Comparing observed behavior (event data generated during process executions) with modeled behavior (process models), is an essential step in process mining analyses. Alignments are the de-facto standard technique for calculating conformance checking statistics. However, the calculation of alignments is computationally complex since a shortest path problem must be solved on a state space which grows non-linearly with the size of the model and the observed behavior, leading to the well-known state space explosion problem. In this paper, we present a novel framework to approximate alignments on process trees by exploiting their hierarchical structure. Process trees are an important process model formalism used by state-of-the-art process mining techniques such as the inductive mining approaches. Our approach exploits structural properties of a given process tree and splits the alignment computation problem into smaller sub-problems. Finally, sub-results are composed to obtain an alignment. Our experiments show that our approach provides a good balance between accuracy and computation time.