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In this paper we compare the $\mathbb J$-stratification (or the semi-modulestratification) and the Ekedahl-Oort stratification of affine Deligne-Lusztigvarieties in the superbasic case. In particular, we classify the cases wherethe $\mathbb J$-stratification gives a refinement of the Ekedahl-Oortstratification, which include many interesting cases such that the affineDeligne-Lusztig variety admits a simple geometric structure.

The Ekedahl-Oort Stratification and the Semi-Module Stratification