Seismic wavefield reconstruction using reciprocity

The primary focus of most reflection seismic surveys is to help locate hydrocarbon recourses. Due to an ever increasing scarcity of these recourses, we must increase the size and quality of our seismic surveys. However, processing such large seismic data volumes to accurately recover earth properties is a painstaking and computationally intensive process. Due to the way reflection seismic surveys are conducted there are often holes in the collected data, where traces are not recorded. This can be due to physical or cost constraints. For some of the initial stages of processing these missing traces are of little consequence. However processes like multiple prediction and removal, interferometric ground roll prediction, and migration require densely sampled data on a regular grid. Thus the need to interpolate undersampled data cannot be ignored. Using the fact that reflection seismic data sets obey a reciprocal relationship in source and receiver locations, combined with recent advances in the field of compressed sensing, we show that properly regularized the wavefield reconstruction problem can be solved with a high degree of accuracy. We exploit the compressible nature of seismic data in the curvelet domain to solve regularized l1 recovery problems that seek to match the measured data and enforce the above mentioned reciprocity. Using our method we were able to achieve results with a 20.45 dB signal to noise ratio when reconstructing a marine data set that had 50% of its traces decimated. This is a 13.44 dB improvement over using the same method run without taking reciprocity into account.