The work of Keller (1959) with decay‐time distributions is extended by incorporating ideas developed by Gross (1953) for viscoelasticity. In addition to the usual premises of linear systems theory, we introduce the postulate that the response is nonresonant. Mathematically, this postulate is that the frequency response, continued off the real frequency axis, is an analytic function of the complex variable ω, except, possibly, at purely imaginary frequencies. The singularities in the response at purely imaginary frequencies are identified with decay times. There are two decay‐time distribution functions, one associated with resistivity and one associated with conductivity. The former is the inverse Laplace transform of the voltage response to a current step, and the latter is the inverse Laplace transform of the current response to a voltage step. These two decay spectra are not the same; in the normal situation where resistivity decreases and conductivity increases with increasing (real) frequency, the conductivity decay times are shorter than the corresponding resistivity decay times. There are several relations between the resistivity decay spectrum and the usual IP measures. The initial value of the time‐domain voltage curve is proportional to the integral over the spectrum of resistivity decay times. The area under the time‐domain voltage curve, divided by its initial value, is the mean of the distributed resistivity decay times. Finally, PFE and phase shift are roughly proportional to the strength of the resistivity decay in the relevant spectral region.
