The mirror structures identified by the depressed or enhanced magnetic field associated with the enhanced or depressed plasma density are widely observed in the solar system plasma. These structures are generated by the mirror instability as a result of sufficiently large temperature anisotropy of T ⊥ > T ∥. Here, T ⊥ and T ∥ are, respectively, to be the temperatures perpendicular and parallel to the magnetic field and β = p/(B 2/2μ 0). Two important observed characteristics are the uneven density-magnetic field compressibility, defined as, among the various mirror events, and the anticorrelation between the temperatures and magnetic field. This study first shows two mirror structures observed in the magnetosheath with distinct β and Cρ,B. Specifically, β ∼ 6.67, Cρ,B &tild;-0.23 and β ∼ 1.44, Cρ,B &tild;-0.67. The linear kinetic theory is adopted to derive the phase relations for the mirror instability which show an inverse relation between Cρ, B and, which are negative for various parameter values, and β. While the correlation may be negative or positive for the mirror unstable and stable parameter regimes, respectively. The theoretical analyses are consistent with the observational results that δT ⊥ δB < 0 for both events and δT ∥ δB < 0 is more pronounced for the high β case. The statistical analysis results are summarized by the relationships between Cρ, B, CT⊥, B, CT∥, B, and β for six mirror wave events that show high agreements between the observations and theory.