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In geophysical transient electromagnetics (TEM) measurements with HTS SQUID magnetometers, a so-called 'frequency dependence' of the stacked time transients on the repetition frequency of the transmitter, and the appearance of so-called 'sign reversals', the crossover of the stacked time transients to negative values, have been observed frequently. Recently, we have shown that both of these effects can be attributed to the summing of remnant responses from earlier transmitted pulses of the repetitive transmitter waveform. Although the step function inductive response for many TEM targets decays monotonically and is positive at all times, instances of sign reversal do occur. We postulate that this sign reversal is due to the typical bipolar waveform of the TEM transmitter and the stacking procedure. In this contribution, we systematically extend our analysis to binary and ternary power-law expressions for the step function response, modeling measured responses for typical ground structures. The conditions are determined under which sign reversals appear. It is shown that the effect occurs mainly in the case where a shallow slope response is followed by a rapidly decaying response at late times. Such a signal is typically measured on a resistive overburden over a conducting medium. As an example, data are presented from a location where a sign reversal was measured with a SQUID whereas none was found in the coil data. A deconvolution procedure for determining the single pulse response from measured SQUID data is proposed.