Engineering topics
Publications and source records attributed to Wahr, J. M..
Empirical models for the monthly and fortnightly ocean tides are estimated using sea surface height data from repeat cycles 10 to 190 of the TOPEX/POSEIDON (T/P) altimetry mission.
The Earth is a dynamic system-it has a fluid, mobile atmosphere and oceans, a continually changing distribution of ice, snow, and groundwater, a fluid core undergoing hydromagnetic motion, a mantle undergoing both thermal convection and rebound from glacial loading of the last ice age, and mobile tectonic plates.
The geoid and the boundary topography caused by mass loads inside the earth were estimated. It is shown that the estimates are affected by compressibility, by a radially varying density distribution, and by the presence of phase boundaries with density discontinuities. The geoid predicted in the chemical boundary case is 30 to 40 percent smaller than that predicted in the phase case. The effects of compressibility and radially varying density are likely to be small. The inner core-outer core topography for loading inside the mantle and for loading inside the inner core were computed.
Theories of nutation are examined critically to develop an extension of the theoretical description based on an earth in nonhydrostatic equilibrium. The estimation of nutation amplitude as a function of frequency is reviewed with reference to contributing variables such as the oceans, mantle anelasticity, and nonhydrostatic structure. Theoretical results by Wahr (1981) are compared to those of VLBI observations, and other VLBI data are used to discuss Wahr and Bergen's (1986) theoretical nutation admittances for an anelastic earth. The contributions associated with the tilt-over mode and with free-core nutations (FCN) are discussed, and the contribution of anelasticity is examined. The VLBI data show that nutation data are important sources of information regarding the earth's interior. Nutation amplitudes are derived with a model for a nonhydrostatically prestressed earth to determine the FCN contributions.
It was shown earlier that 1 x 10 to the -14th Doppler data and 3 cm accuracy range measurements to a small Mercury Relativity Satellite in a polar orbit with four-hour period can give high-accuracy tests of gravitational theory. A particular conceptual design has been developed for such a satellite, which would take less than 10 percent of the approach mass for a possible future Mercury Orbiter Mission. The spacecraft is similar to the Pioneer Venus Orbiter, but scaled down by about a factor four in linear dimensions. A despun antenna 30 cm in diameter is used for tracking. The transmitted power is roughly 0.2 watts at K-band and 0.5 watts at X-band. The orbit parameters for individual eight-hour arcs and the gravity field of Mercury through degree and order 10 are determined mainly from the Doppler data. A 50 MHz K-band sidetone system provides the basic ranging accuracy. The spacecraft mass is 50 kg or less.
Atmospheric mass loads and deforms the earth's crust. By performing a convolution sum between daily, global barometric pressure data and mass loading Green's functions, the time dependent effects of atmospheric loading, including those associated with short-term synoptic storms, on surface point positioning measurements and surface gravity observations are estimated. The response for both an oceanless earth and an earth with an inverted barometer ocean is calculated. Load responses for near-coastal stations are significantly affected by the inclusion of an inverted barometer ocean. Peak-to-peak vertical displacements are frequently 15-20 mm with accompanying gravity perturbations of 3-6 micro Gal. Baseline changes can be as large as 20 mm or more. The perturbations are largest at higher latitudes and during winter months. These amplitudes are consistent with the results of Rabbel and Zschau (1985), who modeled synoptic pressure disturbances as Gaussian functions of radius around a central point. Deformation can be adequately computed using real pressure data from points within about 1000 km of the station. Knowledge of local pressure, alone, is not sufficient. Rabbel and Zschau's hypothesized corrections for these displacements, which use local pressure and the regionally averaged pressure, prove accurate at points well inland but are, in general, inadequate within a few hundred kilometers of the coast.
The 5.5 years of VLBI observations primarily collected under project IRIS are used to search for evidence of the free-core nutation (FCN). The observations are consistent with an irregular excitation process, and a model which assumes a step excitation in the FCN amplitude to about 2.0 milliseconds of arc in late 1985 fits the data well. Theoretical analysis appears to rule out the strong Mexican earthquake of September 19, 1985, as a cause of the excitation.
The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, both analytical and numerical models for the pole tide are constructed. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.
Variations in the geocentric position of the earth's rotation axis (polar motion) cause deformation within the earth. The effects of this deformation on radial and horizontal positions of points on the earth's surface, on baseline lengths between those points, and on surface gravity are estimated. The effects of the oceans and of the earth's anelasticity on this deformation are found to be negligible. Peak-to-peak variations in radial motion are typically 10-20 mm over a year. Horizontal displacements are less than 7-8 mm. Variations in baseline length can be as large as 30-40 mm. Variations of up to 13 microgal in surface gravity are possible. These numbers are all small enough that they can probably not be used to learn about the earth. However, they are large enough to affect noticeably present high-quality geodetic observations.
Seasonal, zonal surface torques between the atmosphere and the earth are estimated and compared, using data from a number of independent sources. The mountain torque is computed both from surface pressure data and from isobaric height data. The friction torque is estimated from the oceanic stress data of Hellerman and Rosenstein. Results for the total torque are inferred from atmospheric angular momentum data. Finally, the globally integrated total torque is compared with astronomical observations of the earth's rotation rate. These comparisons help us to assess the quality of the different results. Zonal torques are also computed using results from a GFDL general circulation model of the atmosphere. A comparison with the corresponding results inferred from real data is presented and interpreted in terms of model accuracy.
The effects of the oceans, which are subject to a resonance due to a free rotational eigenmode of an elliptical, rotating earth with a fluid outer core having an eigenfrequency of (1 + 1/460) cycle/day, on the body tide and nutational response of the earth to the diurnal luni-tidal force are computed. The response of an elastic, rotating, elliptical, oceanless earth with a fluid outer core to a given load distribution on its surface is first considered, and the tidal sea level height for equilibrium and nonequilibrium oceans is examined. Computations of the effects of equilibrium and nonequilibrium oceans on the nutational and deformational responses of the earth are then presented which show small but significant perturbations to the retrograde 18.6-year and prograde six-month nutations, and more important effects on the earth body tide, which is also resonant at the free core notation eigenfrequency.
The earth is believed to possess a free nutational mode due to its rotating, elliptical, fluid core, with an eigenfrequency of approximately (1 + 1/460) cycle per sidereal day as seen from the sidereally rotating earth. This free 'core nutation' has not yet been undisputably observed. Furthermore, there has been considerable doubt that any known mechanism could excite this mode to an observable level. It is shown here that diurnal atmospheric and oceanic loading of the earth's surface provides an efficient excitation mechanism which depends critically on the physical damping of the mode. Possible effects of the mode on geodetic measurements are discussed. The effects of 'wobble' and 'nutation' on astrometric observations are also considered.
The long period luni-solar tidal potential is known to cause periodic changes in the earth's rotation rate. It is found that the effect of a dissipationless fluid outer core is to reduce the amplitudes of these tidal perturbations by about 11 percent. When the fluid core effect is added to Agnew and Farrell's (1978) estimate of the effect of an equilibrium ocean, the result is in accord with observation. The effects of dissipative processes within the fluid core are also examined. Out-of-phase perturbations are found which could be as large as about 10 ms at 18.6 yr. It is concluded, however, that the poorly understood decade fluctuations in the earth's rotation rate will prohibit observation of this effect.
The complete tidal response of an elliptical, rotating, elastic Earth is found to contain small displacements which do not fit into the conventional Love number framework. Corresponding observable tidal quantities (gravity, tilt, strain, Eulerian potential, etc.) are modified by the addition of small latitude dependent terms.