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Data and wavefield dimensionality

To implement a better imaging condition that is also feasible, it is important to understand 3-D prestack data and wavefield dimensionality. 3-D prestack seismic data are defined in a 5-D continuum (t,xs,ys,xg,yg) Biondi (1998), where t is time, xs,ys and xg,yg are the surface coordinates of the sources and the receivers, respectively.

After applying the first step of shot-profile migration (source and receiver wavefield construction) the dimensionality of the data increases. Thus, for each shot position (xs,ys) the source and the receiver wavefields ${\bf u}(x,y,z,t)$ and ${\bf d}(x,y,z,t)$ are defined in four dimensions (Figure [*]), where (x,y,z) are the image space dimensions.

 
match3
Figure 1
Data dimensionality. The source and receiver wavefields are 6-D datasets.
match3
view

In the following analysis, we explain how to combine the source and the receiver wavefields to obtain an image. For simplicity, we restrict our analysis to 2-D prestack data. In this case, the source and the receiver wavefields are 4-D datasets defined in (x,z,t) for each shot position xs.


next up previous print clean
Next: 1-D imaging conditions Up: Valenciano and Biondi: Deconvolution Previous: Introduction
Stanford Exploration Project
7/8/2003