= Solution
Use a <rock strength envelope>: at each depth plot the smaller <differential stress> needed for frictional failure and for sustained ductile <material creep> at a specified <strain rate>. \b[Shallow <rock> generally strengthens with depth because effective confining <pressure> increases; sufficiently deep hot <rock> weakens because thermally activated <material creep> becomes efficient.]
\Image[/past-exam-of-the-plate-tectonics-course-of-the-university-of-oxford/2023-strength-profiles.png]
{title=Illustrative rock-strength envelopes for a continental interior and an old central-Pacific plate; these are conceptual profiles, not measurements}
At shallow depth, <Byerlee's law> or a <Mohr-Coulomb failure criterion> gives a relation of the form
$$
\tau_f=C+\mu(\sigma_n-P_f),
$$
where $C$ is cohesion, $\mu$ a <coefficient of friction>, $\sigma_n$ the compressive <normal stress> and $P_f$ the <pore pressure>. Increasing overburden generally increases <effective stress>, hence the <frictional strength>. Conversion from fault <shear stress> to <differential stress> depends on the stress regime and fault orientation; a sketch should not label a universal numerical slope. High <pore pressure> or weak <fault gouge> can lower the <frictional strength> substantially.
A simplified <dislocation creep> relation is
$$
\dot\epsilon=A\sigma^n\exp\!\left[-\frac{Q+PV^*}{RT}\right],
\qquad
\sigma_{\rm creep}=\left(\frac{\dot\epsilon}{A}\right)^{1/n}\exp\!\left[\frac{Q+PV^*}{nRT}\right].
$$
Here $Q$ is <activation energy>, $V^*$ <activation volume>, $R$ the <molar gas constant> and $T$ absolute <temperature>; $A$ and $n$ depend on composition and deformation mechanism. At fixed <strain rate>, increasing <temperature> usually decreases the required <stress> strongly. The competing effects of <pressure>, <water weakening of rocks>, <grain size> and composition also matter. The intersection with frictional failure gives a <brittle-ductile transition>, not a change from solid to liquid.
For the Indian continental interior, a useful first sketch has an upper-crustal strength peak, a weaker lower <continental crust>, and renewed strength in <lithospheric mantle> beneath the <Moho>. <Quartz>-bearing <rocks> can undergo ductile <material creep> at conditions where colder, drier <olivine>-rich <mantle> retains appreciable strength. This creates a possible two-peak, or “jelly sandwich”, <rock strength envelope>. With further depth the <mantle> also weakens. A cold <craton> can retain strong <lithospheric mantle> to much greater depths than a tectonically heated continental region.
For the central Pacific, show thin <mafic> <oceanic crust> above a relatively thick layer of strong <lithospheric mantle>. There need not be a conspicuous weak lower-crustal layer. Much of the integrated strength can reside below the <Moho>, with a broad strength peak followed by ductile weakening towards the <asthenosphere>. Cooling and age control the thickness: young hot <oceanic lithosphere> would give a much shallower and weaker profile than an old central-Pacific plate.
The plotted <Moho> depths of about 38 km and 7 km, and all plotted <stresses>, are illustrative assumptions. “India” alone does not specify a unique <geothermal gradient>, <water> content or <strain rate>, and the Pacific includes plates of different ages. The robust comparison is the possible crust–mantle layering in a continent versus the thin <oceanic crust> and mantle-dominated strength of an old oceanic plate. The <Moho> is a compositional boundary; neither it nor the deepest small plotted strength is automatically the seismic <lithosphere-asthenosphere boundary>.
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