Analytical visco-elastic relaxation models
Analytical visco-elastic relaxation models
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DOI：
10.1029/96gl00620
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发表时间：
1996-04
影响因子：
5.2
通讯作者：
L. Vermeersen;R. Sabadini;G. Spada
中科院分区：
文献类型：
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作者：
L. Vermeersen;R. Sabadini;G. Spada
在过去，使用PREM或1066b分层地球模型的松弛过程已经在数值上解决，或者直接在时域（初始值模型）或在拉普拉斯变换域（正态模型）中求解。解析求解n层分层模型的方法只适用于较小的n值。我们简要概述了一般径向分层n层自重力麦克斯韦流变模型的解析方法。分析模型允许以非常高的精度确定无数松弛模式的松弛时间，因为它们推导的长期行列式是一个分析函数。通过明确比较具有凸地幔黏度剖面的5层和30层不可压缩Maxwell模型的结果，我们发现，当5层模型具有30层模型的体积平均结构和流变特性时，两种模型之间的结果差异很小。在两种模型中，Love数的流体值都达到了相同的预期极限，这一事实使假定的所谓非模态贡献没有任何余地。这种广义解析法在可压缩线性流变学中的应用比较复杂，但很简单。
In the past, relaxation processes employing PREM or 1066B-stratified earth models have been solved numerically, either directly in the time domain (initial value models) or in the Laplace-transformed domain (normal mode models). Solving N-layer stratified models analytically has only been performed for small values of N. We present a brief outline of the analytical method of general radially stratified N-layer, self-gravitating, Maxwell rheological models. The analytical models allow for the relaxation times of the myriad of relaxation modes to be determined with very high accuracies, as the secular determinant from which they derive is an analytical function. We show by explicitly comparing results on a 5 and 30-layer incompressible Maxwell model with a convex mantle viscosity profile, that the differences in the results between the two models are small when the 5-layer model has the volume-averaged structural and rheological properties of the 30-layer model. The fact that in both models the fluid values of the Love numbers reach the same expected limits leaves no room for hypothetical so-called non-modal contributions. The application to compressible linear rheologies of this generalized analytical normal mode method is more involved, but straightforward.