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，$\lambda {\rm{(}}r{\rm{)}}$和$\mu (r)$为Lamé参数，$\eta (r)$为黏度，$\lambda {\rm{(}}s{\rm{)}}$和$\mu (s)$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