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RMS Velocity

If the homogeneous medium is replaced by a stack of horizontal layers then the traveltime equation can be replaced by a series expansion in the offset coordinate:
 
t2(x) = C0+C1x2+C2x4+...   , (1.4)

where C0=t(0)2, C1=1/vRMSN2, and the other coefficients are complicated terms. Here, the RMS velocity vRMSN for the stack of N layers is defined by
 
vRMSN2 $\textstyle \cong$ $\displaystyle \frac{\sum_i^{N} v_i^2 \Delta t_i}{\sum_{i=1}^{N} \Delta t_i} ,$ (1.5)

where $\Delta t_i$ is the vertical 2-way time through the ith layer, and t(0) in equation 1.3 becomes equal to $\sum_{k=1}^{N} \Delta t_i$ the 2-way vertical traveltime to the Nth layer. Note that vRMSN depends on the the number of layers N, so we say that the Nth reflector has a different vRMSN value than, say, the N-4 reflector.

Plugging equation 1.5 into 1.4 and truncating after 2 terms yields the traveltime equation for short offsets and a multilayered media:

 
t(x) = $\displaystyle \sqrt{t(0)^2 + x^2/v^2_{RMS_N} }.$ (1.6)

The approximation in the above equation is valid for small values of offset x(Yilmaz, 1987). Once the vRMSN velocity is found for each reflector then the interval velocities vn can be found by the Dix formula:
V2n = $\displaystyle \frac{ v^2_{RMS_n}t(0)_n-v^2_{RMS_{n-1}}t(0)_{n-1}}
{t(0)_n - t(0)_{n-1} },$ (1.7)

where t(0)n denotes the vertical reflection traveltime to the nth layer. The validity of this formula is easily proven by using the definition of vRMSNand simple algebraic manipulation.

In summary we have learned some new words.
1. STATION: Recording site connected to a group of geophones. Data from this site is transmitted along one channel in recording line.
2. GEOPHONE Group: Geophones serially connected, and summed signal is fed to one channel.
3. SPREAD LENGTH: Length of recording line.
4. ZO SECTION: Seismic traces obtained by recording seismic energy with a geophone that has zero offset from the source.
5. CSG: Common shot gather of traces recorded with a common shot.
6. CMG: Common midpoint gather of traces where each of the traces have the same midpoint position between the shot and receiver.
7. SHOT AND GROUP INTERVALS: Intervals between shot points and stations.
8. APPARENT VELOCITY: Velocity of an arrival as measured along a horizontal line.
9. ENDLINE AND MIDPOINT RECORDING GEOMETRIES: Shot at end of recording line = endline. Shot at midpoint of recording line = midpoint.
10. The fold number is the number of traces in a CMG. It is the number of traces in a gather with a common reflection point.


next up previous contents
Next: Basic Processing Steps Up: Seismic Experiment Previous: Apparent Velocity
Gerard Schuster
1998-07-29