Cocenters of Hecke algebras play an important role in studying mod $\ell$ or $\mathbb C$ harmonic analysis on connected $p$-adic reductive groups. On the other hand, the depth $r$ Hecke algebra is well suited to study depth $r$ smooth representations. In this paper, we study depth $r$ rigid cocenters of a connected reductive $p$-adic group over rings of characteristic zero or $\ell \neq p$. More precisely, under some mild hypotheses, we establish a Jordan decomposition of the depth $r$ rigid cocenter, hence find an explicit basis of depth $r$-rigid cocenters. Speaker(s): Ju-Lee Kim (MIT)