Through one-way reciprocity, Wapenaar et al. (2004) shows how to synthesize reflection data from passively collected seismic data for 3D inhomogeneous media. Key in the proof is the distinction that correlations from only single sources may be calculated and then summed over many sources to produce the correct result. This is simple when utilizing earthquake codas Nowack et al. (2003) or using novel experimental geometries for active surveys Yu and Schuster (2004). This is impossible when imaging with truly passive data where the source is the unknown ambient noisefield.
I assume that field data from a passive recording campaign can neither be parameterized by nor separated into wavefields from individual sources. In this case, correlation of the entire long data volume leads to an unavoidable summation of the wavefields from all the subsurface sources. Through Fourier analysis of correlation, I will show this inherent summation due to processing all sources as one large wavefield.
Summing the wavefields from all sources violates the rigorous definition of the result of correlating traces from a passive data collection. The output volume is not identical to the conventional reflection experiment. This report assumes the utility Artman and Shragge (2003) and mathematic justification Artman et al. (2004) for direct migration of passive data as a starting point. Several synthetic models are presented to highlight the complexity introduced by not separating individual wavefields for processing as well as successful imaging with the direct migration technique. Finally, images from the passive array installed at the Valhall oil prospect in the North sea will be introduced.