Slip rate on a silent fault
LiDAR strips across the Tāwhiri Range, South Island, reveal a 15 km-long fault trace cutting three fluvial terraces. The terraces are offset vertically by 12 ± 1 m (T3), 45 ± 3 m (T2) and 90 ± 5 m (T1). Tephra layers on the terrace surfaces give ages of 18.2 ± 0.8 ka, 61 ± 3 ka and 131 ± 6 ka respectively. A trench across the trace exposes a 2.9 ± 0.4 m dip-slip displacement in loess overlying T3, overlain by an unfaulted soil dated at 1,100 ± 150 yr BP. The fault dips 55–65° and has no historical earthquakes. A 50 km GPS array gives 4.5 ± 0.5 mm/yr across the region, but only 0.8 ± 0.3 mm/yr across the fault itself. Regional seismicity is sparse, and the nearest active fault is 40 km away. A colleague proposes that the fault is inactive and should be removed from the national seismic hazard model.
1. Calculate the preferred vertical displacement rate and slip rate for the fault, and use the single-event displacement to estimate a recurrence interval. Show your working and state the main uncertainties.
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Vertical displacement rates
- T1: 90 m / 131 ka = 0.69 mm/yr
- T2: 45 m / 61 ka = 0.74 mm/yr
- T3: 12 m / 18.2 ka = 0.66 mm/yr
The three estimates agree within their uncertainties, giving a weighted mean of about 0.70 mm/yr vertical. The fault dips 55–65°, so slip rate = vertical rate / sin(dip). At 60°, sin 60° = 0.87, so the slip rate is 0.70 / 0.87 ≈ 0.80 mm/yr; the plausible range is about 0.76–0.85 mm/yr.
Recurrence
Recurrence = single-event displacement / slip rate = 2.9 m / 0.80 mm/yr ≈ 3.6 kyr. Using the displacement range (±0.4 m) and slip-rate range gives roughly 3.1–4.4 kyr. About 1.1 kyr has elapsed, which is only about 30% of a mean cycle, so the fault is not 'overdue'.
Uncertainties
Tephra ages may date terrace abandonment rather than the offset surface; erosion or deposition can reduce apparent offset; the 2.9 m event may not be characteristic; the dip is poorly constrained and directly scales the slip rate; and three terrace points may not record a constant rate. The recurrence is a long-term average, not a prediction.
2. Evaluate the colleague's proposal that the fault is inactive. Your answer should address the GPS discrepancy, the absence of historical earthquakes, and the trench evidence.
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Verdict: the fault should not be treated as inactive.
The local GPS rate of 0.8 ± 0.3 mm/yr agrees with the geological slip rate of about 0.8 mm/yr within uncertainty, so there is no real GPS–geology discrepancy. The regional 4.5 mm/yr is likely distributed across several structures rather than localised on this fault. A short GPS record also cannot resolve a locked fault that is accumulating elastic strain.
Absence of historical earthquakes is weak evidence. With a recurrence of roughly 3.6 kyr, the probability of an event in the ~180-year instrumental record is only a few percent. The trench shows Holocene surface rupture, and the unfaulted soil only shows that the last event predates 1.1 ka; it does not show the fault is dead. The fault should stay in the hazard model, though its contribution is modest compared with faster faults. A long recurrence does not mean no hazard: a ~2.9 m single-event displacement would be damaging if it ruptured beneath nearby infrastructure.
3. Identify the two additional datasets that would most improve the hazard assessment, and explain how each would change the interpretation.
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1. A second palaeoseismic trench with datable material above and below the youngest faulted horizon. This would test whether the 1.1 ka event is local or fault-wide, measure slip per event at another site, and show whether the recurrence is regular or clustered. If no Holocene rupture is found, the fault may be segmented or lower-slip; if a similar event is found, the hazard is confirmed.
2. A seismic reflection/refraction profile or microearthquake focal mechanisms to constrain fault dip and down-dip geometry. Dip matters because slip rate and recurrence scale with 1/sin(dip). A shallower dip would raise the slip rate and shorten the recurrence; a steeper dip would do the opposite. Additional cosmogenic nuclide dating of each terrace surface would also test whether the ages are abandonment ages and whether the offsets are constant.