The Moments of the Impulse Response, a New Paradigm For the Interpretation of Transient Electromagnetic Data

We define the nth moment of the transient electromagnetic impulse response as the definite integral with respect to time of the time-domain "quadrature" magnetic-field impulse response weighted by time to the nth power. The time-domain quadrature response is the full impulse response with the delta function component at zero time removed. The zeroth moment (n=0) is numerically equal to the frequency-domain inductive limit, and the first moment is the resistive-limit response. The higher-order moments successively put greater emphasis on the late-time data, and hence can bring out features in the data that are more conductive or deeper.