Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2024 / Paper 3 / 8 / c / ii / Solution

At $x=10{\delta }_D$, the daily component is multiplied by $e^{-10}\simeq 4.54\times 10^{-5}$ and has a lag of ten radians. The annual component instead has $x/{\delta }_Y=10/\sqrt{365}\simeq 0.5234$. HenceThe sketch is nearly a smooth annual sinusoid, with annual amplitude about $0.5925A$ and annual phase lag about $0.5234$ radians, corresponding to about $30.4$ days on the chosen year scale. The tiny daily component is retained in the formula rather than declared identically zero.