Stacking global GPS verticals and horizontals to solve for the fortnightly and monthly body tides: Implications for mantle anelasticity

Abstract

The availability of long-term position measurements from permanent GPS stations distributed around the Earth makes it feasible to extract small, globally coherent, long-period geophysical signals from the data. Using 11 years of daily vertical and horizontal positions from over 600 permanent GPS stations worldwide, we solve for the amplitude and phase of the fortnightly and monthly body tides by stacking the surface displacements against spherical harmonics and isolating the fortnightly and monthly signals in the stacks. We use our solutions to help constrain the Earth's anelastic properties, which are not well understood within the tidal frequency band. Our error estimates include the effects of the following: (1) random noise across the fortnightly and monthly tidal bands; (2) fortnightly and monthly ocean tide model errors; (3) errors in the diurnal and semidiurnal ocean tide models that alias into the fortnightly and monthly frequency bands; (4) errors in the solid Earth Green's functions used to compute ocean tidal loading corrections; and (5) leakage from GPS draconitic signals at periods close to the fortnightly and monthly frequencies. The mantle anelasticity coefficients we infer from our solutions are consistent with a ω α frequency dependence of mantle Q with α in the range 0.1-0.3.

Anelasticity and Lateral Heterogeneities in Earth's Upper Mantle: Impact on Surface Displacements, Self‐Attraction and Loading, and Ocean Tide Dynamics

“…Applying the classical α-law over the seismic to tide frequency band, Benjamin et al (2006), Kang et al (2015), and Ray and Egbert (2012) showed that anelasticity has an impact on the geoid (body tide), and a value of α in the range of 0.15-0.30 can fit geodetic observations reasonably well. Different from the traditional normal mode (TNM) theory used to study body tides, Benjamin et al (2006), Lau et al (2015), and Wahr and Bergen (1986) developed an extended normal mode (ENM) approach, which predicts a more accurate perturbation of body tides due to anelasticity (Lau et al, 2016).…”

The Complex Love Numbers of Long‐Period Zonal Tides Retrieved From Global GPS Displacements: Applications for Determining Mantle Anelasticity

“…From Table 1, we can find that our estimates have certain (not too large) deviations from the values suggested by IERS Convention 2010. When comparing our estimates for the Mm and Mf with those of Krásná et al (2013) and Kang et al (2015), we can find that Krásná et al (2013)'s results have large deviations from our and Kang et al (2015)'s results (and the IERS reference values), and their imaginary parts h I and l I are even positive values (marked by gray areas in Table 1). As for the estimation errors of the Mf and Mm tides, our results are generally less than those of Kang et al (2015).…”

“…This bootstrap procedure has been widely used for uncertainty estimations in various geophysical studies (e.g., Chen et al, 2013;Ding & Chao, 2015;Häfner & Widmer-Schnidrig, 2013;Widmer, et al, 1992). Kang et al (2015) further considered the errors of the ocean load tide model and the load Green's function. Compared with the uncertainties estimated from the real data based on the bootstrap procedure, such errors are too small and hence we ignore them in this study.…”

“…Different from Kang et al. (2015), in which the SHS method was used, we will use the optimal sequence estimation (OSE) method (Ding & Chao, 2015; Ding & Shen, 2013b). This method is not sensitive to the geographical distribution of stations (Ding & Chao, 2015, 2017), but sensitive to the background noise of different stations; and it has been proven to be better than the SHS method for isolating target signals (Majstorović et al., 2019).…”

Seasonal Surface Loading Helps Constrain Short‐Term Viscosity of the Asthenosphere

“…While exhibiting the spatial variability necessary for sensitivity to Earth's rheology at the appropriate depths, such observations are therefore too short in period to impinge directly on the question of postseismic deformation in the Earth's lower crust or asthenosphere. In contrast, the Earth's body tides, which likewise show evidence of lower mantle anelasticity at semidiurnal right through to decadal timescales (Benjamin et al, ; Kang et al, ), are large‐scale phenomena and are therefore largely insensitive to the rheology of the outermost few hundred kilometers of the Earth.…”