  The aim of this paper is to study the Okounkov bodies associated to abundant
divisors. As a main result, we prove that the valuative Okounkov bodies of an
abundant divisor encode all the numerical properties. We apply this result to
recover the asymptotic base loci of an abundant divisor from the valuative
Okounkov bodies. We also give a criterion of when the valuative and limiting
Okounkov bodies of an abundant divisor coincide by comparing their Euclidean
volumes. To obtain these results, we prove some variants of Fujita's
approximations for Okounkov bodies using Iitaka fibrations.
