Magneto-seismological estimates of plasma gradients as a function of height in the atmosphere relative to τ₅₀₀₀ = 1. The left hand panel shows the magneto-seismologically determined radial expansion (solid line) with the 95% confidence level shown (dashed lines). The diamonds and crosses show the expansion inferred from the measurements of the Gaussian width and modelling (estimated), respectively, with standard errors given. The middle panel shows magneto-seismological estimate for the gradient of the magnetic field (solid) and the inferred magnetic expansion (crosses). The right hand panel is the density gradient determined using the measured displacement amplitude (solid) with 95% confidence intervals (dashed), and a combination of the modelled (estimated) width and measured phase speed (crosses). The red lines are exponential fits to the data points.