One-Way Wave Equation Migration (OWEM) is a depth migration algorithm used for seismic imaging. A parallel version of this algorithm is widely implemented using MPI. Heterogenous architectures that use GPUs have become popular in the Top 500 because of their performance/power ratio. In this paper, we discuss the methodology and code transformations used to port OWEM to GPUs using OpenACC, along with the code changes needed for scaling the application up to 18,400 GPUs (more than 98%) of the Titan leadership class supercomputer at Oak Ridget National Laboratory. For the individual OpenACC kernels, we achieved an average of 3X speedup on a test dataset using one GPU as compared with an 8-core Intel Sandy Bridge CPU. The application was then run at large scale on the Titan supercomputer achieving a peak of 1.2 petaflops using an average of 5.5 megawatts. After porting the application to GPUs, we discuss how we dealt with other challenges of running at scale such as the application becoming more I/O bound and prone to silent errors. We believe this work will serve as valuable proof that directive-based programming models are a viable option for scaling HPC applications to heterogenous architectures.