Castagna Mudrock Line Calculator: Predict Vs from Vp

Shear velocity is the quiet workhorse of quantitative seismic work: you need it for Poisson ratio, for AVO modeling, for Gassmann fluid substitution, for geomechanics. And yet dipole sonic logs that measure Vs directly are far rarer than plain P-wave sonics, especially in older wells. In 1985 Castagna, Batzle, and Eastwood published the fix that the industry still uses daily: in water-saturated clastic rocks, Vs tracks Vp along a nearly perfect straight line, which they named the mudrock line:

Vs = 0.8621 x Vp – 1.1724 (both in km/s)

Why a straight line works, and why it fails usefully

Clastic rocks span a continuum from soft clay-rich mudstone to stiff clean sandstone, and along that continuum both velocities rise together in lockstep as porosity closes and cementation stiffens the frame. The nonzero intercept is what makes the ratio behave: at low Vp the predicted Vs is proportionally much smaller, so Vp/Vs climbs steeply in slow rocks. That is why soft wet sediments show Vp/Vs of 3 or more while tight sands sit near 1.6.

The genuinely clever part is what happens when the assumption breaks. Replace brine with gas and Vp drops sharply (the fluid no longer stiffens compression) while Vs barely moves (fluids carry no shear). The measured point jumps off the mudrock line, and that departure is precisely the physics that class 3 AVO anomalies, fluid factor attributes, and crossplot interpretation all exploit. The line earns its keep as much by being violated as by being obeyed.

Worked example

• A wet shaly interval logs Vp = 3,000 m/s with no dipole sonic available
• Vs = 0.8621 x 3.0 – 1.1724 = 1.414 km/s
• Vp/Vs = 2.12, Poisson ratio = 0.36, entirely normal for water-bearing shaly section
• If the measured Vs later comes in near 1.7 km/s at the same Vp, suspect cleaner or gas-bearing sand rather than a bad log

Scope notes worth respecting: the relation was calibrated on siliciclastics, and carbonates follow their own distinct Vp-Vs trends (Castagna and coworkers published separate limestone and dolomite lines). Organic-rich shales can sit off-trend because kerogen is soft. And at very low velocities the line predicts negative Vs, which is the equation politely telling you the sediment is outside its world. Where a measured dipole exists, always prefer it; the mudrock line is the understudy, not the star.

Related Calculators and Reference

The Vp/Vs and Poisson ratio this predicts can be explored further in the Poisson ratio calculator, the predicted Vs is exactly what Gassmann fluid substitution needs as a starting point, and the AVO intercept-gradient calculator shows what happens when gas pushes a sand off the line. The SEG Wiki entry on the mudrock line covers the original 1985 study.