Fast iterative implementation of large‐scale nonlinear geostatistical inverse modeling

摘要: [1] In nonlinear geostatistical inverse problems, it often takes a significant amount of computational cost to form linear inversion systems by linearizing the forward model. More specifically, storage associated with sensitivity matrix H (m × n, where m and n are numbers measurements unknowns, respectively) is high, especially when both large in for instance, 3-D tomography problems. In this research, instead explicitly forming directly solving system, we use MINRES, Krylov subspace method, solve iteratively. During each iteration only compute products Hx HTx any appropriately sized vectors x, which problem twice. As result, reduce memory requirement from O(mn) O(m)+O(n). This iterative methodology combined Bayesian method Kitanidis (1996) large-scale The advantages our demonstrated using numerical hydraulic transient pressure (250,000 unknowns ∼100,000 measurements). case, ∼200 GB would otherwise be required fully store at Newton step during optimization. CPU can also significantly reduced terms total number simulations. end, discuss potential extension other methods such as Successive Linear Estimator.