  Let $\alpha\in(0,1)$ be an irrational, and $[0;a_1,a_2,...]$ the continued
fraction expansion of $\alpha$. Let $H_{\alpha,V}$ be the one-dimensional
Schr\"odinger operator with Sturm potential of frequency $\alpha$. Suppose the
potential strength $V$ is large enough and $(a_i)_{i\ge1}$ is bounded. We prove
that the spectral generating bands possess properties of bounded distortion,
bounded covariation and there exists Gibbs-like measure on the spectrum
$\sigma(H_{\alpha,V})$. As an application, we prove that $$\dim_H
\sigma(H_{\alpha,V})=s_*,\quad \bar{\dim}_B \sigma(H_{\alpha,V})=s^*,$$ where
$s_*$ and $s^*$ are lower and upper pre-dimensions.
