Andrew J. Michael 2026-10-25
Left: ordinary frictional strengthening with depth followed by thermally activated material creep. Right: a very weak shallow faulted layer above a narrow strong region near 10 km, followed by essentially the same weakening material creep branch. These are the shapes actually plotted in Figure 2. The right curve is not a strong upper crust over a uniformly weak lower crust; neither diagram displays a second mantle-strength peak.
For the left curve, increasing overburden increases the effective normal load on faults. A schematic Coulomb friction law iswhere is cohesion, the coefficient of friction, the compressive normal stress and the pore pressure. With ordinary rock friction and approximately hydrostatic pressure, increases roughly linearly with depth. The stress needed for frictional sliding therefore increases, as in the straight shallow branch. Byerlee's law summarizes the relatively high friction found in many laboratory rocks.[ref]
At higher temperature, dislocation creep or another ductile mechanism accommodates the imposed deformation at lower stress. For example,Here is strain rate, an activation energy, the molar gas constant and absolute temperature. At fixed strain rate, increasing lowers the required stress. The operative envelope is approximately , expressed in a consistent stress convention; the peak marks the brittle-ductile transition. This accounts for the left curve's peak near 100 MPa and its decline toward small strength by about 20 km.
For the right curve, normal high-friction sliding with depth-independent fluid-pressure ratio cannot explain the nearly vertical weak shallow branch. Plausible weakening includes high pore pressure tracking the overburden, low-friction fault gouge, or a connected network of pre-existing weak faults. Roughly constant small yields roughly constant small frictional strength. The abrupt increase near the base of this layer requires a change of conditions: for example, the weak fluid-rich fault network terminates or becomes discontinuous, leaving stronger intact or less altered rock below. A change in mineralogy or deformation localization can also give a contrast. Simply saying “there are fluids” does not explain the return to high strength. Below the strong region, thermal material creep again lowers the strength.
The figure alone does not identify the weakening mechanism or a particular lithological boundary. In particular, a 10 km strength maximum is not evidence for a 10 km deep Mohorovičić discontinuity. The strong-fault/weak-fault evidence and the distinction between fault strength and surrounding crustal strength are discussed in Stress orientations at intermediate angles to the San Andreas Fault, California by Jeanne L. Hardebeck and Andrew J. Michael.
Support for the left curve comes from high laboratory friction and substantial in situ differential stress; support for the right curve comes from low inferred fault traction, weak fault materials or high pore pressure. No single observation directly measures the whole plotted envelope.
For the left, stronger shallow-crust model:
- Many friction experiments on ordinary rocks give a coefficient of friction around 0.6–0.85. Together with approximately hydrostatic pressure, these values predict increasing frictional strength with depth.
- Deep-borehole measurements of stress and pore pressure in some continental settings indicate a crust close to frictional failure at appreciable differential stress. Jointly with appropriate fault orientations, these support a strong frictional upper crust.
For the right, weak shallow-layer model:
- On well-studied plate-boundary faults, low resolved shear stress inferred from the orientation of principal stresses relative to the active fault plane can support low effective traction.
- The absence of the expected localized long-term frictional heating anomaly can support weak sliding. Directly measured high pore pressure or very low-friction fault gouge would give a physical explanation. The heat-flow and stress evidence is particularly developed for the San Andreas Fault; it is an analogue argument, not an observation that the entire Cascadia upper crust follows that curve.[ref]Stress orientations at intermediate angles to the San Andreas Fault, California by Jeanne L. Hardebeck and Andrew J. Michael. 2004, introduction and discussion of strong and weak fault models
To discriminate, measure the strength-controlling quantities through depth and across both faults and their surroundings. Obtain borehole stress, pore pressure and temperature profiles where feasible; use borehole breakouts and hydraulic tests to constrain effective stress. Recover fault and host rocks and test their friction and material creep at relevant fluid conditions. The right curve specifically predicts an end to the shallow weakening near its sharp rise: investigate changes in permeability of a porous medium, alteration and fault gouge with depth, rather than testing only a surface sample.
Combine those measurements with heat flux transects, magnetotelluric sounding for conductive fluids, accurate earthquake depths and focal mechanisms, and GNSS or InSAR observations of deformation. The latter can help constrain the depth distribution of locking and postseismic relaxation, but neither locking nor seismicity alone gives absolute strength. Earthquake stress drop is a change in stress, not the pre-event stress. Low heat flux can also reflect heat transport or transient weakening; high electrical conductivity can have causes other than free water. A joint explanation of all these data is needed to choose between the models locally.