Calculating Seismic
Velocity From Logs
If the interval thicknesses and interval velocities are given,
for example by a digitized sonic log or a seismic model of a hypothetical
rock sequence, we can calculate what the seismic times would be
at various reflectors, recorded at detectors spaced along a geophone
spread. When this model is plotted to scale with all major reflectors
and the resulting ray paths, it is called ray tracing. The equations
work for both shear and compressional waves when the respective
interval velocities are used.
The
near trace time to a reflector is:
1: To = 2 * Sum (Hint / Vint)
The
interval travel time in a layer is:
2: Tint = 2 * Hint / Vint
The
average velocity is defined as:
3: Vavg = 2 * Sum (Hint) / To
The
RMS velocity is defined as:
4: Vrms = ((Sum ((Vint ^ 2) * Tint)) / To) ^ 0.5
Note that Vrms is usually close to the stacking velocity (Vstk)
needed to obtain a good quality stack of common depth point
seismic data when beds are relatively flat. More sophisticated
migration techniques are needed in steep dips.
The
far trace time, from ray path geometry is:
5: Tx = (2 * ((X / 2) ^ 2 + (Sum (Hint)) ^ 2) ^ 0.5) / Vrms
Normal
moveout is:
6: NMOc = Tx  To
These
equations are used to evaluate various layered models (ray tracing),
and the reverse equations are used to calculate
interval velocity from seismic data. The equations apply to both
compressional and shear data, when appropriate inputs are used.
Note
that seismic times are always two way times, and that integrated
sonic log times are usually one way times.
