Some Calculations of Ocean Loading Strain Tides in Great Britain

Abstract

Summary The effect of ocean tides on earth tide measurements can be calculated by convolving ocean tidal data with surface mass loading Green’s functions. Two charts of the MZ ocean tide near Great Britain are available, and convolutions have been performed with each. The calculations give the variation of ocean loading strain tides across the country, and differences between the two cases demonstrate the sensitivity of the load strain tide to variations in the tidal model. Perturbations in the strain field due to tides in more distant oceans are also calculated. Convolutions have been made for the 01 tide in local seas, but the indications are that 01 ocean load strain tides are strongly influenced by the tides in more distant oceans. Surface strain measurements in aseismic areas of the Earth principally show strains due to tidal effects. The tidal strains arise from two related sources. The first is the direct gravitational attraction of the Moon and Sun on the solid Earth; this is fairly easily calculable given an Earth model and the kinematics of the Earth-MoonSun system (Longman 1959; Munk & Cartwright 1966). Secondly, the tides in the seas provide a time varying load over the Earth’s surface, which gives rise to additional strains. These load strain tides have the same frequencies as the solid Earth tides, since both are ultimately derived from the same source, the Earth-Moon-Sun system. It is therefore not possible to separate the effects of the two sources by frequency analysis. It is possible that tidal strain (and tilt and gravity) measurements could be used to investigate the Earth’s elastic moduli at shallow depths, but in order to carry out such an investigation the load strain tides expected for any particular Earth model needs to be calculated. Estimates of load tides may also be useful in improving the accuracy of long baseline interferometers, and other sensitive instruments which use Earth based length standards. Tables of strain as a function of angular distance from a point load, the so-called Green’s functions, have recently been calculated for several Earth models (Farrell 1972a). It is possible to convolve these functions with ocean tidal amplitudes to give the load strain tides at any point on the Earth’s surface. The remainder of this account describes how such convolutions have been made for load strain tides in Great Britain, principally for the A42 tidal constituent.