 2) The regional or background response can be subtracted from the data and the residual anomaly can be modelled. Because the modeling algorithms are fast, they can be incorporated into inversion schemes linked to database packages such as Geosoft montaj.