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.


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