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A high-degree spherical harmonic series is used to compute the radial deformation of the Earth by oceanic tidal loading. By exploiting fast numerical transforms, this approach is found to be much more efficient, but no less accurate, than the traditional Green's function approach. The method is used to derive an atlas of load tide maps for 10 constitutents of the NSWC ocean tide model.
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Mathematical and programming techniques to numerically calculate Earth response to global semidiurnal and diurnal ocean tide models were developed. Global vertical crustal deformations were evaluated for M sub 2, S sub 2, N sub 2, K sub 2, K sub 1, O sub 1, and P sub 1 ocean tide loading, while horizontal deformations were evaluated for the M sub 2 tidal load. Tidal gravity calculations were performed for M sub 2 tidal loads, and strain tensor elements were evaluated for M sub 2 loads. The M sub 2 solution used for the ocean tide included the effects of self-gravitation and crustal loading.
Goddard Ocean Tide model GOT99.2 is a new solution for the amplitudes and phases of the global oceanic tides, based on over six years of sea-surface height measurements by the TOPEX/POSEIDON satellite altimeter. Comparison with deep-ocean tide-gauge measurements show that this new tidal solution is an improvement over previous global models, with accuracies for the main semidiurnal lunar constituent M2 now below 1.5 cm (deep water only). The new solution benefits from use of prior hydrodynamic models, several in shallow and inland seas as well as the global finite-element model FES94.1. This report describes some of the data processing details involved in handling the altimetry, and it provides a comprehensive set of global cotidal charts of the resulting solutions. Various derived tidal charts are also provided, including tidal loading deformation charts, tidal gravimetric charts, and tidal current velocity (or transport) charts. Finally, low-degree spherical harmonic coefficients are computed by numerical quadrature and are tabulated for the major short-period tides; these are useful for a variety of geodetic and geophysical purposes, especially in combination with similar estimates from satellite laser ranging.
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The earth's imperfectly elastic response to body and loading tidal forces is discussed using complex Love numbers and complex mass loading coefficients. Exact analytical expressions were derived relating the energy dissipation within an inhomogeneous, compressible solid earth to the surface values of these complex characteristic numbers, thus relating the global dissipation function Q to the phase shifts in the potential, gravity, tilt, strain and displacement tides. Integration of a global ocean tidal model shows that energy dissipated in the solid earth due to ocean loading is at least 10% of that dissipated in the body tides.
In central California, periodic earthquake occurrence suggests a relationship with annual hydrological, atmospheric, thermal, and tidal loadings. Here, in catalogs of declustered earthquakes within 100 km from Parkfield, CA, we study a semiannual periodicity for the monthly number of ≤7.2-km-deep earthquakes and the monthly median hypocenter depth over 1994–2002 and 2006–2014. Peak-trough months in fitted periodic components differ between time spans and event populations. Deeper earthquakes present no semiannual and a weak annual periodicity. Although modeled pore pressure shows a Spring peak, when added to the elastic Coulomb stress from surface hydrospheric loads, it fails to predict a 6-month periodicity for 2006–2014. In 1994–2002, the pore-pressure amplitude appears to be of same order as the elastic stress and may have had a stronger effect. In 2006–2014, we did not find load model parameters explaining the observed pattern or apparent changes following the 2003 San Simeon and 2004 Parkfield earthquakes.
SUMMARY We examine the cyclic amplitude variation of seismic noise recorded by continuous three-component broad-band seismic data with durations spanning 91–713 d (2008–2011) from three different networks: Anza seismic network, IDA network and the transportable seismic array. These stations surround the San Jacinto Fault Zone (SJFZ) in southern California. We find the seismic noise amplitudes exhibit a cyclical variation between 0.3 and 7.2 Hz. The high-frequency (≥0.9 Hz) noise variations can be linked to human activity and are not a concern. Our primary interest is signals in the low frequencies (0.3–0.9 Hz), where the seismic noise is modulated by semi-diurnal tidal mode M2. These long-period (low-frequency) variations of seismic noise can be attributed to a temporal change of the ocean waves breaking at the shoreline, driven by ocean tidal loading. We focus on the M2 variation of seismic noise at f = 0.6 Hz, travelling distances of ∼92 km through the crust from offshore California to the inland Anza, California, region. Relative to the shoreline station, data from the inland stations show a phase lag of ∼ –12°, which we attribute to the cyclic change in M2 that can alter crustal seismic attenuation. We also find that for mode M2 at 0.6 Hz, the amplitude variations of the seismic quality factor (Q) depend on azimuth and varies from 0.22 per cent (southeast to northwest) to 1.28 per cent (northeast to southwest) with Q = 25 for Rayleigh waves. We propose the direction dependence of the Q variation at 0.6 Hz reflects the preferred orientation of subfaults parallel to the main faulting defined by the primarily N45°W strike of the SJFZ.
The observed triaxial ellipsoid shape of Mimas, in conjunction with a mean density of 1137 kg/cu cm, is presently used as the basis of hydrostatic equilibrium and nonhydrostatic models of internal structure whose outer layers are sufficiently strong to support part of the tidal load. Such plausible internal structures are consistent with the shape and density constraints as (1) a two-layer model in hydrostatic equilibrium, (2) a hydrostatic model with four layers of equal depth, and (3) a nonhydrostatic constant-density model with an elastic lithosphere; these models admit either homogeneous or heterogeneous accretion, as well as either a cold thermal history or melting and differentiation.
The VLBI data set spanning Aug. 1919 to the present is a major constituent of ITRF2000 because of the time span, the geometric strength and the accuracy of the modeling. Formal velocity errors for the best stations are less than 0.3 mm/yr while the probable frame definition error for station velocities is approximately 0.4 mm/yr. The primary systematic errors are the troposphere and tidal loading (solid Earth and ocean). However, the scale of the VLBI TRF is probably only weakly affected because of continued improvements in the tropospheric mapping function and gradient estimation. There are some weaknesses in the spatial distribution of data, particularly in the southern hemisphere, and the quality of the mobile VLBI results is now suboptimal. The deployment of the TIGO system to Chile will improve the geometric coverage. The current state of the art of VLBI analysis will be discussed.
Two papers on tidal dissipation were completed and published. The first of these extended our earlier work, which focused on the dominant M2 constituent, to include 7 additional constituents. In addition to confirming a total deep water dissipation total very close to 1 TW, this study demonstrated significant differences in the distribution of dissipation between diurnal and semi-diurnal constituents. The second paper involved an extensive modeling study of tides in the present day and the last glacial maximum. In this study we showed that accuracy of tidal solutions for the present day Ocean were significantly improved by including a parameterization of internal tide drag over rough topography in the deep ocean. It was also demonstrated that a complete self-consistent treatment of Ocean self attraction and tidal loading was required for accurate solutions.
The current cache of S/X-band geodetic/astrometric VLBI data accumulated since 1979 is approx. 5 million observations and is increasing by approx. 300,000 observations per year. The long time interval and access to all such VLBI data for re-analysis have contributed to their usefulness for the terrestrial and celestial reference frames, Earth orientation parameters, tidal and non-tidal loading, and troposphere. While data access and integrity have been maintained through the Mark III data base system as storage devices and media have evolved, past transitions have been major projects. A new format and retention concept to ensure eternal archiving and access should make use of self-documentation, generalized media, network connectivity and multiple redundancy. Similarly permanent organizations or sequences of organizations are also necessary.
The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.
Forward modeling of non-tidal atmospheric loading displacements at geodetic tracking stations have not routinely been included in Doppler Orbitography and Radiopositionning Integrated by Satellite (DORIS) or Satellite Laser Ranging (SLR) station analyses for either POD applications or reference frame determination. The displacements which are computed from 6-hourly models such as the ECMWF and can amount to 3-10 mm in the east, north and up components depending on the tracking station locations. We evaluate the application of atmospheric loading in a number ways using the NASA GSFC GEODYN software: First we assess the impact on SLR & DORIS-determined orbits such as Jason-2, where we evaluate the impact on the tracking data RMS of fit and how the total orbits are changed with the application of this correction. Preliminary results show an RMS radial change of 0.5 mm for Jason-2 over 54 cycles and a total change in the Z-centering of the orbit of 3 mm peak-to-peak over one year. We also evaluate the effects on other DORIS-satellites such as Cryosat-2, Envisat and the SPOT satellites. In the second step, we produce two SINEX time series based on data from available DORIS satellites and assess the differences in WRMS, scale and Helmert translation parameters. Troposphere refraction is obviously an important correction for radiometric data types such as DORIS. We evaluate recent improvements in DORIS processing at GSFC including the application of the Vienna Mapping Function (VMF1) grids with a-priori hydrostatic (VZHDs) and wet (VZWDs) zenith delays. We reduce the gridded VZHD at the stations height using pressure and temperature derived from GPT (strategy 1) and Saastamoinen. We discuss the validation of the VMF1 implementation and its application to the Jason-2 POD processing, compared to corrections using the Niell mapping function and the GMF. Using one year of data, we also assess the impact of the new troposphere corrections on the DORIS-only solutions, most importantly on the scale of the weekly solutions.
The effects of long-wavelength (> 100 km), seasonal variability in continental water storage on vertical crustal motions are assessed. The modeled vertical displacements (delta-r(sub M)) have root-mean-square (RMS) values for 1994-1998 as large as 8 mm with ranges up to 30 mm, and are predominantly annual in character. Regional strains are on the order of 20 nanostrain for tilt and 5 nanostrain for horizontal deformation. We compare delta-r(sub M) with observed Global Positioning System (GPS) heights (delta-r(sub O)) (which include adjustments to remove estimated effects of atmospheric pressure and annual tidal and non-tidal ocean loading) for 147 globally distributed sites. When the delta-r(sub O) time series are adjusted by delta-r(sub M), their variances are reduced, on average, by an amount equal to the variance of the delta-r(sub M). Of the delta-r(sub O) time series exhibiting a strong annual signal, more than half are found to have an annual harmonic that is in phase and of comparable amplitude with the annual harmonic in the delta-r(sub M). The delta-r(sub M) time series exhibit long-period variations that could be mistaken for secular tectonic trends or post-glacial rebound when observed over a time span of a few years.
This research aims to apply combined wave and tidal current loads to a small-scale floating marine current turbine in a wave tank, where an actuation system applies hydrodynamic and mooring forces on the hardware based on results from a simulation. We use a real-time hybrid test setup with physical wave forcing from the wave tank and simulated current and mooring forces implemented through a tensioned cable array. For this paper, we developed an optimization algorithm that adjusts the hardware geometry of the cable array to achieve more efficient tension allocation across the cables for the loads that need to be actuated. By adjusting the points where the cables are attached to the floating platform and the angles between the platform and the winches, an optimal cable geometry can be found to minimize tension variations in the lines, maintain the desired pretension, and prevent excessive tensions. We present the optimization problem formulation, the actuation system evaluation approach, and optimization results that show effective cable actuation setups that are being considered for implementation in the wave tank tests.
Abstract We examine ocean tides in the barotropic version of the Model for Prediction Across Scales (MPAS‐Ocean), the ocean component of the Department of Energy Earth system model. We focus on four factors that affect tidal accuracy: self‐attraction and loading (SAL), model resolution, details of the underlying bathymetry, and parameterized topographic wave drag. The SAL term accounts for the tidal loading of Earth's crust and the self‐gravitation of the ocean and the load‐deformed Earth. A common method for calculating SAL is to decompose mass anomalies into their spherical harmonic constituents. Here, we compare a scalar SAL approximation versus an inline SAL using a fast spherical harmonic transform package. Wave drag accounts for energy lost by breaking internal tides that are produced by barotropic tidal flow over topographic features. We compare a series of successively finer quasi‐uniform resolution meshes (62.9, 31.5, 15.7, and 7.87 km) to a variable resolution (45 to 5 km) configuration. We ran MPAS‐Ocean in a single‐layer barotropic mode forced by five tidal constituents. The 45 to 5 km variable resolution mesh obtained the best total root‐mean‐square error (5.4 cm) for the deep ocean ( 1,000 m) tide compared to TPXO8 and ran twice as fast as the quasi‐uniform 8 km mesh, which had an error of 5.8 cm. This error is comparable to those found in other forward (non‐assimilative) ocean tide models. In future work, we plan to use MPAS‐Ocean to study tidal interactions with other Earth system components, and the tidal response to climate change.
In recent years, Kalman filtering has emerged as a suitable technique to determine terrestrial reference frames (TRFs), a prime example being JTRF2014. The time series approach allows variations of station coordinates that are neither reduced by observational corrections nor considered in the functional model to be taken into account. These variations are primarily due to non-tidal geophysical loading effects that are not reduced according to the current IERS Conventions (2010). It is standard practice that the process noise models applied in Kalman filter TRF solutions are derived from time series of loading displacements and account for station dependent differences. So far, it has been assumed that the parameters of these process noise models are constant over time. However, due to the presence of seasonal and irregular variations, this assumption does not truly reflect reality. In this study, we derive a station coordinate process noise model allowing for such temporal variations. This process noise model and one that is a parameterized version of the former are applied in the computation of TRF solutions based on very long baseline interferometry data. In comparison with a solution based on a constant process noise model, we find that the station coordinates are affected at the millimeter level.