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GCSeismic 
Velocities
*
By
D.S. MacPherson1
Search and Discovery Article #40150 (2005)
Posted April 4, 2005
*Adapted from the Geophysical Corner column by the author in
AAPG Explorer, April, 2005, entitled “Seismic Velocities Prove themselves
Crucial Variables.” Appreciation is expressed to the author, to Alistair R.
Brown, editor of Geophysical Corner, and to Larry Nation, AAPG Communications
Director, for their support of this online version.
1Geophysical Training International, Dallas, Texas ([email protected])
The realm of our
seismic data typically has been horizontal distance and vertical time -- but now
we are flooded with seismic data that is displayed in distance and depth.
Seismic velocities originally came to us as a by-product of the process of
stacking the data. By the geometry of the acquisition program we reference for
this column, there was a large redundancy in the reflection information designed
to produce many reflections off of the same subsurface point.
Figure 1 illustrates the very naïve assumption that source and receiver locations with the same mid-point would be reflected of the same subsurface point. The stacking process consisted of correcting each reflection for "normal moveout" that was the direct result of two parameters. These are the source-to-receiver offset and the subsurface velocity. When all of the reflectors were perfectly aligned, the traces with a common midpoint could be summed to produce a stacked trace.
The source-to-receiver
offset was known from the acquisition geometry, but the unknown quantity was the
velocity. The method used here was to correct the reflection events with a large
suite of velocities to determine the velocity that optimally aligned the
reflection events. Having picked the optimal "alignment" velocities, the traces
were appropriately corrected sample by sample and then stacked as shown in
Figure 1.
It was, of course, recognized that in the presence of dipping reflectors, the traces contributing to the stack did not have a reflection point directly under their common midpoint. Having produced a stack of the corrected reflections, the composite trace had to be migrated -- that is, the stacked reflections had to be shifted in time and distance to their appropriate points of origin by poststack migration.
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uBackgrounduFigure captionsuMoveout equationuPrestack migration
uBackgrounduFigure captionsuMoveout equationuPrestack migration
uBackgrounduFigure captionsuMoveout equationuPrestack migration
uBackgrounduFigure captionsuMoveout equationuPrestack migration
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Moveout
Equation and Stacking The equation that
relates the acquisition geometry (source-to-receiver offset, or SRO) to
the subsurface The velocity in this equation is a "time-weighted root-mean-square average" of all the individual velocity layers. For this reason, the stacking velocity is referred to as both Vstack and Vrms. These have become synonymous, even though the moveout equation stated in Figure 2 is actually an approximation. The important work
of C. Hewett Dix gave us a second equation that is really the key to
using stacking
If we can derive
Vint from the TO -- Vrms pairs, a depth corresponding to each time can
be easily calculated, thereby converting time reflection data to depth.
The velocity appropriately used to convert reflection times to depth is
a "time weighted average velocity," referred to as Vave. This is simply
the travel distance divided by the travel time. Converting stacking
In the presence of
a dipping reflector, simple geometry shows us that traces that have a
common midpoint do not actually have a common reflection point, but the
data was forced to stack by using anomalous stacking
When computer power ultimately allowed us to fix the problem of getting the reflections into the correct subsurface location prior to stack with prestack migration, we had to re-look at the velocity analysis process. Every trace prior to stacking has a unique source and receiver location. We do not know where any given reflection actually came from, but the trajectory of all the possible reflection points lies on an ellipse with the source and receiver locations at the two focus points. The strategy here is to sweep every sample of every trace in the data set into all of its possible points of origin. When all of these "swept" traces are added together, constructive interference builds the image of the actual reflector locations. This is illustrated in Figure 3. This process
bypasses moveout correction -- and since the shape of every ellipse is a
function of the
Figure 3 shows the
common midpoint traces that previously would have been corrected for moveout then stacked. Now they are migrated before stack to be in the
correct location on the reflector. For this diagram, we have displayed
the traces that have been migrated into a single bin location in a 3-D
data cube. The moveout correction is implicit in the migration if the
In the presence of
a layered earth, the migration velocity is also a Vrms average of the
layer In either case, if
we stack the data to produce stacking The relationship between Vrms, Vint and Vave is shown in Figure 4.
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