Statistical palaeomagnetic field modelling and dynamo numerical simulation
Statistical palaeomagnetic field modelling and dynamo numerical simulation
复制标题
统计古磁场建模和发电机数值模拟
DOI：
10.1111/j.1365-246x.2005.02613.x
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发表时间：
2005
影响因子：
2.8
通讯作者：
G. Glatzmaier
中科院分区：
文献类型：
--
作者：
C. Bouligand;G. Hulot;A. Khokhlov;G. Glatzmaier
通过依赖于两个数值发电机模拟，这种调查是可能的，我们测试的有效性和灵敏度的统计古磁场建模方法称为巨高斯过程（GGP）建模方法。这种方法目前用于分析稳定极性时期的古地磁数据，并推断有关地球主磁场（MF）过去表现方式的一些信息，以及可能受到核幔边界（CMB）条件的影响。一个模拟已运行均匀CMB条件下，其他更现实的非均匀对称性破缺CMB条件。在这两个模拟中，它被发现，所需的GGP方法，该领域的行为作为一个短期记忆过程。然而，在非齐次的情况下，发现一些严重的非平稳性，导致非常显着的偏离高斯分布的高斯系数，与GGP方法的假设相矛盾。一个类似的，但不太严重的非平稳性的情况下，发现均匀的模拟，这恰好显示一个更像地球的时间行为比非均匀的情况下。这表明，GGP建模方法仍然可以用于尝试估计地球发电机产生的场的平均μ和协方差矩阵γ（τ）（一阶和二阶统计矩）。对这两个模拟进行了详细的研究，以评估通过检查μ和γ（τ）的估计来检测潜在发电机过程的统计对称性破缺特性的可能性。正如预期的那样（由于地球自转在发电机过程中的作用），这些估计揭示了球对称破缺的性质。赤道对称性破缺性质也检测到在这两个模拟，表明这种对称性破缺性质可以自发地发生均匀CMB条件下。相比之下，轴对称破缺仅在非均匀模拟中检测到，证明了CMB条件所施加的约束。然而，发现这个轴对称破缺的签名比赤道对称破缺的签名弱得多。我们注意到，这可能是为什么只有赤道对称性破缺的性质（在时间平均场的众所周知的轴向四极项的形式）已明确地发现到目前为止，通过分析真实的数据。然而，这也可能是因为这些分析在试图估计μ时都假设了γ（τ）的简单形式。建议提供，以确保未来的尝试GGP模型与真实的数据正在进行一个更一致的，也许更有效的方式。
By relying on two numerical dynamo simulations for which such investigations are possible, we test the validity and sensitivity of a statistical palaeomagnetic field modelling approach known as the giant gaussian process (GGP) modelling approach. This approach is currently used to analyse palaeomagnetic data at times of stable polarity and infer some information about the way the main magnetic field (MF) of the Earth has been behaving in the past and has possibly been influenced by core–mantle boundary (CMB) conditions. One simulation has been run with homogeneous CMB conditions, the other with more realistic non-homogeneous symmetry breaking CMB conditions. In both simulations, it is found that, as required by the GGP approach, the field behaves as a short-term memory process. Some severe non-stationarity is however found in the non-homogeneous case, leading to very significant departures of the Gauss coefficients from a Gaussian distribution, in contradiction with the assumptions underlying the GGP approach. A similar but less severe non-stationarity is found in the case of the homogeneous simulation, which happens to display a more Earth-like temporal behaviour than the non-homogeneous case. This suggests that a GGP modelling approach could nevertheless be applied to try and estimate the mean µ and covariance matrix γ(τ) (first-and second-order statistical moments) of the field produced by the geodynamo. A detailed study of both simulations is carried out to assess the possibility of detecting statistical symmetry breaking properties of the underlying dynamo process by inspection of estimates of µ and γ(τ). As expected (because of the role of the rotation of the Earth in the dynamo process), those estimates reveal spherical symmetry breaking properties. Equatorial symmetry breaking properties are also detected in both simulations, showing that such symmetry breaking properties can occur spontaneously under homogeneous CMB conditions. By contrast axial symmetry breaking is detected only in the non-homogenous simulation, testifying for the constraints imposed by the CMB conditions. The signature of this axial symmetry breaking is however found to be much weaker than the signature of equatorial symmetry breaking. We note that this could be the reason why only equatorial symmetry breaking properties (in the form of the well-known axial quadrupole term in the time-averaged field) have unambiguously been found so far by analysing the real data. However, this could also be because those analyses have all assumed to simple a form for γ(τ) when attempting to estimate µ. Suggestions are provided to make sure future attempts of GGP modelling with real data are being carried out in a more consistent and perhaps more efficient way.