The Model Reference Card

The Course in One Card

Twelve parts reduce to a single working question: given this rock and this data, which model do I reach for? This section answers it as a decision card. Each row names a rock situation, the model that fits it, the parameters someone must choose to run that model, and the edge where the model fails and you must stop trusting it. Read the card top to bottom and you have the whole subject as a set of choices, each with a reason and a limit.

The Sands, by How Stuck the Grains Are

Start with the sands, ordered by how stuck their grains are. A clean, uncemented sand is a grain pack, so the SOFT-SAND model of Part 5 fits, taking a critical porosity, a coordination number, and an effective pressure; its edge is that it assumes no cement, so it reads too soft for a rock that has any. A consolidated or diagenetically stiffened sand calls for the STIFF-SAND model instead, the same endpoints connected along the upper line; its edge is the mirror image, it will read a truly loose sand too fast. A high-porosity sand held up by cement at the grain contacts needs the CONTACT-CEMENT model, which takes the cement modulus, the cemented porosity, and the coordination number; its edge is that a very little cement stiffens the rock enormously, so the model is exquisitely sensitive to how much cement you assume and to whether it sits at the contacts or coats the grains.

Beyond the Sands, and the Two Rows That Are Not Frames

Leave the clean sands and the rock gets more structured. A shaly sand is two soft solids with pores of two shapes, so XU-WHITE of Part 6 fits, taking the clay fraction and a pore aspect ratio for each mineral; its edge is that those aspect ratios must be calibrated locally, they are not universal constants. A carbonate is a stiff mineral pierced by pores whose SHAPE, not amount, sets the velocity, so the inclusion machinery, DEM driven by XU-PAYNE aspect ratios per pore type, is the tool; its edge is that it needs the pore-type split, usually from core or thin sections, and that its stiff isolated pores are exactly where Gassmann starts to fail. Underneath all of them sits the BOUNDS check of Part 2: Hashin-Shtrikman brackets any mixture, and any prediction that falls outside the bounds is wrong before it is tested. Run it on every mixture as a sanity rail.

Two rows are not about the frame at all. A fluid change on ANY saturated rock is GASSMANN of Part 4, taking the dry frame, the mineral, the porosity, and the two fluids; its edge is that it holds only in the low-frequency seismic band and only for connected pores, so it is a seismic tool, not a log-frequency or laboratory one. And a stack of layers too thin for the wave to resolve is BACKUS of Part 9, taking the layer fractions and each layer's moduli; its edge is that it produces an anisotropic medium, so treating the result as isotropic throws away the very Thomsen parameters the layering created. The card looks like a lookup table, but it is really one discipline written seven ways: let the rock and the data choose the model, know what each model assumes, and stop at its edge. The next section takes three of these models off the page and into runnable Python.

References

• Mavko, G., Mukerji, T., & Dvorkin, J. (2009). The Rock Physics Handbook (2nd ed.). Cambridge University Press.
• Avseth, P., Mukerji, T., & Mavko, G. (2005). Quantitative Seismic Interpretation. Cambridge University Press.