Acoustic measurements of unheated supersonic underexpanded jets with ideally expanded Mach numbers of 1.14, 1.38, and 1.50 are presented. Of the three components of supersonic jet noise, the focus is on the broadband shock-associated noise (BBSAN) component. Motivated by the modelling of BBSAN using the wavepacket framework, a traversable microphone ring is used to decompose the acoustic pressure into azimuthal Fourier modes. Unlike noise radiated downstream, BBSAN is dominated by azimuthal modes 1-3, which are approximately 3-4 dB/St stronger than the axisymmetric component. Crucially, the relative contribution of successive modes to BBSAN is sensitive to the observer angle and jet operating condition. Four azimuthal modes are necessary to reconstruct the total BBSAN signal to within 1 dB/St accuracy for the conditions presented here. The analysis suggests, however, that the number of modes required to maintain this accuracy increases as the peak frequency shifts upward. The results demonstrate the need to carefully consider the azimuthal content of BBSAN when comparing acoustic measurements to predictions made by jet noise models built on instability theory.