The output format should be time t, radius r, vertical displacement u(r,t), horizontal displacement v(r,t), and geoid displacement N(r,t), e.g.
| t_1 | r_1 | u(r_1,t_1) | v(r_1,t_1) | N(r_1,t_1) |
| t_1 | r_2 | u(r_2,t_1) | v(r_2,t_1) | N(r_2,t_1) |
| ... | ... | ... | ... | ... |
Changes in the earth's rotation vector lead to changes in sea-level. For glacial isostatic adjustment, changes in the rotation velocity have a trivial effect on the sea-level whereas polar wander contributes a small but non-negligible amount to sea-level change. Polar wander has a first order effect on the degree 2,1 harmonic of the rotational potential and this change in potential can be used to calculate relative sea-level via the tidal k and h Love numbers (Han & Wahr, 1989, pp1-6 of : Slow deformation and Transmission of Stress in the Earth, Cohen & Vanicek (eds); Milne & Mitrovica, 1996, GJI, 126, F13-F20). A single operator combining the calculation of the polar wander and the sea-level change resulting from it may be formed and written in normal mode form (Bills & James, 1996, GRL, 23, 3023-3026). Of the three cited papers, only Milne & Mitrovica gives the complete theory and corresponding results - Han & Wahr neglect the "1" term in their derivation (eq 3) and Bills & James neglect the "k-h" term in their figure 1.
Because of the different approaches used in calculating the rotational contribution to sea-level change, we just ask for the time-dependent sea-level change (difference between solid and geoidal surface) at the site 45N, 90W in response to the instantaneous loading of an 800 km radius disc with rectangular profile centred at 65N, 90W (same as in section 2) for times 0, 1, 2, 5, 10, 20 and infinity ka after loading. Ignore the effects of ocean loading for this calculation.
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