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ANALYTICAL VISCO-ELASTIC RELAXATION MODELS

机译:粘弹性松弛分析模型

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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. [References: 16]
机译:过去,已经直接在时域(初始值模型)或在拉普拉斯变换域(正模模型)中对采用PREM或1066B分层地球模型的松弛过程进行了数值求解。仅对较小的N值进行了分析求解N层分层模型。我们简要介绍了一般径向分层N层,自重,麦克斯韦流变模型的分析方法。分析模型允许以非常高的精确度确定无数种弛豫模式的弛豫时间,因为从中推导出的长期决定因素是一种解析函数。通过显式比较具有凸套粘度曲线的5层和30层不可压缩Maxwell模型的结果,当5层模型具有体积平均的结构和流变特性时,两个模型之间的结果差异很小30层模型。在两个模型中,Love数的流体值达到相同的预期极限这一事实为假设的所谓非模态贡献没有余地。广义分析法线模式方法在可压缩线性流变学中的应用涉及更多,但很简单。 [参考:16]

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