Anelasticity across seismic to tidal timescales: a self-consistent approach
Anelasticity across seismic to tidal timescales: a self-consistent approach
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DOI：
10.1093/gji/ggw401
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发表时间：
2017
影响因子：
2.8
通讯作者：
H. Lau;U. Faul;J. Mitrovica;D. Al-Attar;J. Tromp;G. Garapić
中科院分区：
文献类型：
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作者：
H. Lau;U. Faul;J. Mitrovica;D. Al-Attar;J. Tromp;G. Garapić
在一项开创性的研究中，Wahr和卑尔根发展了广泛采用的伪正态模式框架，用于预测滞弹性效应对地球体潮的影响。Lau等人最近推导出了一种扩展的简正波处理方法（以及称为直接解方法的理论的一个小变体），该方法充分利用了过去四分之一世纪自由振荡地震学的理论发展，避免了传统理论中用于预测滞弹性效应的一系列假设和近似。这两个理论之间有两个显著的区别：（1）传统理论只考虑弹性地球本征模的摄动，而新理论将这组本征模扩大到包括滞弹性行为中出现的松弛模;（2）传统理论将潮汐Love数的复摄动近似为弹性模量的复摄动的标度形式，而新理论计算每个本征模的全复微扰。在这项研究中，我们突出了上述差异，使用一系列的合成计算，并表明，传统的理论可以引入显着的错误，由于滞弹性和相关的预测潮汐滞后角的复杂摄动的勒夫数的预测。对于我们采用的简化地球模型，计算的滞后角相差0.20%.The假设在传统的理论有重要的影响，以前的研究，使用模型预测，以纠正观测的体潮信号或分析观测的体潮变形推断地幔滞弹性结构。最后，我们还强调了表观衰减（即从观测中推断或使用上述理论预测的衰减）和固有衰减（即通过实验研究的材料特性）之间的根本区别，两者通常都用滞后角或Q−1表示。特别是，我们证明了潜在的显着（两个或更多的因素）的偏差引入Q-1的估计和它的频率依赖性的研究，处理Q-1确定的潮汐相位滞后或测量实验为相等的。观测到的或理论上预测的滞后角（或表观Q−1）与由于惯性、自引力和与能量收支相关的影响而产生的固有物质性质不同。通过考虑这些差异，我们得出，对于一个特殊的情况下，一个表达式，准确地映射表观衰减预测使用扩展的正常模式形式主义的刘等人。到固有衰减。该理论允许更广义的映射，可用于连接观测和预测的潮汐滞后角的地幔物质的实验室实验的结果。
In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau et al. have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ∼20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or Q−1. In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of Q−1 and its frequency dependence in studies that have treated Q−1 determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent Q−1) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau et al. into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.