As a geophysical mathematician for Exxon, I am involved in the research and development of seismic algorithms that are used in the exploration and production of hydrocarbon reservoirs (oil and gas). An important part of the exploration task is deciphering and integrating various types of data in order to illuminate the subsurface of the earth. Seismic waves propagate and scatter in a complex fashion in accordance with the wave equation, and the seismic reflection method tells us that we can record, process, and interpret reflections from the subsurface geology to produce a picture of reflecting interfaces in the earth. The geometry and geophysical properties which are extracted from the solutions to the wave equation directly impact the drilling decisions for new and existing wells. I develop computer algorithms that use various approximations to the wave equation in order to transform the surface-recorded data so that it is easier to establish the structure of the subsurface.

The accuracy and efficiency of a method are based largely on the velocity variation and geometry that we expect and to what extent they honor the wave equation. For this reason, we need to build a collection of methods so that we can choose the appropriate one for our data. The processing for two-dimensional data gathered over an area with a gently varying velocity field with simple geology might require only five billion computer operations.