Anderson's Three Worlds
Learning objectives
- Use the free-surface argument to fix one principal stress vertical and two horizontal
- Classify the stress state by the ordering of Sv, SHmax, and Shmin into normal, strike-slip, and reverse regimes
- Match each regime to the fault style it produces and the tectonic setting it belongs to
- Place the canon state, Sv the largest, in the normal-faulting world
One Vertical, Two Horizontal
Section 1.2 established the fact that organizes all of in-situ stress: because the earth's surface carries no shear, one principal stress stands very nearly vertical and the other two lie horizontal. Ernest Anderson, in 1951, drew the consequence. Name the three the vertical stress , the larger horizontal , and the smaller ; then the entire character of the stress field, and the kind of faulting it drives, is decided by which of the three is biggest and which is smallest. There are exactly three orderings, and each is a world with its own geology.
Cycle the three worlds in the figure. In the normal-faulting regime the vertical stress is the largest, : gravity dominates, the crust is being pulled apart, and it fails on steep normal faults that drop one block down, the setting of rifts, deltas, and passive margins. In the strike-slip regime the vertical stress is the middle one, : the crust slides horizontally past itself on near-vertical faults, the setting of transform boundaries like the San Andreas. In the reverse-faulting (thrust) regime the vertical stress is the smallest, : tectonic compression has driven both horizontals above the overburden, and the crust fails on shallow thrusts that stack one block over another, the setting of mountain fronts and fold belts. The fault a region makes is a direct readout of which stress is vertical.
Reading the Regime, and the Canon
This classification is not academic bookkeeping; it is the first thing a geomechanicist establishes about a field, because the regime sets everything downstream. It decides which way a borehole will break out, which trajectory is safest to drill, which faults are prone to slip, and how the fracture gradient compares with the overburden. Our canon state, MPa, is a normal-faulting state, the most common regime in producing basins and the one this course carries throughout. Establishing that ordering is step one of the mechanical earth model in Part 8. But the ordering alone does not say how far apart the stresses can spread, because friction sets a limit on how much the crust can carry before it fails. That limit is the next section, and together the two build the stress polygon, the map of every state the crust allows.
References
- Anderson, E. M. (1951). The Dynamics of Faulting (2nd ed.). Oliver & Boyd.
- Zoback, M. D. (2007). Reservoir Geomechanics. Cambridge University Press.
- Jaeger, J. C., Cook, N. G. W., & Zimmerman, R. W. (2007). Fundamentals of Rock Mechanics (4th ed.). Blackwell.