Vs From Vp

The Log That Is Not There

Two of the workflows this course has built lean on the shear velocity. AVO reads the way a reflection changes with angle, and that angular behavior is governed by the contrast in $V\_p/V\_s$ across the interface. Gassmann fluid substitution needs the shear modulus to carry the dry frame from one fluid to another. Yet the shear velocity is the log most often absent: many wells were logged for $V\_p$ and density alone, and older wells for $V\_p$ only. So a routine and unavoidable task is to predict $V\_s$ from what you do have, and the empirical backbones of the previous section are exactly the tool. Someone measured $V\_p$ and $V\_s$ together on many brine-saturated rocks and fitted the relationship; you evaluate that fit at your measured $V\_p$ and read off a shear velocity.

Mudrock and the Lithology Lines

The oldest and simplest is Castagna's mudrock line, $V\_s = (V\_p - 1.36)/1.16$, a single straight fit for water-wet clastics. Greenberg and Castagna refined it in 1992 into separate lines for pure lithologies: sandstone, limestone, dolomite, and shale each get their own regression, because a given $V\_p$ implies a different $V\_s$ depending on what the rock is made of. At $V\_p = 3.0$ km/s the mudrock line gives $V\_s = 1.41$, the sandstone line 1.56, and the limestone line 1.52. Step up to $V\_p = 3.5$ and they read 1.85, 1.96, and 1.85; at $V\_p = 4.0$ they read 2.28, 2.36, and 2.16. The lithology matters: a limestone and a sandstone at the same $V\_p = 4.0$ differ by 0.2 km/s in predicted $V\_s$, which is the difference between a right and a wrong AVO gradient. Choose the line for the rock you have, and where a zone is a mix, the full Greenberg-Castagna scheme averages the pure-lithology predictions by volume fraction.

Brine Lines and the Classic Error

There is one discipline these lines demand, and it is the source of a common and costly mistake. Every one of them was fitted to brine-saturated rock. They tell you the shear velocity a rock would have if its pores held water. A gas sand does not: gas lowers the P-wave velocity sharply while leaving the shear velocity almost untouched, so its measured $V\_p/V\_s$ is far lower than any brine line predicts. Feed the gas sand's low $V\_p$ straight into a brine line and it will hand back a shear velocity that is too low, poisoning the very AVO analysis you were trying to set up. The correct move respects the physics of Part 4. Predict $V\_s$ on the brine leg, either at a nearby wet interval or by first substituting the zone to brine, then run Gassmann forward to put the hydrocarbon back and let it lower $V\_p$ while shear stays fixed. The brine line supplies the frame's shear behavior; Gassmann supplies the fluid effect. With a shear velocity in hand for every zone, the one property still missing from many old wells is density, and that is the next section.

References

• Castagna, J. P., Batzle, M. L., & Eastwood, R. L. (1985). Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks. Geophysics, 50(4), 571-581.
• Greenberg, M. L., & Castagna, J. P. (1992). Shear-wave velocity estimation in porous rocks: Theoretical formulation, preliminary verification and applications. Geophysical Prospecting, 40(2), 195-209.