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Acoustic waveform inversions can provide estimates of volume flow rate and erupted mass, enhancing the ability to estimate volcanic emissions. Previous studies have generally assumed a simple acoustic source (monopole); however, more complex and accurate source reconstructions are possible with a combination of equivalent sources (multipole). We deployed a high‐density acoustic network around Yasur volcano, Vanuatu, including acoustic sensors on a tethered aerostat that was moved every ∼15–60 min. Using this unique data set we invert for the acoustic multipole source mechanism using a grid search approach for 80 events to examine volume flow rates and dipole strengths. Our method utilizes finite‐difference time‐domain modeling to obtain the full 3‐D Green's functions that account for topography. Inversion results are compared using a monopole‐only, multipole (monopole and dipole), simulations that do not include topography, and those that use a subset of sensors. We find that the monopole source is a good approximation when topography is considered. However, initial compression amplitude is not fully captured by a monopole source so source directionality cannot be ruled out. The monopole solution is stable regardless of whether a monopole‐only or multipole inversion is performed. Inversions for the dipole components produce estimates consistent with observed source directionality, though these inversions are somewhat unstable given station configurations of typical deployments. Our results suggest that infrasound waveform inversion shows promise for realistic quantitative source estimates, but additional work is necessary to fully explore inversion stability, uncertainty, and robustness.