Joint inversion in coupled quasi‐static poroelasticity
Joint inversion in coupled quasi‐static poroelasticity
复制标题
耦合准静态孔隙弹性联合反演
DOI：
10.1002/2013jb010272
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
G. Stadler
中科院分区：
文献类型：
--
作者：
M. Hesse;G. Stadler
大地测量现在提供了详细的时间序列图，说明由于地下孔隙流体的注入和抽出而引起的人为地面沉降和抬升。耦合孔隙弹性模型允许整合的大地测量和水力数据在联合反演，因此有可能提高表征的地下和我们的能力，监测孔隙压力的演变。我们制定了一个贝叶斯逆问题来推断的横向渗透性变化的含水层从大地测量和水力数据和先验信息。我们计算后验渗透率分布的最大后验（MAP）估计和后验的高斯近似。计算MAP估计需要解决一个大规模的最小化问题的多孔弹性方程，为此，我们提出了一个有效的牛顿共轭梯度优化算法。后验的高斯近似的协方差矩阵由对数后验的逆Hessian给出，我们通过利用数据失配Hessian的低秩特性来构造。一阶和二阶导数使用随时间变化的孔隙弹性方程的伴随计算，使我们能够充分利用瞬态数据。使用三个越来越复杂的模型问题，我们发现以下一般性质的孔隙弹性反演：增加标准的水力井数据，表面变形数据提高含水层表征。地表变形对浅层含水层的影响最大，但即使是对1公里以下含水层的定性也提供了有用的信息。一般来说，推断高渗透率区域更加困难，并且其表征需要频繁测量以解决相关的短响应时间尺度。在水平含水层中，地表变形的垂直分量提供了含水层中压力分布的平滑图像。在已知力学性质的条件下，耦合反演是一种很有前途的方法来检测流动障碍和监测孔隙压力的演变。
Geodetic surveys now provide detailed time series maps of anthropogenic land subsidence and uplift due to injection and withdrawal of pore fluids from the subsurface. A coupled poroelastic model allows the integration of geodetic and hydraulic data in a joint inversion and has therefore the potential to improve the characterization of the subsurface and our ability to monitor pore pressure evolution. We formulate a Bayesian inverse problem to infer the lateral permeability variation in an aquifer from geodetic and hydraulic data and from prior information. We compute the maximum a posteriori (MAP) estimate of the posterior permeability distribution and a Gaussian approximation of the posterior. Computing the MAP estimate requires the solution of a large‐scale minimization problem subject to the poroelastic equations, for which we propose an efficient Newton‐conjugate gradient optimization algorithm. The covariance matrix of the Gaussian approximation of the posterior is given by the inverse Hessian of the log posterior, which we construct by exploiting low‐rank properties of the data misfit Hessian. First and second derivatives are computed using adjoints of the time‐dependent poroelastic equations, allowing us to fully exploit transient data. Using three increasingly complex model problems, we find the following general properties of poroelastic inversions: Augmenting standard hydraulic well data by surface deformation data improves the aquifer characterization. Surface deformation contributes the most in shallow aquifers but provides useful information even for the characterization of aquifers down to 1 km. In general, it is more difficult to infer high‐permeability regions, and their characterization requires frequent measurement to resolve the associated short‐response timescales. In horizontal aquifers, the vertical component of the surface deformation provides a smoothed image of the pressure distribution in the aquifer. Provided that the mechanical properties are known, coupled poroelastic inversion is therefore a promising approach to detect flow barriers and to monitor pore pressure evolution.