Theory review

With one schematic, the fundamentals of the correlation conjecture concept are easily digested. Figure 1 shows the incident plane wave acting as a virtual or 'ghost' source as it is reflected from the free surface. One final arm-wave will cover the rest of the plane waves needed for a successful passive seismic experiment and not pictured in the figure. Conventional seismology assumes an impulsive source and a randomly distributed subsurface that we attempt to deconvolve. The premise of this experiment lies in switching those two roles. If we have a structured earth and a random distribution of sources buried within it we can deconvolve, in much the same manner, our recorded signals to return the impulse response of the earth. Therefor, the perfect experiment would have sufficient noise activity to illuminate the free surface from every incidence angle, and around all azimuths.

 

noise
Figure 1 (a)Given a simple earth model, an upcoming plane wave will be recorded with measurable move-out unless incidence angle is zero or its azimuth is perpendicular to the receiver line. (b) Each plane wave reflecting from the free surface provides only one reflection path to each receiver. (c) Correlating all traces with each other yields a second data space with components indicative of subsurface structure and the incident energy.

Cross correlating each trace with every other trace manufactures a 5D data volume of pseudo-shots very analogous to conventional data, although here, the structure of the earth will be in the form of its autocorrelation. Visualization of the 3D volume constructed from one line is much easier on the brain and one notices that the main diagonal of the cube is the autocorrelations (analogous to zero offset and the CMP location) and successive lessor diagonals are correlations of traces with increasing offset. At the same time, the correlation process will illuminate our need to know our source timing and shape.

Given any one receiver line, only ray-paths contained in the plane defined by the receiver line and the 90^o azimuth to it will have zero move-out across the line. These events will contribute a direct event of infinite velocity and no reflected energy as azimuth will be maintained along its travel path. This thought experiment highlights the problem that only direct ray paths traveling in the same azimuth as the receiver line will catch a ghost reflection. This topic is addressed more fully in the next paper in this volume Artman (2002b).

To investigate the efficacy of these assertions, I will use the existing data from a Santa Clara, California seismology campaign that benefits from the recent shooting of a 2D profile across the same area.