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Reverse Time Migration: Imaging.
How will we create an image out of this mess?
Consider to watch in time one single point of the U(x,z,t) wave field, where x=ix*dx, z=iz*dz and t=it*dt. For example select the xx=ixx*dx, zz=izz*dz point. Watch this point, how the wave field is changing in time.
With other words; we get the value of the U(xx, zz, t) buffer element, at the successive time steps (t=0, dt, 2dt, 3dt...). It will be a simple time function.
We have two kind of U() wave field. One, when we used the time reversed seismic traces and one when we used the source wave. Let's call the one from the reversed seismic waves as Pxxzz(t) and the other Qxxzz(t).
What can we see on these time functions as time progresses?
At the beginning, nothing. Then, we will see some disturbances at the time, when the propagating wave hits the (xx,zz) point. After that, we expect again nothing. We expect to see the same pattern on both time functions.
The (xx,zz) point can be a reflector point only, when the up-going wave in the Pxxzz(t) and the down-going wave in the Qxxzz(t) functions coincide.
To check this condition we simply compute the zero shift cross correlation between the two time functions. This zero shift cross correlation is one single number. This number will be the value at the (xx,zz) location on the final depth image.
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