b'David Annetts best of Exploration GeophysicsFeaturethe tau domain amplitude coefficients Ai, can be extractedExtraction of the resistive limit of a target under conductive through inversion of the equation: cover D(t 1 )R(t 1 , 1 ) R(t 1 , m ) Because resistive limits are additive, the resistive limit response.A 1of a target at depth can be derived through simple subtraction\x1f \x1f \x1f= \x1f(13) of an assumed or modelled background, analogous to: : : regional-residual separation in gravity interpretation. . A m D(t n ) R(t n , 1 ) R(t n , m ) Extraction of the inductive limit of a target under conductive coverwhere D(t) is the data, R(t,t) the convolution of m exponentials with the transmitter waveform, as measured in each of theThe response at the inductive limit of a local target can be n time windows of the EM system. This inversion procedurederived by comparison with a pre-computed set of blanked is discussed in texts such as Menke (1989) or Stolz (1998).decays (Macnae et al. 1998). This process makes the assumption Stabilisation through positivity or smoothing constraints has(Liu and Asten 1993; King 1998) that the conductive cover acts been found to be a requirement. only to delay and broaden the response of the target at depth. If the free-space step response is given by equation (1), then CDI Imaging the step response of a target under thin conductive cover of conductance S is given by the sum of the overburden step The mathematical basis of this procedure can be foundresponse O(t) at the receiver and the convolution of the free-in Macnae and Lamontagne (1987) and Macnae et al.space step response of the target with the impulse response I(t) (1990). Essentially, the process involves determining theof the overburden as seen at the target:correspondence between a set of delay times t and a set of depths z. This is achieved through finding sets of times t andR(t)=O(t)+A i exp(t / i )*I(t) (15)depths z at which the amplitude A(l) of the step response decay is equal to the amplitude A(z) of calculated secondaryifield if the mirror image transmitter was at depth 2z in theWe can perform the convolution of a predetermined set of ground. The cumulative conductance at any depth z isexponentials with the (calculated) impulse response at the proportional to dtldz, and the conductivities at depth z aretarget. In equation (15), because of linearity we can strip the then given by background response O(t) to get the anomalous response of the target alone. If a look-up table is created of the results of a 1 2t set of these convolutions, it is possible to simply estimate the =0 z2 (14) free space coefficients A i , using the same linearmathematics as described in equation (13).51 PREVIEW OCTOBER 2020'