Gap-native time-domain geomagnetic depth sounding of mantle conductivity from hourly observatory records

Under segment-rejection workflows, electromagnetic sounding of the mantle from observatory records is limited less by the Fourier transform than by segmentation. Such workflows discard otherwise usable data around gaps, dilute transient storm energy within long windows, and estimate responses only after imposing a fixed source geometry. We present a time-domain alternative (TD-GDS) that estimates mantle conductivity directly from hourly series, without transforming the data at any stage. Its forward operator is a modal relaxation spectrum, verified against an independent propagator solution across five decades of period and structurally non-negative by construction. An epoch-wise source-aware spatial separation feeds two gap-native estimation arms: non-negative least squares and a state-space scheme that co-estimates the source. On clean, continuous synthetic data the chain reproduces the frequency-domain benchmark. Under gaps the two diverge: the segmented Fourier chain’s usable period range collapses by an octave and more as coefficient-level gaps rise, and its deep-layer error grows by an order of magnitude. The time-domain arms hold the full range at unchanged accuracy. Non-segmented Fourier estimators keep the range too, which isolates segmentation rather than the transform as the limiting step. The same pattern is reproduced on real records: on two independent observatory networks, after injecting gaps sampled from the empirical outage distribution of real observatory records, the gap-native chain retains the long-period range and remains consistent with responses predicted by three published conductivity models. The segmented chain retains no long-period estimate to compare. A negative control quantifies the effect of omitting source-aware separation. Local-time-locked ring-current asymmetry produces a coherent bias in single-station estimates that is shared by every sample, so robust weighting cannot remove it and only modelling the geometry can. The full chain is demonstrated end to end using six years of data from 12 mid-latitude observatories, recovering the major storms at correct absolute times and returning a conductivity profile consistent with published models. It also quantifies its own resolution limit: six years leave published lower-mantle models statistically indistinguishable. The discriminating information lies beyond the resolved band and therefore requires the substantially longer observatory records this chain is built to exploit. Uncertainties are reported with the systematic terms separated, including errors-in-variables attenuation that a variance estimator does not capture. TD-GDS complements frequency-domain practice under the non-ideal conditions in which long-period data are acquired.