We report the observation of the first two harmonics of the horizontally polarized kink waves excited in a coronal loop system lying at south-east of AR 11719 on 2013 April 11 .
The detected periods of the fundamental mode ( P _ { 1 } ) , its first overtone ( P _ { 2 } ) in the northern half , and that in the southern one are 530.2 \pm 13.3 , 300.4 \pm 27.7 , and 334.7 \pm 22.1 s , respectively .
The periods of the first overtone in the two halves are the same considering uncertainties in the measurement .
We estimate the average electron density , temperature , and length of the loop system as ( 5.1 \pm 0.8 ) \times 10 ^ { 8 } cm ^ { -3 } , 0.65 \pm 0.06 MK , and 203.8 \pm 13.8 Mm , respectively .
As a zeroth order estimation , the magnetic field strength , B = 8.2 \pm 1.0 G , derived by the coronal seismology using the fundamental kink mode matches with that derived by a potential field model .
The extrapolation model also shows the asymmetric and nonuniform distribution of the magnetic field along the coronal loop .
Using the amplitude profile distributions of both the fundamental mode and its first overtone , we observe that the antinode positions of both the fundamental mode and its first overtone shift towards the weak field region along the coronal loop .
The results indicate that the density stratification and the temperature difference effects are larger than the magnetic field variation effect on the period ratio .
On the other hand , the magnetic field variation has a greater effect on the eigenfunction of the first overtone than the density stratification does for this case .