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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
.
uBackgrounduFigure captionsuMoveout equation
uPrestack
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Moveout Equation and Stacking Velocities The equation that relates the acquisition geometry (source-to-receiver offset, or SRO) to the subsurface velocities was given to us by C. Hewitt Dix and is called the Dix Moveout Equation. The geometry and the subsurface model related to the velocities are shown in Figure 2, along with the moveout equation. The equation compares the reflection arrival time (TT) of a reflection at an offset SRO with the reflection travel time (TO) at zero offset. The difference between these two times is the moveout correction applied to the reflection events for a trace at offset SRO. The The important work
of C. Hewett Dix gave us a second equation that is really the key to
using stacking velocities for depth conversion. For any given
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 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 velocities and then migrated. This was the compromise that was practical with the computer power at hand.
Prestack When computer power
ultimately allowed us to fix the problem of getting the reflections into
the correct subsurface location prior to stack with prestack 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 velocities, where does this
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 In the presence of
a layered earth, the In either The relationship between Vrms, Vint and Vave is shown in Figure 4.
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