Mirror mode waves are commonly observed in planetary magnetosheaths. Their magnetic signatures are often periodic but occasionally appear as intermittent increases of field magnitude (peaks) or as intermittent decreases (dips). We define quantitative mirror structure identification criteria and statistically analyze the distributions of the various forms. A survey of all the relevant magnetometer data in the Jovian magnetosheath reveals that mirror mode structures are present 61.5% of the time. Two-thirds of the events include waves that are either quasi-periodic or aperiodic, while 19% contain dips and 14% contain peaks. The amplitude and period of quasi-periodic and periodic structures appear to increase as the residence time of the flowing plasma within the sheath increases. Peaks are primarily observed on the dayside in the high ¿ plasmas of the middle magnetosheath. Dips are observed mostly in low ¿ plasma near the magnetopause and on the flanks. A phenomenological model for the evolution of mirror structures that accounts for these observations has been developed. We propose that the mirror structures form near the bow shock and undergo an initial growth phase during which their amplitude increases linearly. Structures that dwell in anisotropic, high ¿ plasma may saturate nonlinearly as described by Kivelson and Southwood <1996>. We interpret field magnitude peaks as the signatures of such nonlinear saturation. Finally, we ascribe the dip signatures to the process of stochastic decay of mirror structures as flow away from the subsolar point carries the structures into lower ¿ plasma.