The Minerals

Part 1, Part 1: Elasticity and the Moduli

Learning objectives

Read the mineral moduli table as the fixed end-members every rock physics model starts from
Explain why carbonates run faster than quartz in Vp despite comparable shear stiffness
Recognize effective clay as a soft, log-derived construct, not a single-crystal measurement
State why a real rock always plots below its mineral point, making the mineral the anchor of every bound and model ahead

The End-Members

Every model in the parts ahead starts from the same fixed points: the moduli of the pure minerals, measured on single crystals and tabulated in the Rock Physics Handbook. They are the anchors, so it is worth seeing them together. With the moduli in gigapascals and density in grams per cubic centimeter: quartz $K = 36.6$ , $\mu = 45$ , $\rho = 2.65$ ; feldspar, on average, $K = 37.5$ , $\mu = 15$ , $\rho = 2.62$ ; calcite $K = 76.8$ , $\mu = 32$ , $\rho = 2.71$ ; dolomite $K = 94.9$ , $\mu = 45$ , $\rho = 2.87$ ; the log-derived effective clay $K = 20.9$ , $\mu = 6.85$ , $\rho = 2.58$ ; anhydrite $K = 56.1$ , $\mu = 29.1$ , $\rho = 2.98$ ; halite $K = 24.8$ , $\mu = 14.9$ , $\rho = 2.16$ ; and pyrite $K = 147.4$ , $\mu = 132.5$ , $\rho = 4.93$ . These numbers do not change from problem to problem; the modeling is all in how you combine them and in how porosity softens the result. On a crossplot the shear modulus $\mu$ is often written $G$ .

Why Carbonates Are Fast

Read the table with the velocity equations in mind and the seismic behavior of whole basins falls out. Calcite and dolomite are far stiffer in bulk modulus than quartz, $K$ of 76.8 and 94.9 against quartz's 36.6, and dolomite matches quartz in shear stiffness besides, so their mineral P-velocities are high: quartz $V_P = 6.04$ P=6.04 km/s, calcite $V_P = 6.64$ P=6.64 km/s, dolomite $V_P = 7.35$ P=7.35 km/s. That is the mineral-scale reason carbonates run fast, before any pore or texture enters. At the other end sits clay: the effective clay in this table is soft, $\mu$ under 7 GPa, and it is a log-derived construct, an average tuned to reproduce how shaly intervals behave on logs, deliberately softer than the moduli you would measure on a pristine clay crystal. Treat it as a calibration point, not a mineral constant.

The Rock Sits Below Its Mineral

The crossplot places the eight minerals by their bulk and shear moduli, and the single most important thing about it is a direction: down. A real rock, made of these minerals plus porosity and grain contacts and cracks, is always softer than its mineral point, because every pore and every compliant contact removes stiffness that the solid crystal had. The mineral is therefore a ceiling: a clean quartz sandstone can approach quartz's moduli only as its porosity approaches zero, and it falls away from that corner as porosity grows. This is exactly why the mineral moduli anchor everything that follows. A bound (Part 2) starts from the mineral and asks how low the rock can go; a frame model (Parts 5 and 6) starts from the mineral and computes how far a given texture pulls it down; a Gassmann substitution (Part 4) starts from the mineral to get the solid modulus it needs.

So Part 1 has laid the ground floor: two moduli, two velocities, one diagnostic ratio, and the eight mineral end-members they all begin from. What Part 1 has not done is combine anything. A real rock is a mixture, quartz and clay and porosity and fluid together, and the moment you try to average two minerals into one modulus you find there is no single right answer, only a range. That range is the subject of Part 2, which opens with the mixing problem: given the ingredients, what are the stiffest and softest rocks they could possibly make?

References

Mavko, G., Mukerji, T., & Dvorkin, J. (2009). The Rock Physics Handbook (2nd ed.). Cambridge University Press.
Simm, R., & Bacon, M. (2014). Seismic Amplitude: An Interpreter's Handbook. Cambridge University Press.