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

At $x=10{\delta }_Y$, the annual attenuation is $e^{-10}$ and the daily attenuation is $e^{-10\sqrt{365}}$, approximately $10^{-83}$. ThusOn the same vertical scale as the surface plot this is almost the constant ${\Theta }_0$. With a sufficiently enlarged scale, a residual annual oscillation of amplitude $4.54\times 10^{-5}A$ remains. Its phase lag is ten radians, interpreted modulo $2\pi$ when comparing periodic maxima.