Abstract
We calculated the co-seismic Earth rotation changes for several typical great earthquakes since 1960 based on Dahlen’s analytical expression of Earth inertia moment change, the excitation functions of polar motion and, variation in the length of a day (ΔLOD). Then, we derived a mathematical relation between polar motion and earthquake parameters, to prove that the amplitude of polar motion is independent of longitude. Because the analytical expression of Dahlen’s theory is useful to theoretically estimate rotation changes by earthquakes having different seismic parameters, we show results for polar motion and ΔLOD for various types of earthquakes in a comprehensive manner. The modeled results show that the seismic effect on the Earth’s rotation decreases gradually with increased latitude if other parameters are unchanged. The Earth’s rotational change is symmetrical for a 45° dip angle and the maximum changes appear at the equator and poles. Earthquakes at a medium dip angle and low latitudes produce large rotation changes. As an example, we calculate the polar motion and ΔLOD caused by the 2011 Tohoku-Oki Earthquake using two different fault models. Results show that a fine slip fault model is useful to compute co-seismic Earth rotation change. The obtained results indicate Dahlen’s method gives good approximations for computation of co-seismic rotation changes, but there are some differences if one considers detailed fault slip distributions. Finally we analyze and discuss the co-seismic Earth rotation change signal using GRACE data, showing that such a signal is hard to be detected at present, but it might be detected under some conditions. Numerical results of this study will serve as a good indicator to check if satellite observations such as GRACE can detect a seismic rotation change when a great earthquake occur.
Highlights
An array of geophysical phenomena can cause Earth’s rotation to change: post glacial rebound, atmospheric angular momentum change, the interaction between seawater and atmosphere, and so on (Lambeck 1980; Chao et al 1987; Trupin et al 1992)
Gross and Chao (2006) calculated co-seismic effects caused by the 2004 Sumatra earthquake (Mw 9.0), noting that the polar motion is 2.32 mas in the direction of 127°E, and that LOD was shortened by 6.8 μs
Considering the effect of earthquake on rotation change discussed above, if the earthquake occurs at the equator, the azimuth angle and the dip angle are 45°, respectively, and the magnitude exceeds 9.0, the rotation change is completely detectable by GRACE, at least by GRACE Follow-on
Summary
An array of geophysical phenomena can cause Earth’s rotation to change: post glacial rebound, atmospheric angular momentum change, the interaction between seawater and atmosphere, and so on (Lambeck 1980; Chao et al 1987; Trupin et al 1992). Nilson et al (2010) computed the co-seismic rotation change caused by the 2010 Chile earthquake (Mw 8.6) based on Dahlen’s method and compared the theoretical results with that observed by VLBI (Very long Baseline Interferometry). They reported that the polar motion is about 2.5 - 3.0 mas, and that the LOD change is about 0.3 μs. The purpose of this study is twofold: to study the effect of earthquake parameters upon the earth’s rotation change to find a general property of seismic-excited rotation change, using Dahlen’s theory due to its simplicity; and, to observe its accuracy when it is used for a single mean fault and more detailed fault slip distribution. We investigated the accuracy of the Dahlen’s theory by conducting a case study of the 2011 Great East Japan earthquake (Mw 9.0)
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