The physical meaning of array invariant is the absolute traveling time of different modal from a source to a receiver under the average sound speed. It can be gotten by the derivative of the arriving time against the corresponding cosecant function of elevation angle for each modal, which can be used for the passive source localization. A vector sensor can be seen as a small volumetric array. It has its capability of elevation angle determination to describe the multi-modal propagation and the single-modal dispersion in shallow water, which may imply a chance to get the array invariant for the source localization. Here, we take advantage of the dispersion based short time Fourier transform and warping transform techniques for the time-frequency analysis of vector sensor signals. This technique can improve acoustic normal mode identification and thereby extract the modal data more accurately for array invariant determination. The idea had been effectively validated during the experiment that took place in ...