The equatorial mass density anomaly (EMA) is an anomalous latitudinal distribution of the atmospheric mass density, with its equinox configuration consisting of a density trough near the Earth's dip equator flanked by density crests around ±25° dip latitude. As a novel feature, this study reveals a pronounced 4-peak longitudinal pattern of the EMA, which is in reminiscence of the wave-4 like structure in the neutral wind and the equatorial ionization anomaly (EIA). It is found that the wave-4 modulation in the EMA trough region is in phase with that in the EMA crest region, in contrast to the 180° phase reversal for the case of EIA. This difference strongly suggest that although the latitudinal structure of the EMA is principally caused by the EIA via ion drag, its wave-4 pattern likely arises from different sources. The direct penetration of the non-migrating diurnal tides DE3 to the F-region height or thermal budget modulation by the composition NO at lower thermosphere are discussed as plausible candidates. Our results reveal a 4-hour phase lag between the wave-4 patterns in neutral density and wind, and a 2% peak-to-peak amplitude of the neutral density wave-4 pattern. These results find good agreements with theoretical predictions based on direct penetration of the DE3 to F-regions heights, hence strongly support this mechanism. Our observations thus add further evidences for the influence of tropical deep convection on the thermospheric dynamics.