Retrodiction Range of geodynamic earth models from twin experiments that account for model inconsistencies and limited resolution of present-day heterogeneity

伴随法反演是重建过去地幔状态的有力工具。它们为根据一系列地质和地球物理观测结果测试动态地球模型开辟了新的途径。到目前为止，在理论水平上，它们的收敛性和唯一性只能通过高度简化的孪生实验来阐明，其中最严重的限制源于对地幔对流参数和当前模型状态的完美知识的（不切实际的）假设。在此，我们建议通过研究(1)不一致的模型参数、成分变化和地幔状态地震推断的有限分辨能力如何进入反演问题，(2)不一致如何映射到反演的地幔流动轨迹，以及(3)随着时间的推移，这些轨迹如何导致虚假非均质性的增长，来提高我们对地幔流动反演的基本理解。有效地限制了可以实现可行的反演的时间范围。为了解决这些基本问题，我们提出了一项专门设计的双胞胎实验的系统研究，其中可接受的参数变化和地震滤波效应被系统地引入到反问题中，以估计对地球动力学反演的影响：1)参考模型和逆模型之间流变参数的偏差；2)层析层析滤波导致地幔非均质场中缺少小尺度结构；3)对地幔浮力的解释不一致，这是由于对总体成分的错误假设。4)过去的板块运动模型中的误差，特别是与参考坐标系点3的选择有关的误差，将涉及一组新的能够表示热化学对流的伴随方程的推导。

Retrodictions with the adjoint method are a powerful tool to reconstruct past mantle states. They open new avenues to test dynamic earth models against a range of geologic and geophysical observables. So far, at a theoretical level their convergence and uniqueness properties have been elucidated only with highly simplified twin experiments, where the most severe limitation stems from the (unrealistic) assumption of perfect knowledge of the mantle convection parameters and the present-day model state. Here we propose to improve our fundamental understanding of mantle flow retrodictions studying (1) how inconsistent model parameters, compositional variations, and the limited resolving power of seismic inferences of the mantle state enter the retrodiction problem, (2) how the inconsistencies map into retrodicted mantle flow trajectories, and (3) how the trajectories contribute to growth of spurious heterogeneity as one goes back in time, effectively limiting the temporal range for which viable retrodictions can be achieved. To address these fundamental questions, we propose a systematic study of specifically designed twin experiments, where admissible parameter variations and seismic filtering effects are introduced systematically into the inverse problem, to estimate the impact on geodynamic retrodictions of: 1) deviations in rheological parameters between the reference and inverse model, 2) absence of small-scale structures in the mantle heterogeneity field due to tomographic filtering, 3) inconsistent interpretations of mantle buoyancies as a result of wrongful assumptions for the bulk composition, 4) errors in past plate motion models in particular related to the choice of reference frame point 3 will involve the derivation of a new set of adjoint equations capable of representing thermo-chemical convection.