Adjoint-based estimation of plate coupling in a non-linear mantle flow model: Theory and examples
Adjoint-based estimation of plate coupling in a non-linear mantle flow model: Theory and examples
复制标题
非线性地幔流模型中板块耦合的伴随估计：理论与实例
DOI：
10.1093/gji/ggv166
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发表时间：
2015
影响因子：
2.8
通讯作者：
M. Gurnis
中科院分区：
文献类型：
--
作者：
V. Ratnaswamy;G. Stadler;M. Gurnis
我们开发并验证了一个系统的方法来推断板块边界强度和流变参数的地幔流模型从表面速度观测。基于一个现实的流变模型，包括屈服和应变率弱化位错蠕变，我们制定了贝叶斯推理框架中的反问题。为了研究与观测结果一致的参数分布，我们计算最大后验（MAP）点，该MAP点周围的参数分布的高斯近似，并采用马尔可夫链蒙特卡罗（MCMC）抽样方法。MAP点和高斯近似的计算需要服从非线性Stokes方程的目标函数的一阶和二阶导数;这些导数使用伴随Stokes方程有效地计算。我们建立了2-D的数值实验与全球地球物理反演中预期的许多元素。这种设置包括三个俯冲带板和薄弱区（板间断层）的几何形状与平均地震特征一致。通过这些实验，我们证明了当温度场已知时，我们可以恢复板块边界的强度，上地幔的屈服应力和应变率指数。当不确定参数的数目增加时，推断的参数之间存在折衷。这些权衡取决于观测数据对地表速度的反映程度，以及板块边界的薄弱程度。当板块边界耦合下降到阈值以下时，由于板块运动对板块耦合的不敏感性，推断出的参数的不确定性增加。比较从高斯近似的参数分布和MCMC采样推断的流变参数之间的权衡，我们得出结论，高斯近似-这是显着便宜的计算-往往是一个很好的近似，特别是局部周围的MAP点。因此，该方法可以应用于全球地球物理反演与已知的板片结构的非线性本构参数和板块耦合因子的推断每个俯冲带的全球问题。
We develop and validate a systematic approach to infer plate boundary strength and rheological parameters in models of mantle flow from surface velocity observations. Based on a realistic rheological model that includes yielding and strain rate weakening from dislocation creep, we formulate the inverse problem in a Bayesian inference framework. To study the distribution of parameters that are consistent with the observations, we compute the maximum a posteriori (MAP) point, Gaussian approximations of the parameter distribution around that MAP point, and employ Markov Chain Monte Carlo (MCMC) sampling methods. The computation of the MAP point and the Gaussian approximation require first and second derivatives of an objective function subject to non-linear Stokes equations; these derivatives are computed efficiently using adjoint Stokes equations. We set up 2-D numerical experiments with many of the elements expected in a global geophysical inversion. This setup incorporates three subduction zones with slab and weak zone (interplate fault) geometry consistent with average seismic characteristics. With these experiments, we demonstrate that when the temperature field is known, we can recover the strength of plate boundaries, the yield stress and strain rate exponent in the upper mantle. When the number of uncertain parameters increases, there are trade-offs between the inferred parameters. These trade-offs depend on how well the observational data represents the surface velocities, and on the weakness of plate boundaries. As the plate boundary coupling drops below a threshold, the uncertainty of the inferred parameters increases due to insensitivity of plate motion to plate coupling. Comparing the trade-offs between inferred rheological parameters found from the Gaussian approximation of the parameter distribution and from MCMC sampling, we conclude that the Gaussian approximation—which is significantly cheaper to compute—is often a good approximation, in particular locally around the MAP point. Thus, the method can be applied to the global problem of inferring non-linear constitutive parameters and plate coupling factors for each subduction zone in a global geophysical inversion with known slab structure.