The electric field profiles of broad-bandwidth coherent terahertz (THz) pulses, emitted by laser-wakefield-accelerated electron bunches, are studied. The near-single-cycle THz pulses are measured with two single-shot techniques in the temporal and spatial domains. Spectra of 0-6 THz and peak fields up to approximately or = 0.4 MV cm(-1) are observed. The measured field substructure demonstrates the manifestation of spatiotemporal coupling at focus, which affects the interpretation of THz radiation as a bunch diagnostic and in high-field pump-probe experiments.