A Revisit of the Time Domain Global Earth Tides
We adopt the linearized Lagrangian equations of motion in the vector form.They govern time varying small elasto-gravitation disturbances away from the equilibrium of a spherical non-rotating and uniformly rotating, self-gravitating, elastic and isotropic earth (without the atmosphere and oceans) with an arbitrary initial stress field.After separation of variables we expand them into a system of differential-integral equations of tidal displacement components as a function of the earth”s radius and time.These expanded equations of motion are solved by means of the explicit second-order finite differences method for which the Courant-Friedrichs-Lewy condition is a necessary condition to assure the stability and convergence to a precision of 1/3000 for the tidal displacement components.We found that the calculated global earth tides in the time domain are quantitatively sensitive to the differences between the Gutenberg-Bullen A (G-B A) and PEM-C earth models.The residual differences of the calculated tidal gravity time series between the two earth models could be as much as 0.4%.The G-B A earth model has a liquid core and the PEM-C earth model has a liquid outer core and a solid inner core although the physical dimensions of the earth”s core as a whole are the same.The residual differences are not due to numerical calculation errors.They could be attributed mainly to the differences of the configuration of the earth”s core of the two earth models.The estimated effects of the rotation of the earth on the tidal displacement may reach the order of 10-2 to 10-1 centimeters,on the tidal gravity 10-2 to 10-1 microgal,and on the horizontal tidal tilts, 10-6 arcsecond.The earth rotation as in the case of the free oscillations of the earth causes coupling of the spheroidal and toroidal components of different degrees and orders of spherical harmonics.We found the spherical and toroidal coupling for the time domain earth tides obeys the well-known coupling rules and can be positively identified.The earlier results of the direct comparisons of the observed tidal gravity at Brussels and the observed tilts at Sclaigneaux, Namur with our calculated time domain tidal gravity and tilts show good agreement.The more recent results of the direct comparisons of the observed tidal gravity at Xichang,Sichuan and Beijiatuan,Beijing,China in May1-15,2008 with the calculated time-domain tidal gravity reconfirmed such good agreement.These direct comparisons were made in the graphic form.More detailed, quantitative and direct comparisons are yet to be made with the precise observed data.The Wenchuan Earthquake of M =8 occurred on May 12,2008.The epicentral distances of the Earthquake to Xichang and Beijiatuan are 360 km and 1500 km, respectively.We did not find easily identifiable perturbations of the Wenchuan Earthquake on the earth tides at Xichang and Beijiatuan.If there were such perturbations they would be minute and likely complicated by other influences.Kuo and his Chinese colleges, however,did find such minute perturbations using a group of tidal gravity and seismic stations.These minute perturbations appeared about ten days and more clearly one day prior to the occurrence of the Wenchuqn Earthquake.The signatures of these precursors were in the short-period seismic frequency range and buried in the disturbance of the tail end of Typhoon Rammasun.The CPU time for calculating a 10-day time series of the earth tide in the time domain on a today”s MacBook Pro takes only a few minute, about one hundred times faster than the on a main frame in 1990”s.With the advent of even more powerful PC”s and handheld PC”s,calculations of the global earth tides in the time domain can be routinely performed.
Earth tides Time-domain earth tides Tidal gravity Tidal tilts Wenchuan Earthquake
Yuanchong Zhang John Tsung Fen Kuo
Department of Applied Physics and Applied Mathematics Columbia University, New York, NY 10027, USA Columbia University, New York, NY 10027 USA
国内会议
武汉
英文
317-337
2014-04-22（万方平台首次上网日期，不代表论文的发表时间）