= Solution
If a restored channel or fan boundary has accumulated displacement $d$ since it formed, a constant <fault slip rate> $v=1.6\,\mathrm{mm\,yr^{-1}}$ gives the <geomorphic offset-age relation>
$$
\boxed{t=\frac d v=625\,d_{\mathrm{metres}}\ \mathrm{yr}.}
$$
The right-hand channel jog is of order one to two of the printed $100$ m scale bars, so apparent offsets of order $100$–$200$ m give \b[about $62.5$–$125$ ka]. These are scale-based order-of-magnitude estimates, not surveyed piercing-point offsets: the amount of deflection along an eroding channel is not automatically equal to the tectonic displacement. For example, a reliably restored $150$ m marker would imply $93.75$ ka.
These times lie in the late <Pleistocene>, when global glacial–interglacial changes could alter vegetation, <sediment> supply and runoff and thereby promote <alluvial fan> deposition or abandonment. The wide interval spans different climatic phases, so it does not identify one event or prove a climatic cause. More importantly, a channel cut into a fan usually dates channel establishment or abandonment; the fan <sediment> can be older. Independent <optically stimulated luminescence dating>, stratigraphic correlation and several matched offsets are needed to assign a depositional age and test a climatic correlation.
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