= Solution
The $31.7^\circ$ result predicts \b[initial failure in a uniform material under the assumed principal-stress orientations]. The actual Figure 3 is a present-day NW–SE cross section through a thick, heterogeneous Alpine stack, extending to about 50 km depth. It contains near-horizontal basal stretches, curved ramps, tightly bent contacts, and steep structures in the internal zones around Viso and the Dora Maira complex. It does not show a single undeformed conjugate pair newly formed in horizontal uniform <rock>.
Several processes explain the departures:
* \b[Mechanical layering and inherited weaknesses.] <Faults> can follow weak bedding, old <fault planes>, or contacts with lower <friction> or <cohesion> than the surrounding <rock>. These can form shallow <décollements> linked by steeper ramps. Figure 2 explicitly distinguishes the near-surface red “geophysical bedrock” boundary at a few hundred metres from the much deeper crystalline basement beneath the <Jurassic>, <Triassic> and <Permian> cover. An age label or a seismic contrast alone does not establish a friction coefficient; clay-rich or <evaporite> detachments are possibilities to test, not lithologies proved by that drawing.
* \b[Rotation after formation.] Continuing <tectonic shortening>, <folding>, stacking and <fault slip> can rotate an initially optimal <fault plane> to steeper or shallower present-day <fault dips>. A steep older structure may be inherited from an earlier deformation episode rather than created at its present orientation.
* \b[Curved faults and local stresses.] <Faults> bend through a layered <crust>; local <principal stress> axes rotate near topography, ramps and interacting faults. The optimum angle is measured relative to the local $\sigma_1$, not necessarily to the regional horizontal direction everywhere.
* \b[Changing strength and deformation mechanism.] Spatial changes in <pore fluid pressure>, <coefficient of friction>, <cohesion> and <temperature> alter which surfaces reactivate. At depth, <ductile deformation> can replace frictional brittle failure, so the same new-fracture construction need not apply throughout the section.
Finally, a section shows \b[apparent dip] unless it is perpendicular to <fault strike>. For an ideal plane, $\tan\delta_{\mathrm{app}}=\tan\delta_{\mathrm{true}}\sin\alpha$, where $\alpha$ is the angle between the section direction and <fault strike>. Obliquity can make a plane look shallower, but cannot on its own explain an apparent dip steeper than its true dip. Do not infer that each black curve is a currently active brittle <earthquake> fault.
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