# the effects of large Earthquake on the excitation of polar motion and the change in length of day

Abstract

In this study, the effects of Earthquake on the excitation of polar motion and the changes in the length of day are investigated. To do so, at first the deformation resulting from Earthquake is computed and then, its effects on the polar motion and length of day are derived. The geodynamic model which determines the crustal deformation is Dahlen's model in which the effects of Earthquake deformation coupled with the rotational motion of the Earth. For this purpose, it is assumed that the Earth is a spherical symmetric, isotropic, elastic and homogeneous media and the Earthquake is caused by the dislocation discontinuities on fault surface. In this case, the solution of the corresponding boundary value problem determines the deformations of the Earth due to Earthquake. On the other hand, the rotational motion of the Earth as a deformable body is governed by the Liouville equation, which determines the motion of polar axis under the applied external torque. Since the polar motion is investigated, only the homogeneous solution of the latter equation must be determines. In this case the solution of Liouville equation is only dependent on the moment of inertia of the Earth. Since, the components of the Inertia tensor of the Earth are dependent on the shape of the earth and its density distribution, and in this case, the Earth undergoes a shape change, therefore, its moments of inertial are no longer constant and depend on the deformation of the Earth. By computing the deformation results from the Earthquake as discussed at the first step, one may derive shape change and changes in the density distribution of the Earth from which, the changes in the component of inertia tensor may be obtained. Finally, the changes in the inertial tensor through Liouville equation can lead to the excitation of polar motion or the variations in the length of day, which determine by the solution of the corresponding equation. The simulated problems in two cases of strike-slip and dip-slip faults reveal that the amplitude of excitation due to strike-slip fault is maximum at equator and decrease toward poles and it is zero at pol. However, in the dip-slip fault, the amplitude at mid-latitude regions is maximum and is zero at both equator and poles. The variation in the length of day is zero at poles and is maximum at equator for strike-slip fault. For dip-slip fault, it is zero at both equator and poles and is maximum over the mid-latitude regions. Moreover, using the geometric parameters of the large Earthquakes from Harvard Earthquake Catalogue, occurred during the period of 1976 to 2014, their effects on the polar motion and length of day are studied within the adapted geodynamical model. The results show that among the selected Earthquakes, the 2011 Japan Earthquake had had the most significant effects on the motion of polar axis and the length of day .This excitation is in westward direction. The combined impact of all Earthquakes is also computed which clarifies that the polar excitation is increasing in the X direction (prime vertical component) and decreasing in the direction of Y (meridian component). For the validation of our results, we use the data of IERS (International Earth Rotation Service) which shows a relatively good agreement.

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#### References

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