My students and I devise new algorithms to improve the imaging of reflection seismic data. Images obtained from seismic data are the main source of information on the structural and stratigraphic complexities in Earth's subsurface. These images are constructed by processing seismic wavefields recorded at the surface of Earth and generated by either active-source experiments (reflection data), or by far-away earthquakes (teleseismic data). The high-resolution and fidelity of 3-D reflection-seismic images enables oil companies to drill with high accuracy for hydrocarbon reservoirs that are buried under two kilometers of water and up to 15 kilometers of sediments and hard rock. To achieve this technological feat, the recorded data must be processed employing advanced mathematical algorithms that harness the power of huge computational resources. To demonstrate the advantages of our new methods, we process 3D field data on our parallel cluster running several hundreds of processors.