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Field Programmable Gate Arrays (FPGA) offer significant potential speedups over conventional microprocessors for some applications. For downward continued migration, complex math and Fast Fourier Transforms (FFT) are the dominant cost. Convolution is the dominant cost for reverse time migration. We implement these core algorithms on a FPGA and show speedups ranging from 5 to 15, including the transfer time to and from the processors. We consider methods to further speed up these migration algorithms.