= Solution
\b[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 is
$$
\tau_f=C+\mu(\sigma_n-P_f),
$$
where $C$ is cohesion, $\mu$ the <coefficient of friction>, $\sigma_n$ the compressive normal <stress> and $P_f$ the <pore pressure>. With ordinary rock friction and approximately <hydrostatic pressure>, $\sigma_n-P_f$ 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>.<Friction of rocks by James Byerlee>{ref}
At higher <temperature>, <dislocation creep> or another ductile mechanism accommodates the imposed deformation at lower <stress>. For example,
$$
\dot\epsilon=A\sigma^n\exp\!\left(-\frac{Q}{RT}\right),\qquad
\sigma_d=\left(\frac{\dot\epsilon}{A}\right)^{1/n}\exp\!\left(\frac{Q}{nRT}\right).
$$
Here $\dot\epsilon$ is <strain rate>, $Q$ an <activation energy>, $R$ the <molar gas constant> and $T$ absolute <temperature>. At fixed <strain rate>, increasing $T$ lowers the required <stress>. The operative envelope is approximately $\min(\sigma_f,\sigma_d)$, 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 $\sigma_n-P_f$ 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. \b[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>.
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