In this talk, I will first give a brief introduction to Thurston earthquake theory and describe a new result on the equivalence between Thurston norms of earthquake measures and cross-ratio distortion norms of circle homeomorphisms. The second part of the talk concerns the earthquake measure induced by the topological conjugacy in Denjoy’s theorem on circle diffeomorphisms. I will show that the Denjoy inequality immediately implies that the Thurston norm of the induced earthquake measure is finite if the rotation number is of bounded type, which then implies that the topological conjugacy is quasisymmetric.