Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2023 / Paper 1 / 4

Use repeat-pass interferometric synthetic-aperture radar. An orbiting radar transmits coherent microwave pulses and records the amplitude and phase of the returning field. Form an interferogram from registered complex images acquired before and after the earthquake, remove the orbital contribution and the topographic phase predicted by a digital elevation model, and correct atmospheric and other long-wavelength phase delays. Where interferometric coherence is adequate, unwrap the residual phase to estimate line-of-sight displacement:with sign set by the instrument's displacement convention. Each $2\pi$ phase cycle represents $\lambda /2$ of range change.

This maps a distributed earthquake displacement field day or night and through cloud, including areas inaccessible on foot. Roughly $10$–$30\mathrm{m}$ ground sampling and a scene spanning many kilometres on both sides of the fault can resolve regional deformation; a narrow surface break benefits from finer pixels or complementary sub-metre optical surveys. Sensitivity to displacement can be millimetres to centimetres in coherent areas, but that does not equal spatial resolution. A single viewing direction measures one component; ascending and descending tracks and GNSS constrain more components. At the rupture itself, large gradients and changed ground cover can destroy interferometric coherence; radar pixel-offset tracking or before/after optical correlation can then recover metre-scale fault offsets.

Map the continuous break near the base of the rugged mountain front, following the low scarp across the smoother fan surfaces, rather than the ridgeline. With the same normalized image coordinates, an approximate trace follows $(0.04,0.56),(0.22,0.52),(0.43,0.60),(0.55,0.64)$, steps toward $(0.62,0.43)$, and continues via $(0.72,0.49),(0.88,0.64),(0.98,0.61)$. Some parts are much clearer than others and should be drawn as inferred or dashed where obscured.

The mountainous upper side of the image is the uplifted footwall; the smoother basin/fan side below is the downthrown hanging wall. A section perpendicular to the front has a normal fault dipping toward the basin. Attachment B has no printed north arrow, so these image-relative labels avoid assigning an unsupported compass direction. The original interpretive figure marks the trace and the central fault step-over.

Mark a fault scarp cutting an alluvial fan on the left-to-central smooth piedmont, approximately $(u,v)=(0.38,0.58)$. Its narrow, aligned height break continues across surfaces that are smoother than the mountains; repeated downthrow on the basin side produces the scarp. Sketch a once-continuous gently sloping fan surface cut by a basin-facing step.

Mark triangular facets on the mountain front in the right-central part, near $(0.78,0.48)$. These are roughly triangular planar mountain faces bounded laterally by incised valleys and below by the fault front. In a front view, draw repeated triangles separated by stream valleys. Triangular facets result from the interaction of normal faulting, uplift and erosion; neither they nor a sharp mountain front alone demonstrates a rupture in the particular historical event.

The rate of surface modification controls how quickly a fault scarp is erased. Strong rainfall, runoff, slope failure and easily eroded lithologies can round or dissect a scarp; dry conditions and resistant rock often preserve it longer. Alluvial fan deposition and aggradation can bury a scarp even if erosion is slow. A young marker surface can preserve an offset that an older, strongly modified surface no longer records.

The balance between fault slip rate, recurrence interval and marker age controls whether renewed displacement outruns this modification. Rapid or repeated normal faulting can maintain a clear front, whereas a long interval after a small displacement permits smoothing. A very young fan deposited after the event may have no offset, while an older surface may retain cumulative rather than single-event fault throw. These two controls explain why absence of an obvious scarp is not proof of an inactive fault.

An overlapping pair of basin-dipping normal fault segments can first accommodate displacement through an unbreached relay ramp. Fault throw tapers toward each tip and transfers between the strands; the intervening block tilts and bends while retaining a continuous ramp-like surface. Draw overlapping parallel traces in plan view and a tilted connecting surface between their different fault throws.

With continued extension, the ramp can be breached by a linking fault. An oblique connector joins the segment tips and takes up a combination of dip-slip and strike-slip displacement; the system becomes a more continuous, zigzag normal fault. Draw this connector diagonally through the overlap, with downthrown arrows on the basin side. Distributed small faults and folding can accompany either arrangement. The central bend around $u\simeq 0.6$ in Attachment B is the candidate transfer zone; the image alone does not uniquely establish the three-dimensional connection at depth.