The Impulse-Response Moments of a Conductive Sphere in a Uniform Field, a Versatile and Efficient Electromagnetic Model

Abstract

The concept of moments of the impulse response, introduced by Smith and Lee (2000), provides another means for rapid interpretation and modelling of transient electromagnetic data. This concept builds on developments made by Macnae et al. (1998Macnae et al. ( , 1999 in modelling the inductive and resistive limits. In fact, the inductive limit is the zeroth-order moment and the resistive limit is the first-order moment. ABSTRACTThe impulse response moments of a conductive sphere in free space excited by a uniform magnetic field can be used to approximate the moments of a sphere in a dipolar field. The numerical computations are straightforward and the approximation is especially good for higher-order moments. The greatest discrepancy is seen on the zeroth-order moment when the radius of the sphere is large. It is possible to improve the accuracy for the zeroth-order moment by modelling the large-radius sphere (in a dipole field) as the combined response of multiple small-radius spheres (each in a locally uniform field). The small spheres are closely packed inside the larger sphere. The discrepancy can be reduced to less than 15 % in this manner.The sphere in a uniform field can also be used to approximate the response of a body that has its currents constrained to flow in a plane with a specific orientation. This means that plate-like bodies or anisotropic spheres can also be modelled.The third-order moment has been calculated from data acquired during a MEGATEM airborne electromagnetic survey of the Reid-Mahaffy test site. There is an anomalous response in the thirdorder moment that can be modelled by a sphere at 170 m depth with a conductivity of 15 S/m and a radius of 40 m. The currents flowing in the sphere are constrained to flow in a vertical plane. This model is consistent with the geology of the area and a hole drilled to test the anomalous zone.

Survey design to maximize the volume of exploration of the InfiniTEM system when looking for discrete targets

“…The primary field H 0 of an infinitesimal dipole transmitter at the sphere can be computed using the expression (Smith and Lee, 2001):…”

“…Rather, we probe the sensitivity of the InfiniTEM system by discretizing the subsurface inside some volume of interest. Smith and Lee (2001) derived the analytic expressions required for computing the impulse response of a sphere in free space excited by a dipolar field that is assumed to be locally uniform at the sphere. An impulse response is defined as the magnetic-field response of the target once it has been subjected to an impulse in current in the transmitter.…”

“…Quantification of the effectiveness of various survey parameters of the InfiniTEM system will be assessed using this concept of the volume of influence. Smith and Wasylechko (2012) used the sphere model of Smith and Lee (2001) to determine sensitivity cross sections of AEM exploration systems. The cross sections were generated by evaluating the response of a sphere in free space excited by an elevated magnetic dipole.…”

“…The sphere model of Smith and Lee (2001) for EM modeling is used to determine the optimal survey parameters for an airborne EM system by calculating sensitivity cross sections. In contrast to the previous approach, sensitivity crosssections are not calculated.…”

A Novel Technique for Synthetic Source of Multiple Electromagnetic Data Sets*

“…The dipole approximation can efficiently calculate the coupling between the target and transmitter and receiver. The coupling coefficient between the transmitter and the target is obtained by using the formula of primary field at the target location motivated by a dipole source at transmitter position [8] . On the similar principle, the coupling coefficient between the receiver and the target can be also acquired.…”