Methodology

The imaging condition for shot-profile migration () is  

$$I({\bf x},z)= \sum_\omega P^g({\bf x},z,\omega)\overline{P^s({\bf x},z,\omega)},$$ (116)

where the image, I, is a function of surface location, $\bf x$,and depth, z, and geophone and source wavefields, P^g,s, are functions of location, depth and frequency, $\omega$. I hypothesized that the correlation in the imaging condition would satisfy that in the passive seismic conjecture and make calculating the correlations prior to processing unnecessary. Further, we could rely on the dispersion relation to handle the unknown phase characteristics of the ambient noise-field rather than hoping that the correlations will collapse these wave-trains into a well-behaved wavelet.

Therefore, without making the intermediate processing step of correlating all traces with each other, we can downward continue the receiver wavefield, P^g, from every location back into the earth. This means we are migrating the entire dataset as one large shot gather. Remembering the cartoon in Figure , we can comfortably accept the same wavefield for P^s since the source wavefield is recorded by each receiver as it reflects from the free surface. Setting P^g = P^s, I then migrate the data with a modified shot-profile algorithm similar to that presented in ().