Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 2

Section A: Earthquakes & Faulting.

For an Andersonian faulting regime appropriate to the stated normal fault, take ${\sigma }_1$ vertical, ${\sigma }_2$ north–south along strike, and ${\sigma }_3$ east–west. Thus the minimum horizontal compression is normal to the fault’s north–south strike. In an east–up cross-section, draw ${\sigma }_1$ vertically and ${\sigma }_3$ horizontally, with ${\sigma }_2$ perpendicular to the page. These are plausible regional principal stress directions, rather than measured directions uniquely recoverable from one photograph.

Use the same conditional optimal normal-fault dip relation as in question 1, with $\delta =55^{\circ }$:The second panel of the original Mohr circle figure has ${\sigma }_3^{\prime }=1$ and ${\sigma }_1^{\prime }=2.03961$; its tangent from the origin has slope $0.364$. Resolving the stresses onto a $55^{\circ }$ plane places its stress point at that tangency. The diagram assumes negligible cohesion, a vertical maximum principal stress and an optimally oriented new or equivalently oriented sliding plane. Without those assumptions, a dip and a statement that sliding began do not uniquely determine the coefficient of friction.

Choose coordinates $(x,y,z)=(\mathrm{east},\mathrm{north},\mathrm{up})$ and use compression-positive effective stress. One possible tensor, in MPa, isIts ordered principal stresses are vertical ${\sigma }_1^{\prime }$, north–south ${\sigma }_2^{\prime }$ and east–west ${\sigma }_3^{\prime }$. On the $55^{\circ }$ east-dipping plane,so $|\tau |/{\sigma }_n^{\prime }=0.36397$, as required by the conditional friction estimate. The scale is illustrative: no absolute stress magnitude is supplied. A corresponding total stress tensor is ${\mathbf{\sigma }}^c={\mathbf{\sigma }}^{\prime }+P_f\mathbf{I}$ for any specified isotropic pore fluid pressure $P_f$.

The thin, pale, steep feature beside the fingers is plausibly a 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 tensorhas 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. The source’s reference to “part d” is circular; the meaningful comparison is with part c.

The coarse angular fragments in the light-coloured band identify a fault breccia, probably cemented and accompanied by finer comminuted material. Repeated brittle fracture, clast rotation and crushing during fault slip produce the fragments; fluid flow can later fill pores and fractures with mineral cement. If the finer material is cohesive it can be termed cataclasite; a loose, very fine seam is fault gouge. The photograph alone does not establish all those cohesion and grain-size distinctions.

Slip is commonly concentrated on a narrow principal slip surface or fine-grained seam at a margin or inside a broader damaged band. Thus the coarsest, widest breccia is not automatically the material that accommodated the largest shear displacement. In this image the sharp, finer-looking boundaries of the coarse band are the best candidates for localized slip. Identifying the uniquely most displaced seam would require displaced markers, thin sections or additional exposure; the coarse band itself records substantial distributed damage.