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

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 ωα frequency dependence of mantle Q with α in the range 0.1–0.3.

[1]  Seongryong Kim,et al.  Evidence of Volatile‐Induced Melting in the Northeast Asian Upper Mantle , 2021, Journal of Geophysical Research: Solid Earth.

[2]  B. Chao,et al.  Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation , 2014 .

[3]  R. Ray,et al.  Long‐period tidal variations in the length of day , 2014 .

[4]  M. Heflin,et al.  Stacking global GPS verticals and horizontals to solve for the fortnightly body tide , 2013 .

[5]  Jim R. Ray,et al.  Subseasonal GNSS positioning errors , 2013 .

[6]  R. Eanes,et al.  Constraints on Energy Dissipation in the Earth's Body Tide from Satellite Tracking and Altimetry , 2013 .

[7]  Xiaoli Ding,et al.  The tidal displacement field at Earth's surface determined using global GPS observations , 2013 .

[8]  Benjamin F. Chao,et al.  Analysis of tidal signals in surface displacement measured by a dense continuous GPS array , 2012 .

[9]  Duncan Carr Agnew,et al.  SPOTL: Some Programs for Ocean-Tide Loading , 2012 .

[10]  Jim R. Ray,et al.  Sub-daily alias and draconitic errors in the IGS orbits , 2011, GPS Solutions.

[11]  R. Ray,et al.  Fortnightly Earth Rotation, Ocean Tides, and Mantle Anelasticity , 2011 .

[12]  Takeo Ito,et al.  Probing Asthenospheric Density, Temperature, and Elastic Moduli Below the Western United States , 2011, Science.

[13]  R. J. Tayler,et al.  New Computations of the Tide‐generating Potential , 2007 .

[14]  G. Masters,et al.  Spherically symmetric attenuation within the Earth from normal mode data , 2007 .

[15]  Mike P. Stewart,et al.  GPS height time series: Short‐period origins of spurious long‐period signals , 2007 .

[16]  O. Francis,et al.  Modelling the global ocean tides: modern insights from FES2004 , 2006 .

[17]  S. Desai,et al.  Constraints on mantle anelasticity from geodetic observations, and implications for the J2 anomaly , 2006 .

[18]  Yuebing Li,et al.  Green's function of the deformation of the Earth as a result of atmospheric loading , 2004 .

[19]  Mike P. Stewart,et al.  Aliased tidal signatures in continuous GPS height time series , 2003 .

[20]  Jacques Hinderer,et al.  The search for the Slichter mode: comparison of noise levels of superconducting gravimeters and investigation of a stacking method , 2003 .

[21]  Michael B. Heflin,et al.  Large‐scale global surface mass variations inferred from GPS measurements of load‐induced deformation , 2003 .

[22]  G. Blewitt.  Self‐consistency in reference frames, geocenter definition, and surface loading of the solid Earth , 2003 .

[23]  Michael B. Heflin,et al.  Site distribution and aliasing effects in the inversion for load coefficients and geocenter motion from GPS data , 2002 .

[24]  Shailen D. Desai,et al.  Observing the pole tide with satellite altimetry , 2002 .

[25]  G. Egbert,et al.  Efficient Inverse Modeling of Barotropic Ocean Tides , 2002 .

[26]  M. Ooe,et al.  Ocean Tide Models Developed by Assimilating TOPEX/POSEIDON Altimeter Data into Hydrodynamical Model: A Global Model and a Regional Model around Japan , 2000 .

[27]  P. Defraigne,et al.  Length of day variations due to zonal tides for an inelastic earth in non-hydrostatic equilibrium , 1999 .

[28]  Richard D. Ray,et al.  A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2 , 1999 .

[29]  S. Dickman,et al.  Constraints on Q at long periods from Earth's rotation , 1998 .

[30]  B. Chao,et al.  Estimation of period and Q of the Chandler wobble , 1996 .

[31]  S. Desai,et al.  Empirical ocean tide models estimated from TOPEX/POSEIDON altimetry , 1995 .

[32]  H. Scherneck.  A parametrized solid earth tide model and ocean tide loading effects for global geodetic baseline measurements , 1991 .

[33]  J. Wahr,et al.  Constraining core undertones using stacked IDA gravity records , 1991 .

[34]  John M. Wahr,et al.  Spectroscopic Analysis of Global Tide Gauge Sea Level Data , 1990 .

[35]  John M. Wahr,et al.  The effects of mantle anelasticity on nutations, earth tides, and tidal variations in rotation rate , 1986 .

[36]  R. Barrera,et al.  Vector spherical harmonics and their application to magnetostatics , 1985 .

[37]  D. L. Anderson,et al.  Preliminary reference earth model , 1981 .

[38]  John M. Wahr,et al.  Body tides on an elliptical, rotating, elastic and oceanless earth , 1981 .

[39]  Don L. Anderson,et al.  The frequency dependence of Q in the Earth and implications for mantle rheology and Chandler wobble , 1979 .

[40]  R. Buland,et al.  Observations from the IDA network of attenuation and splitting during a recent earthquake , 1979, Nature.

[41]  R. S. Hart,et al.  Attenuation models of the earth , 1978 .

[42]  F. Gilbert,et al.  An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra , 1975, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[43]  J. Mendiguren.  Identification of Free Oscillation Spectral Peaks for 1970 July 31, Colombian Deep Shock using the Excitation Criterion , 1973 .

[44]  W. Farrell.  Deformation of the Earth by surface loads , 1972 .

[45]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[46]  W. Bosch,et al.  EOT11A - Empirical Ocean Tide Model from Multi-Mission Satellite Altimetry , 2008 .

[47]  S. Bettadpur,et al.  Temporal Variability of Earth’s Gravitational Field from Satellite Laser Ranging , 1996 .

[48]  F. Dahlen,et al.  The period and Q of the Chandler wobble , 1981 .