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Deformation of a spherical, viscoelastic, and incompressible Earth for a point load with periodic time change
Geophysical Journal International ( IF 2.8 ) Pub Date : 2020-06-01 , DOI: 10.1093/gji/ggaa268
He Tang 1 , Jie Dong 2 , Lan Zhang 1 , Wenke Sun 1
Affiliation  

Planetary-scale mass redistributions occur on Earth for certain spatiotemporal periods, and these surface mass changes excite the global periodic loading deformations of a viscoelastic Earth. However, the characteristics of periodic viscoelastic deformations have not been well investigated even in a simple earth model. In this study, we derive the semi-analytical Green's functions (fully analytical Love numbers) for long-standing point sources with given periods using a modified asymptotic scheme in a homogeneous Maxwell spherical earth model. Here, the asymptotic scheme is needed in order to obtain accurate semi-analytical time-dependent Green's functions. The amplitudes and phases of the Green's functions may be biased if only the series summations of the Love numbers are used because the influence of viscoelasticity is degree-dependent. We compare the viscoelastic and elastic periodic Green's functions with different material viscosities and loading periods and investigate the amplitude increase percentage and phase delay of the periodic displacement and geoid change. For example, our analysis revealed that the viscosity increases the amplitude by 40–120 per cent and delays the phase approximately −100° to 60° for the displacement and geoid change when bearing a 10-yr loading period, assuming a viscosity of 1018 Pa s and a shear modulus 4 × 1010 Pa.

中文翻译:

球形,粘弹性和不可压缩地球在点荷载下随时间变化的变形

在一定的时空周期内,行星尺度的质量重新分布会在地球上发生,并且这些表面质量的变化会激发粘弹性地球的整体周期性载荷变形。但是,即使在简单的地球模型中,周期性粘弹性变形的特征也没有得到很好的研究。在这项研究中,我们在齐次Maxwell球面地球模型中使用改进的渐近格式,得出了具有给定周期的长期点源的半解析格林函数(完全解析的Love数)。在这里,需要渐进方案以获得准确的半分析时间相关格林函数。格林'的振幅和相位 如果仅使用Love数的序列求和,则s函数可能会存在偏差,因为粘弹性的影响取决于程度。我们比较了具有不同材料粘度和加载周期的粘弹性和弹性周期性格林函数,并研究了周期性位移和大地水准面变化的振幅增加百分比和相位延迟。例如,我们的分析表明,当承受10年的载荷时,当位移为10年时,由于位移和大地水准面变化,粘度会使振幅增加40%至120%,并使相位延迟大约-100°至60°。s函数具有不同的材料粘度和加载周期,并研究了周期性位移和大地水准面变化的振幅增加百分比和相位延迟。例如,我们的分析表明,当承受10年的载荷时,当位移为10年时,由于位移和大地水准面变化,粘度会使振幅增加40%至120%,并使相位延迟大约-100°至60°。s函数具有不同的材料粘度和加载周期,并研究了周期性位移和大地水准面变化的振幅增加百分比和相位延迟。例如,我们的分析表明,当承受10年的载荷时,当位移为10年时,由于位移和大地水准面变化,粘度会使振幅增加40%至120%,并使相位延迟大约-100°至60°。18 Pa s和剪切模量4×10 10  Pa。
更新日期:2020-06-27
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