• ISSN 2097-1893
  • CN 10-1855/P

黏弹地球地震变形理论研究进展和展望

唐河 孙文科

引用本文: 唐河,孙文科. 黏弹地球地震变形理论研究进展和展望. 地球与行星物理论评,2021,52(1):11-26
Tang H, Sun W K. Progress and prospect of deformation theory in the viscoelastic earth. Reviews of Geophysics and Planetary Physics, 2021, 52(1):11-26

黏弹地球地震变形理论研究进展和展望

doi: 10.19975/j.dqyxx.2020-005
基金项目: 国家自然科学基金资助项目(41774088,41974093,41331066,41474059)
详细信息
    通讯作者:

    孙文科(1956-),男,教授,博士生导师,主要从事地震位错理论及应用、重力变化的观测与解释、重力卫星GRACE的应用研究. E-mail:sunw@ucas.ac.cn

  • 中图分类号: P315.01, P315.4, P315.2

Progress and prospect of deformation theory in the viscoelastic earth

Funds: Supported by the National Natural Science Foundation of China (Grant No. 41774088, 41974093, 41331066, 41474059)
  • 摘要:Love(1911)研究了自重球体的弹性变形后,基于不同的黏弹性地球模型,许多科学家都对地震变形问题进行了深入研究,主要发展了基于半无限空间和球形地球模型的黏弹地球地震变形理论. 地震变形问题通常经积分变换、基函数展开等技术处理后,简化为求解满足特定震源和地表边界条件的常微分方程组问题. 针对这一独特的数学物理边值问题,本文以全解析、半解析和数值积分解等求解形式概述了近几十年发展的基于规则几何形态地球模型的黏弹地球地震变形理论,并讨论了各种方法的特点. 此外,针对三维地球模型,本文也简单回顾了目前的研究进展和存在问题. 总之,本文综述了过去半个多世纪以来的黏弹地球地震变形理论的发展历史、研究现状和最新进展,并讨论目前存在的问题和未来的发展趋势.

     

  • 图  1  分层球形地球模型中黏弹地震变形转化为复域等效弹性变形(一致性原理)示意图. (a)为Burgers体黏弹性变形. (b)为复域内等效弹性变形. Burgers体由Maxwell体和Kelvin体串联得到,弹簧原件表示弹性变形,阻尼器表示黏性变形,$\rho (r)$为密度,$\lambda {\rm{(}}r{\rm{)}}$$\mu (r)$为Lamé参数,$\eta (r)$为黏度,$\lambda {\rm{(}}s{\rm{)}}$$\mu (s)$为复域Lamé参数,它们均是半径r的函数,下标“K”和“M”分别表示Kelvin体和Maxwell体. 地球模型中:内核为弹性固体,外核为液态,地壳和地幔为黏弹性介质

    Figure  1.  The diagram of transforming a viscoelastic seismic deformation problem into an equivalent elastic deformation problem in complex domain (the correspondence principle) in a layered spherical Earth model. (a) the viscoelastic deformation of the Burgers body. (b) the equivalent elastic deformation in complex domain. The Burgers body is obtained by a series connection of a Maxwell body and a Kelvin body. Spring element represents elastic deformation; damper represents viscous deformation; $\rho (r)$ is density, $\lambda {\rm{(}}r{\rm{)}}$ and $\mu (r)$ are Lamé parameters, $\eta (r)$ is viscosity; $\lambda {\rm{(}}s{\rm{)}}$ and $\mu (s)$ is the complex Lamé parameters. Subscripts "K" and "M" represent Kelvin body and Maxwell body, respectively. All parameters are functions of radius r. In the Earth model: the inner core is elastic solid; the outer core is liquid; the crust and mantle are viscoelastic media

    图  2  由复Love数或Green函数,经逆Laplace变换计算时间域内Love数或Green函数的方法示意图. 负半实轴上的灰色点表示奇异点,“…”表示省略的奇异点.(a)中的黑色圆圈表示用Bromwich回路积分计算该奇异点处的留数,向上的有向直线表示逆Laplace积分定义式,对应路径${\rm{Re}} {\rm{(}}s{\rm{) = }}c$;(b)中阴影中的五角星表示Post-Widder方法计算点;(c)中有向矩形回路表示回路积分路径;(d)中半圆形表示积分核近似方法的路径,其内虚线表示纵向积分的实际路径,黑色点表示采样位置,$a$为引入参数,$t$为时间

    Figure  2.  The method of calculating Love numbers or Green function in time domain by inverse Laplace transform from complex Love numbers or Green function. The grey points on the negative semireal axis denote singular points. “…” denotes omitted singular points. The black circle in (a) represents the residue at the singular point calculated by Bromwich contour integral. The upward directed straight line ${\rm{Re}} {\rm{(}}s{\rm{) = }}c$ represents the inverse Laplace transform by the definition. In (b) the pentagram in the shadow represents the calculation point of the Post-Widder method. The directed rectangular in (c) represents the contour integration path. The semicircle in (d) represents the path of the integral kernel approximation method. Here the dotted line inside (d) represents the actual path of the vertical integration, the black dot represents the sampling position, $a$ is the introduced parameter, and $t$ is the time

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  • 收稿日期:  2020-07-02
  • 录用日期:  2020-08-05
  • 网络出版日期:  2021-09-13
  • 刊出日期:  2021-01-01

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