Bunge Hans-Peter, Richards M A, Baumgardner J R
Department of Geosciences, Princeton University, NJ 08544, USA.
Philos Trans A Math Phys Eng Sci. 2002 Nov 15;360(1800):2545-67. doi: 10.1098/rsta.2002.1080.
Data assimilation is an approach to studying geodynamic models consistent simultaneously with observables and the governing equations of mantle flow. Such an approach is essential in mantle circulation models, where we seek to constrain an unknown initial condition some time in the past, and thus cannot hope to use first-principles convection calculations to infer the flow history of the mantle. One of the most important observables for mantle-flow history comes from models of Mesozoic and Cenozoic plate motion that provide constraints not only on the surface velocity of the mantle but also on the evolution of internal mantle-buoyancy forces due to subducted oceanic slabs. Here we present five mantle circulation models with an assimilated plate-motion history spanning the past 120 Myr, a time period for which reliable plate-motion reconstructions are available. All models agree well with upper- and mid-mantle heterogeneity imaged by seismic tomography. A simple standard model of whole-mantle convection, including a factor 40 viscosity increase from the upper to the lower mantle and predominantly internal heat generation, reveals downwellings related to Farallon and Tethys subduction. Adding 35% bottom heating from the core has the predictable effect of producing prominent high-temperature anomalies and a strong thermal boundary layer at the base of the mantle. Significantly delaying mantle flow through the transition zone either by modelling the dynamic effects of an endothermic phase reaction or by including a steep, factor 100, viscosity rise from the upper to the lower mantle results in substantial transition-zone heterogeneity, enhanced by the effects of trench migration implicit in the assimilated plate-motion history. An expected result is the failure to account for heterogeneity structure in the deepest mantle below 1500 km, which is influenced by Jurassic plate motions and thus cannot be modelled from sequential assimilation of plate motion histories limited in age to the Cretaceous. This result implies that sequential assimilation of past plate-motion models is ineffective in studying the temporal evolution of core-mantle-boundary heterogeneity, and that a method for extrapolating present-day information backwards in time is required. For short time periods (of the order of perhaps a few tens of Myr) such a method exists in the form of crude 'backward' convection calculations. For longer time periods (of the order of a mantle overturn), a rigorous approach to extrapolating information back in time exists in the form of iterative nonlinear optimization methods that carry assimilated information into the past through the use of an adjoint mantle convection model.
数据同化是一种研究地球动力学模型的方法，该模型要与观测数据和地幔流动的控制方程同时保持一致。这种方法在地幔环流模型中至关重要，在这类模型中，我们试图约束过去某个时间的未知初始条件，因此不能指望用第一性原理对流计算来推断地幔的流动历史。地幔流动历史最重要的观测数据之一来自中生代和新生代板块运动模型，这些模型不仅对地幔表面速度提供约束，还对地幔内部由于俯冲大洋板块产生的浮力的演化提供约束。在此，我们展示了五个地幔环流模型，其同化了过去1.2亿年的板块运动历史，这是一个有可靠板块运动重建数据的时间段。所有模型都与地震层析成像所显示的上地幔和中地幔的非均匀性高度吻合。一个简单的全地幔对流标准模型，包括从上地幔到下地幔粘度增加40倍且主要是内部产热，揭示了与法拉龙和特提斯俯冲相关的下沉流。增加35%来自地核的底部加热会产生可预测的效果，即产生显著的高温异常以及在地幔底部形成一个强烈的热边界层。通过模拟吸热相反应的动力学效应，或者通过包含从上地幔到下地幔粘度陡增100倍的方式，显著延迟地幔通过过渡带的流动，会导致过渡带出现大量非均匀性，同化的板块运动历史中隐含的海沟迁移效应会增强这种非均匀性。一个预期的结果是无法解释1500公里以下最深地幔中的非均匀性结构，该结构受侏罗纪板块运动影响，因此不能通过对年龄限于白垩纪的板块运动历史进行顺序同化来模拟。这一结果意味着，对过去板块运动模型进行顺序同化在研究核幔边界非均匀性的时间演化方面是无效的，需要一种将现今信息向时间回溯外推的方法。对于短时间段（可能几十百万年的量级），这样一种方法以粗略的“反向”对流计算的形式存在。对于更长时间段（一个地幔翻转的量级），一种将信息向时间回溯外推的严格方法以迭代非线性优化方法的形式存在，该方法通过使用伴随地幔对流模型将同化信息带入过去。
