A typical geoacoustic inversion procedure involves powerful source transmissions received on a large-aperture receiver array. A more practical approach is to use a single moving source and/or receiver in a low signal to noise ratio (SNR) setting. This paper uses single-receiver, broadband, frequency coherent matched-field inversion and exploits coherently repeated transmissions to improve estimation of the geoacoustic parameters. The long observation time creates a synthetic aperture due to relative source-receiver motion. This approach is illustrated by studying the transmission of multiple linear frequency modulated (LFM) pulses which results in a multi-tonal comb spectrum that is Doppler sensitive. To correlate well with the measured field across a receiver trajectory and to incorporate transmission from a source trajectory, waveguide Doppler and normal mode theory is applied. The method is demonstrated with low SNR, 100-900 Hz LFM pulse data from the Shallow Water 2006 experiment.