Effects of Major Seismic Events on the Rotation of the Earth

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S-Y A spherical theory is advanced for perturbations of the Earth‘s rotation by major earthquakes and explosions. Explicit expressions are obtained for the dependence of the secular polar shift on the dimensions, depth, and location of the seismic event. Numerical results show that a single shallow earthquake of magnitude 8.5, occurring at a suitable latitude and with a favourable strike-azimuth, may suffice to maintain the Chandler wobble for about one year. Hence, it is deduced that earthquakes may at most 8ccouIlt for 30 per cent of the observed secular polar shift. 1. Introdoction The equations of rigid gyroscopic motion were given by Euler in 1758. On the basis of this theory, he suggested in 1765 that the Earth might undergo a free precession with period of A/(C-A) sideral days. Assuming this to be true, a spectator partaking in the Earth’s motion should observe periodic changes in latitude with a period of about 10 months. However, no such period could be found. Instead, Chandler established in 1891 the existence of a 428-days period in the spectrum of the latitude variation. The lengthening of the period was explained by Newcomb, in 1892, to be the result of the Earth’s elasticity. A theoretical veriiication was given by Love (1909), based on first-order theory of the figure of the Earth. This 14-month precessional motion of the instantaneous axis of rotation about the Earth’s axis of figure is known today as the Chandler Wobble. (Fig. 1.) Spectral analyses of latitude time series disclosed that the motion is damped with a ‘ Q ’ value between 30 and 40. The wobble must therefore be maintained by a certain source of energy. Munk & Macdonald (1960, p. 174) conclude that: ‘The statistical properties of the latitude time series are those associated with a damped oscillator excited at random. . . . Irregular variations of the atmosphere are the most likely cause of the wobble.’ Recently, however, observational evidence has been presented in support of the hypothesis that earthquakes may excite the wobble and produce the observed polar shift. To explain these arguments we shall recapitulate the theoretical background of the subject: The fundamental law of dynamics as experienced by earth-bound spectators is given by the Liouville equation (Munk & Macdonald 1960)