Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a flat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected; the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Set. D, 47(12): 1147-1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if tire density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth's rotation both on the surface wave solutions and the interfacial wave solutions should be considered.

A comprehensive study of the 26th December 2004 Sumatra earthquake: possible implications on Earth rotation and investigations on the coseismic and postseismic stress diffusion associated with the seismic rupture

In this work a multidisciplinary study of the December 26th, 2004 Sumatra earthquake has been carried out. We have investigated both the effect of the earthquake on the Earth rotation and the stress field variations associated with the seismic event. In the first part of the work we have quantified the effects of a water mass redistribution associated with the propagation of a tsunami wave on the Earth’s pole path and on the length-of-day (LOD) and applied our modeling results to the tsunami following the 2004 giant Sumatra earthquake. We compared the result of our simulations on the instantaneous rotational axis variations with some preliminary instrumental evidences on the pole path perturbation (which has not been confirmed yet) registered just after the occurrence of the earthquake, which showed a step-like discontinuity that cannot be attributed to the effect of a seismic dislocation. Our results show that the perturbation induced by the tsunami on the instantaneous rotational pole is characterized by a step-like discontinuity, which is compatible with the observations but its magnitude turns out to be almost one hundred times smaller than the detected one. The LOD variation induced by the water mass redistribution turns out to be not significant because the total effect is smaller than current measurements uncertainties. In the second part of this work of thesis we modeled the coseismic and postseismic stress evolution following the Sumatra earthquake. By means of a semi-analytical, viscoelastic, spherical model of global postseismic deformation and a numerical finite-element approach, we performed an analysis of the stress diffusion following the earthquake in the near and far field of the mainshock source. We evaluated the stress changes due to the Sumatra earthquake by projecting the Coulomb stress over the sequence of aftershocks taken from various catalogues in a time window spanning about two years and finally analyzed the spatio-temporal pattern. The analysis performed with the semi-analytical and the finite-element modeling gives a complex picture of the stress diffusion, in the area under study, after the Sumatra earthquake. We believe that the results obtained with the analytical method suffer heavily for the restrictions imposed, on the hypocentral depths of the aftershocks, in order to obtain the convergence of the harmonic series of the stress components. On the contrary we imposed no constraints on the numerical method so we expect that the results obtained give a more realistic description of the stress variations pattern.

Earth Rotation and Gravity Field Parameters from Satellite Laser Ranging

We present the results from a simultaneous estimation of the gravity field, Earth rotation parameters, and station coordinates from combined SLR solutions incorporating up to nine geodetic satellites: LAGEOS-1/2, Starlette, Stella, AJISAI, Beacon-C, Lares, Blits and LARES. These solutions cover all three pillars of satellite geodesy and ensure full consistency between the Earth rotation parameters, gravity field coefficients, and geometry-related parameters. We address benefits emerging from such an approach and discuss particular aspects and limitations of the gravity field recovery using SLR data. The current accuracy of SLR-derived polar motion, by the means of WRMS w.r.t. IERS-08-C04 series, is at a level of 118-149 μas, which corresponds to 4 to 5 mm on the Earth’s surface. The WRMS of SLR-derived Length-of-Day, when the gravity field parameters are simultaneously estimated, is 56 μs/day, corresponding to about 26 mm on the ground, and the mean bias of SLR-derived Length-of-Day is 6.3 μs/day, corresponding to 3 mm.

Beyond the diffraction limit of optical/IR interferometers I. Angular diameter and rotation parameters of Achernar from differential phases

Context. Spectrally resolved long-baseline optical/IR interferometry of rotating stars opens perspectives to investigate their fundamental parameters and the physical mechanisms that govern their interior, photosphere, and circumstellar envelope structures. Aims. Based on the signatures of stellar rotation on observed interferometric wavelength-differential phases, we aim to measure angular diameters, rotation velocities, and orientation of stellar rotation axes. Methods. We used the AMBER focal instrument at ESO-VLTI in its high-spectral resolution mode to record interferometric data on the fast rotator Achernar. Differential phases centered on the hydrogen Br gamma line (K band) were obtained during four almost consecutive nights with a continuous Earth-rotation synthesis during similar to 5h/night, corresponding to similar to 60 degrees position angle coverage per baseline. These observations were interpreted with our numerical code dedicated to long-baseline interferometry of rotating stars. Results. By fitting our model to Achernar's differential phases from AMBER, we could measure its equatorial radius R-eq = 11.6 +/- 0.3 R-circle dot, equatorial rotation velocity V-eq = 298 +/- 9 km s(-1), rotation axis inclination angle i = 101.5 +/- 5.2 degrees, and rotation axis position angle (from North to East) PA(rot) = 34.9 +/- 1.6 degrees. From these parameters and the stellar distance, the equatorial angular diameter circle divide(eq) of Achernar is found to be 2.45 +/- 0.09 mas, which is compatible with previous values derived from the commonly used visibility amplitude. In particular, circle divide(eq) and PA(rot) measured in this work with VLTI/AMBER are compatible with the values previously obtained with VLTI/VINCI. Conclusions. The present paper, based on real data, demonstrates the super-resolution potential of differential interferometry for measuring sizes, rotation velocities, and orientation of rotating stars in cases where visibility amplitudes are unavailable and/or when the star is partially or poorly resolved. In particular, we showed that differential phases allow the measurement of sizes up to similar to 4 times smaller than the diffraction-limited angular resolution of the interferometer.