Solution (source code)

= Solution

The thin, pale, steep feature beside the fingers is plausibly a \b[mineral-filled opening fracture, a <mineral vein>], rather than the whole coarse <fault breccia> band. <Calcite> is a plausible filling in this appearance, but its mineral identity would need a field or laboratory test. Opening normal to its approximately vertical north–south plane requires the smallest <principal stress> to be approximately east–west, consistent with the extension direction above.

For example, a compression-positive <effective stress> tensor
$$
\boldsymbol\sigma'=\begin{pmatrix}-1&0&0\\0&4&0\\0&0&9.3961\end{pmatrix}\ \mathrm{MPa}
$$
has east–west tension and can open a weak fracture whose <tensile strength> is at most $1$ MPa. More generally opening requires $\sigma_3-P_f<-T_0$, where $T_0$ is <tensile strength>. This illustrates <hydraulic opening of a mineral vein>: raising $P_f$ by $11$ MPa at the illustrative total stresses in part c translates all effective <principal stresses> by $-11$ MPa, producing this tensor without rotating its axes.

The vein and <fault slip> need not have formed simultaneously at those exact magnitudes: <pressure> transients, local stress changes and slip can alternate. Their orientations can nevertheless reflect the same normal-faulting stress regime. \b[The source’s reference to “part d” is circular; the meaningful comparison is with part c.]