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

伴随方法反演是重建过去地幔状态的有力工具。他们开辟了新的途径，以测试动态地球模型对一系列地质和地球物理观测。到目前为止，在理论水平上，他们的收敛性和唯一性已经阐明只有高度简化的孪生实验，其中最严重的限制源于（不切实际的）假设的地幔对流参数和现今的模型状态的完美知识。在这里，我们建议提高我们对地幔流追溯的基本理解，研究（1）不一致的模型参数，成分变化，以及地幔状态的地震推断的有限分辨率如何进入追溯问题，（2）不一致如何映射到追溯的地幔流轨迹，以及（3）轨迹如何有助于假不均匀性的增长，因为一个人回到过去的时间，有效地限制了可以实现可行的追溯的时间范围。为了解决这些基本问题，我们提出了一个专门设计的孪生实验的系统研究，其中允许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追溯的影响：1）参考模型和逆模型之间的流变参数的偏差，2）由于层析过滤，地幔不均匀性场中没有小尺度结构，3）由于对整体成分的错误假设，对地幔浮力的解释不一致，4）过去的板块运动模型中的误差，特别是与参考系点3的选择有关的误差，将涉及能够表示热化学对流的一组新的伴随方程的推导。

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.