### Browsing by Author "Pagiatakis, Spiros, D."

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Item Ocean tide loading on a self-gravitating, compressible, layered, anisotropic, viscoelastic and rotating earth with solid inner core and fluid outer corePagiatakis, Spiros, D.A novel ocean tide loading model is developed which allows the earth to be self-gravitating, compressible, layered, anisotropic, viscoelastic and rotating, with solid inner core and fluid outer core. The deformation equations of the earth are developed, following the analytical mechanics approach. The standard-linear-solid-type rheology, as well as the grain-boundary relaxation model for the dissipation mechanism within the earth are adopted in this study. The thermodynamic state of the earth is accounted for, through its absolute temperature, Gibbs free activation energy, viscosity and Q profiles. For the numerical integration of the equations of deformation, the following models are considered: a) PREM for the elasticity parameters of the earth appropriately modified at tidal frequencies, using dispersion relations, b) SL8 model for the Q profile of the earth, c) viscosity profile with the following viscosities: 2.5 x 10[to the power of 22] poise for the lower mantle, 10[to the power of 22] poise for the transition zone and 10[to the power of 17] poise for the LVZ, d) SAMMIS ET. AL, [1977] model for the Gibbs free activation energy profile (for the transition zone and lower mantle), with an adiabatic temperature gradient of 0.3 K/km. The value of 125 kCal/Mole for the LVZ is considered, and e) STACEY'S [1977] thermal model for the temperature profile of earth. Complex load number h'[subscript n], k'[subscript n] and l'[subscript n], are calculated and the results are the following: a) The rotation of the earth has an effect on the load numbers that can be as much as 1.8%, 3.1% and 3.3% respectively, depending on the degree of expansion. There is a weak latitude dependence of the load numbers for n ≤ 4; when latitude varies from 0° to ±45°, its effect is of the order of 0.4%. b) The effect of anisotropy in the upper mantle can be as much as 1.9%, 2.3% and 2.5% respectively, depending on the degree of expansion. c) At the semidiurnal periods, the load numbers on a viscoelastic earth are about 0.2% larger than their corresponding values on an elastic earth. At fortnightly periods, viscoelastic h'[subscript 100], k'[subscript 100] and l'[subscript 100] are larger than their corresponding elastic values by 0.5%, 1.5% and 1.3%, respectively/ For other values of n, the effect of viscosity is smaller. Complex Green's functions are determined for displacements, gravity and tilt; they are given in the same form a those of FARRELL [1972], for easy implementation with existing software. The predictive power of the model is tested against accurately determined M[subscript 2] gravity tide residuals at 10, globally distributed, tidal stations. It is shown that the difference between observed residual gravity and predicted load gravity tide amplitudes is reduced for all tested stations as much as 63%, when compared to predictions on an elastic, isotropic and nonrotating earth. There is also an improvement in the phases of the predicted load gravity tide. All the novel features of this research are included in the new version of the LOADSDP software package [PAGIATAKIS, 1982]. LOADSDP software can be used to evaluate displacements, gravity perturbations and tilt at arbitrary locations on the surface of the earth with an accuracy better than 1%.Item Ocean tide loading on a self-gravitating, compressible, layered, anisotropic, viscoelastic and rotating earth with solid inner core and fluid outer corePagiatakis, Spiros, D.A novel ocean tide loading model is developed which allows the earth to be self-gravitating, compressible, layered, anisotropic, viscoelastic and rotating, with solid inner core and fluid outer core. The deformation equations of the earth are developed, following the analytical mechanics approach. The standard-linear-solid-type rheology, as well as the grain-boundary relaxation model for the dissipation mechanism within the earth are adopted in this study. The thermodynamic state of the earth is accounted for, through its absolute temperature, Gibbs free activation energy, viscosity and Q profiles. For the numerical integration of the equations of deformation, the following models are considered: a) PREM for the elasticity parameters of the earth appropriately modified at tidal frequencies, using dispersion relations, b) SL8 model for the Q profile of the earth, c) viscosity profile with the following viscosities: 2.5 x 10[to the power of 22] poise for the lower mantle, 10[to the power of 22] poise for the transition zone and 10[to the power of 17] poise for the LVZ, d) SAMMIS ET. AL, [1977] model for the Gibbs free activation energy profile (for the transition zone and lower mantle), with an adiabatic temperature gradient of 0.3 K/km. The value of 125 kCal/Mole for the LVZ is considered, and e) STACEY'S [1977] thermal model for the temperature profile of earth. Complex load number h'[subscript n], k'[subscript n] and l'[subscript n], are calculated and the results are the following: a) The rotation of the earth has an effect on the load numbers that can be as much as 1.8%, 3.1% and 3.3% respectively, depending on the degree of expansion. There is a weak latitude dependence of the load numbers for n ≤ 4; when latitude varies from 0° to ±45°, its effect is of the order of 0.4%. b) The effect of anisotropy in the upper mantle can be as much as 1.9%, 2.3% and 2.5% respectively, depending on the degree of expansion. c) At the semidiurnal periods, the load numbers on a viscoelastic earth are about 0.2% larger than their corresponding values on an elastic earth. At fortnightly periods, viscoelastic h'[subscript 100], k'[subscript 100] and l'[subscript 100] are larger than their corresponding elastic values by 0.5%, 1.5% and 1.3%, respectively/ For other values of n, the effect of viscosity is smaller. Complex Green's functions are determined for displacements, gravity and tilt; they are given in the same form a those of FARRELL [1972], for easy implementation with existing software. The predictive power of the model is tested against accurately determined M[subscript 2] gravity tide residuals at 10, globally distributed, tidal stations. It is shown that the difference between observed residual gravity and predicted load gravity tide amplitudes is reduced for all tested stations as much as 63%, when compared to predictions on an elastic, isotropic and nonrotating earth. There is also an improvement in the phases of the predicted load gravity tide. All the novel features of this research are included in the new version of the LOADSDP software package [PAGIATAKIS, 1982]. LOADSDP software can be used to evaluate displacements, gravity perturbations and tilt at arbitrary locations on the surface of the earth with an accuracy better than 1%.Item Ocean tide loading, body tide and polar motion effects on very long baseline interferometryPagiatakis, Spiros, D.Response functions for radial and horizontal displacements, gravity perturbations and tilt due to ocean tide loading were derived, using Green’s functions computed by Farrell for the Gutenberg-Bullen A earth model. The general procedure of convolving response functions with an ocean tide model was used in this study. The ocean tide model used was that developed by Schwiderski, using the six leading constituents of the tidal spectrum. The derived response functions for gravity perturbations were tested against existing determinations of the effect from actual data, at eight stations covering the whole earth. This comparison yielded a mean of the absolute differences between the observed gravity perturbations and those obtained in this study of 0.32 µGal with a root-mean-square scatter of 0.19 µGal. A body tide model was also developed. The ephemerides of the moon and the sun were based on approximate formulae. Tests performed on the above approximate formulae indicated that the right ascension and declination of the moon and the sun can be obtained with an accuracy of the order of one minute of arc with respect to the values obtained in the astronomical ephemerides. This uncertainty affects the evaluation of the radial displacement of the terrain by less than 1 cm. The mathematical models for terrain deformations due to body tide and ocean loading ad well as an interpolation procedure for polar motion were added to the Canadian VLBI software package. VLBI data pertaining to the observing period of May 1977, obtained by a 3-station VLBI array were used to test the above models. Due to the large standard errors of these data, there is little that can be concluded from the analysis at this time. There is an improvement in the distribution of the delay-rate residuals. Their root-mean-square scatter decreases by 9.2x10[squared by -5] picoseconds/second while the root-mean-square scatter of the group-delay residuals increases by 3 picoseconds. C-range and co-tidal charts for north America were also produced, showing the radial and the horizontal displacements of the terrain due to load for the six leading tidal constituents.Item Ocean tide loading, body tide and polar motion effects on very long baseline interferometryPagiatakis, Spiros, D.Response functions for radial and horizontal displacements, gravity perturbations and tilt due to ocean tide loading were derived, using Green’s functions computed by Farrell for the Gutenberg-Bullen A earth model. The general procedure of convolving response functions with an ocean tide model was used in this study. The ocean tide model used was that developed by Schwiderski, using the six leading constituents of the tidal spectrum. The derived response functions for gravity perturbations were tested against existing determinations of the effect from actual data, at eight stations covering the whole earth. This comparison yielded a mean of the absolute differences between the observed gravity perturbations and those obtained in this study of 0.32 µGal with a root-mean-square scatter of 0.19 µGal. A body tide model was also developed. The ephemerides of the moon and the sun were based on approximate formulae. Tests performed on the above approximate formulae indicated that the right ascension and declination of the moon and the sun can be obtained with an accuracy of the order of one minute of arc with respect to the values obtained in the astronomical ephemerides. This uncertainty affects the evaluation of the radial displacement of the terrain by less than 1 cm. The mathematical models for terrain deformations due to body tide and ocean loading ad well as an interpolation procedure for polar motion were added to the Canadian VLBI software package. VLBI data pertaining to the observing period of May 1977, obtained by a 3-station VLBI array were used to test the above models. Due to the large standard errors of these data, there is little that can be concluded from the analysis at this time. There is an improvement in the distribution of the delay-rate residuals. Their root-mean-square scatter decreases by 9.2x10[squared by -5] picoseconds/second while the root-mean-square scatter of the group-delay residuals increases by 3 picoseconds. C-range and co-tidal charts for north America were also produced, showing the radial and the horizontal displacements of the terrain due to load for the six leading tidal constituents.