Inverse problems are crucial in various scientific and engineering fields requiring intricate mathematical and computational modeling. An example of such a problem is the Full Waveform Inversion (FWI), which is used in a number of geophysical applications like oil reservoir discovery. Central to solving FWI is Reverse Time Migration (RTM), a Geophysical algorithm for high-resolution subsurface imaging from seismic data that poses considerable computational challenges due to its extensive memory and computation demands. A typical approach to address the memory constraints of RTM includes decomposing the processing tasks in multiple GPUs, checkpointing the intermediate results, and rematerializing the computation from checkpoints when needed. This paper introduces a novel checkpoint prefetching mechanism called GPUZIP. It combines Revolve, a well-known checkpoint algorithm, and GPU-based data compression to improve checkpoint memory utilization. GPUZIP was designed to allow the flexible utilization of different compression algorithms and target applications. Experimental results show that the combination of prefetching and GPU data compression enabled by GPUZIP significantly improves the computation-to-communication ratio for the RTM application. Speed-ups of up to 3.90x and a remarkable 80x Host-to-Device data transfer reduction when running a well-known geophysics benchmark have been achieved. The proposed approach mitigates the computational challenges of RTM and suggests that potential applicability and performance improvements could also be achieved in other scientific computing fields.