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Changes in the electromagnetic (EM) field after an earthquake rupture but before the arrival of seismic waves (“early EM signals”) have sometimes been reported. Quantitative evaluations are necessary to clarify whether the observed phenomena are accounted for by known theories and to assess whether the phenomenon can be applied to earthquake early warning. Therefore, analytical expressions for the magnetic field generated by an impulsive line-current are derived for a conductive half-space model, and for a two-layer model; the somewhat simpler situation of a conductive whole-space is also considered. By analyzing the expressions obtained for the generated EM field, some expected features of the early EM signals are discussed. First, I verify that an early EM signal arrives before the seismic waves unless conductivity is relatively high. Second, I show that early EM signals are well approximated by the whole-space model when the source is near the ground surface, but not when it is at depth. Third, I show that the expected amplitudes of early EM signals are within the detection limits of commonly used EM sensors, provided that ground conductivity is not very high and that the source current is sufficiently intense. However, this does not mean that the EM signals are easily distinguishable, because detector sensitivity does not account for additive noise or false positive detections

An analytical expression for early electromagnetic signals generated by impulsive line-currents in conductive Earth crust, with numerical examples