Technical Papers - Airborne Electromagnetics

The Moments of the Impulse Response: A new paradigm for the Interpretation of Transient Electromagnetic Data

Richard S. Smith, Fugro Airborne Surveys, Ottawa, Canada and Terry J. Lee, Canberra, Australia

Abstract

The n^th moment of the transient electromagnetic impulse response is the integral with respect to time of the impulse response weighted by time to the n^th power. The low-order moments reduce to familiar quantities: the zeroth moment (n=0) is the inductive limit, the first moment is the resistive limit. Furthermore, the higher-order moments can be of particular benefit - they put greater emphasis on the late-time data, and hence can bring out features in the data that are more conductive or deeper. 

An advantage of the method outlined for calculating the moments (and hence the inductive and resistive limit) is that these quantities are independent of any distortion of the waveform from an ideal impulse. Hence, it is not necessary to deconvolve the data prior to estimating the moments. 

If the conductor has a single exponential decay, the moments are proportional to the n^th power of the time constant of the exponential. This means that it is relatively easy to estimate the time constant from the moments. For the case of a conductive sphere model, the moments of the impulse response can be calculated more simply than the full transient solution. The moments of the sphere response are proportional to the response parameter to the n^th power, which is why the more conductive features are emphasised for the higher-order moments.

In a field example, the high-order moments emphasise conductive features, but also show the noise present in the late-time data. A discrete feature evident in moments 3 through ten has been modeled as a conductor at 90 m depth with a radius of 45 m and a conductivity of 9.4 S/m.

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