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Secrets of Reverse Time Migration
It is in fact just the same a depth migration as the phase shift migration described previously.
Why do they call it "Reverse Time" migration? We will see it now ... Go step by step ...
Why is it called Time Migration ?
It is in fact a clean depth migration. But, while we were stepping in depth steps in the phase shift migration (introduced on the former pages), here we will step in time. This is the only reason, why they call it Time Migration. We will see later on; the obtained image is in depth.
Next question: why is it called Reverse Time Migration ?
This needs a bit more considerations.
The idea of the method is; push back the recorded seismic signal into the ground and let it find its way to the position, where it came from. This is very similar to the "stereo" technology, known in the acoustic industry since a long time.
Here we have a little problem. In the "stereo" method we broadcast the records the same way, as they were recorded. The beginning of a song comes first. The sound waves pass over the listeners and dissolve, disappear somewhere in the air. This is fine. In the acoustic industry we need only a virtual image, where we might be able to identify the general directions, where the sound comes from. In our case we need a proper image of the reflector surfaces.
In case of a seismic trace; the matter is different.
Let's imagine a seismic trace, which contains only one reflected signal. When we try to push back this seismic trace into the ground in the natural way, first we see nothing. The data before the (only one) reflected signal is zero. When the signal reaches the inserting point, the wave starts to propagate in the ground. I continues, expands, ... and on the end somehow dissipates and disappears. The data behind the signal is also zero. The end of the trace is not properly defined. We could select some seconds longer recording, or we might have shortened the record during the data processing. As a result, we get an undefined nothing.
Now, try to reverse first the seismic trace in time, before forcing it back to the ground. Once something is a solution of the wave equation; using (+), or (-) sign of the time makes no difference.
Imagine, we are forcing back the trace into the ground from the end. It does not matter, where is the end of the trace, because the data behind the signal is zero, so nothing will happen, until the signal reaches the inserting point. Once it reaches it, the wave starts to propagate in the ground, forming some kind of circular shape. It will propagate, until the pushing reaches the zero time of the seismic trace. There it stops. It stops, because there will be nothing remaining to be forced back.
Example: one single reflection (reversed in time)
The last shape of the wave will show the maximum possible distance, where the returned seismic wave might have propagated.
In the real word we don't know, where our reflected waves are in the seismic trace and also we don't know, how many reflections we might expect. We know only one thing, for sure: the zero time. This is our only fix point on a seismic record. We measure everything from this point.
This is the only reason, why we have to reverse our trace. On the reversed trace we are able to measure exactly, how much time still remains; while pushing back the recorded seismic data int the ground.
It is very important to notice: we know, the original wave started from the surface (at the source location) and it returned from a reflecting point to the surface (to the receiver location). So the forced back wave will never reach the last position pictured on the last image, because we must preserve some time for the returning path as well.
Suppose, a reflection is at T two way time. The wave traveled down during t1 time and spent t2 time to come back to the surface. It does not matter, how much is the T; and how big is the t2. The t1 time will be always the time what still remains until we reach the zero time in the push back procedure. We will see this in detail on the next age.
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