On the Secular Degree 2 Deformation of the Earth

Post-glacial rebound (PGR) contributes to global deformation characterized by the degree 2 zonal spherical harmonics. It also moves the Earth's principal axis (true polar wander, TPW), resulting in global deformation expressed with the degree 2 tesseral spherical harmonics. Their combined contribution might reach 1 mm/yr (Mitrovica et al., 2001), and could affect estimation of plate motion parameters. Global pattern of mantle convection governs long-wavelength geoid undulation (Hager & Richards, 1989). Antipodal pairs of hot/cold plumes characterize the pattern, and changes in the convection may give rise to degree 2 vertical crustal movements (Gurnis et al., 2000). In this study we try to detect degree 2 secular deformation of the Earth from 3-D velocity data of worldwide continuous GPS sites. We looked for vertical velocity field having the shape of zonal, tesseral and sectorial degree 2 spherical harmonics (the latter two have cosine and sine terms), and horizontal velocities proportional to their spatial gradients, using weighted least-squares method. Plate motion parameters (Euler vectors) were estimated simultaneously. With numerical experiments, we confirmed beforehand that the velocity precisions and GPS point distribution are sufficient for the purpose. The tesseral and sectorial components were significant with maximum of about 1 mm/year. They are considered real from 3 reasons, i.e. (1) their directions (ratios of cosine and sine terms) were similar for vertical and horizontal fields although estimated separately, (2) the ratios of vertical and horizontal velocity amplitudes (ratio of the secular Love/Shida numbers) were similar for tesseral and sectorial components, and (3) results were robust against tests to split the data set into two. The centers of uplift were, however, located near Indonesia and off the east coast of North America, fairly different from those expected by the current TPW direction. The estimated zonal component was insignificant, which is consistent with the small dJ2/dt from SLR. Correlation between degree 2 parameters and Euler vectors were small; the latter changed little by introducing the former. The pattern of the obtained degree 2 velocity field is somewhat similar to the prediction (Gurnis et al., 2000), but the amplitudes are larger by an order of magnitude.