This paper presents single receiver geoacoustic inversion of a combustive sound source signal, recorded during the 2017 Seabed Characterization Experiment on the New England Mud Patch, in an area where water depth is around 70?m. There are two important features in this study. First, it is shown that high-order modes can be resolved and estimated using warping (up to mode number 18 over the frequency band 20-440?Hz). However, it is not possible to determine mode numbers from the data, so that classical inversion methods that require mode identification cannot be applied. To solve this issue, an inversion algorithm that jointly estimates geoacoustic properties and identifies mode number is proposed. It is successfully applied on a range-dependent track, and provides a reliable range-average estimation of geoacoustic properties of the mud layer, an important feature of the seabed on the experimental area.