Introduction

() provides a one-dimensional proof that sparked the idea of imaging the subsurface without a source. By auto-correlating time series collected on the surface of the earth, he shows that one can produce the equivalent to a zero-offset time section. () extends the one-dimensional proof of that conjecture, through plane-wave decomposition, to full space. Importantly, he also shows that by cross-correlating each receiver with every other, one constructs pseudo shot gathers as a function of offset. These gathers are identical to conventional shot gathers and can be treated as such throughout further processing steps.

 

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Figure 1 (a) Cartoon showing the incident plane-wave energy reflecting from the free surface and then again from a buried reflector. (b) Time-series built from arrivals depicted in left panel. (c) Correlations of signals from receivers r1 and r2.

The cartoon in Figure shows schematically how an upcoming wave-train, $P(\theta)$, will reflect from the surface and act as a source at receiver r1 for the subsurface reflection recorded at r2. An intuitive understanding of this experiment and the manufacture of pseudo shot gathers can be developed by progressing through the panels of Figure from the earth model in panel (a) through the raw data recording in panel (b) to the correlated records in panel (c) where the fast-axis is now in units of correlation lag.

The correlation step has two important functions when applied to raw passive data. First, it collapses to an impulse the long source functions of the ambient sound energy recorded at each station. Second, it develops hyperbolic move-out of these impulses as a single input trace is correlated with data from stations at increasing offset. Figure shows a representative gather from a synthetic passive dataset over a two-layer earth-model.

 

shot Figure 2 Representative pseudo shot gather from data cube generated by cross-correlating all traces from a modeled passive seismic dataset. The raw data trace that has been correlated with all the others serves as the source location for the gather. Notice the ``virtual multiple'' at 0.11 seconds. This arises due to the partial correlation of the two reflectors between themselves. The greater the velocity contrast, the less visible this event. Its zero-offset time is equal to the difference in time between the two events.

After the pseudo shot gathers are constructed through correlation, a conventional five-dimensional data volume is ready for any common processing flow such as sorting and migration. However, I show that it is possible to migrate the raw data directly with a shot-profile migration algorithm that has been modified to use an areal source rather than a conventional impulse or wavelet. I present comparisons of both methods performed on modeled data and comment on some of their characteristics and costs.