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The model-based spheroidal excitation approach is extended to accurately compute the transient electromagnetic response of a highly conducting and permeable object. The complete formulation is presented in the convolution form. The method is applicable to data from various sensors that measure the transient field or voltage in either the on- or off-time regime and for an arbitrary transmitter waveform. The technique is tested against state-of-the-art time-domain electromagnetic induction sensor data. The results show good agreements between modeled and measured data. In addition, numerical studies demonstrate the importance of accounting for the transmitter waveform.