We study MHD wave propagation in a gravitationally stratified isothermal viscous atmosphere of the Sun, permeated by a uniform magentic field. We perform numerical simulations by launching a slow wave on the upper boundary. The driven slow wave propagates down from lowβ- to high-β plasma across the region where the plasma β is unity. It is found that mode conversion takes place at z ≈ -1.8 in the layer β ≈ 1. The amplitudes of horizontal and vertical velocites are smaller than those obtained in the absence of viscosity.

Using the MHD coronal seismology technique, we estimated the magnetic field for three spicules observed in 2008 June. For this study, we used the high resolution Ca II H line (3968.5 ˚A) images observed by the Hinode SOT and considered a vertical thin flux tube as a spicule model. To our knowledge, this is the first attempt to estimate the spicule magnetic field using the Hinode observation. From the observed oscillation properties, we determined the periods, amplitudes, minimum wavelengths, and wave speeds. We interpreted the observed oscillations as MHD kink waves propagating through a vertical thin flux tube embedded in a uniform field environment. Then we estimated spicule magnetic field assuming spicule densities. Major results from this study are as follows : (1) we observed three oscillating spicules having durations of 5-7 minutes, oscillating periods of 2-3 minutes, and transverse displacements of 700-1000 km. (2) The estimated magnetic field in spicules is about 10-18 G for lower density limit and about 43-76 G for upper density limit. (3) In this analysis, we can estimate the minimum wavelength of the oscillations, such as 60000 km, 56000 km, and 45000 km. This may be due to the much longer wavelength comparing with the height of spicules. (4) In the first event occurred on 2008 June 03, the oscillation existed during limited time (about 250 s). This means that the oscillation may be triggered by an impulsive mechanism (like low atmospheric reconnection), not continuous. Being compared with the ground-based observations of spicule oscillations, our observation indicates quite different one, i.e., more than one order longer in wavelength, a factor of 3-4 larger in wave speed, and 2-3 times longer in period.