Principal Component Geostatistical Approach (PCGA) for Large-Scale and Joint Subsurface Inverse Problems

The geostatistical approach (GA) to inversion has been applied to many engineering applications to estimate unknown parameter functions and quantify the uncertainty in estimation. Thanks to recent advances in sensor technology, large-scale/joint inversions have become more common and the implementation of the traditional GA algorithm would require thousands of expensive numerical simulation runs, which would be computationally infeasible.

To overcome the computational challenges, we present the Principal Component Geostatistical Approach (PCGA) that makes use of leading principal components of the prior information to avoid expensive sensitivity computations and obtain an approximate GA solution and its uncertainty with a few hundred numerical simulation runs. As we show in this presentation, the PCGA estimate is close to, even almost same as the estimate obtained from full-model implemented GA while one can reduce the computation time by the order of 10 or more in most practical cases. Furthermore, our method is “black-box” in the sense that any numerical simulation software can be linked to PCGA to perform the geostatistical inversion. This enables a hassle-free implementation of GA to multi-physics problems and joint inversion with different types of measurements such as hydrologic, chemical, and geophysical data obviating the need to explicitly compute the sensitivity of measurements through expensive coupled numerical simulations. Lastly, the PCGA is easily implemented to run the numerical simulations in parallel, thus taking advantage of high performance computing environments. We show the effectiveness and efficiency of our method with several examples such as 3-D transient hydraulic tomography, joint inversion of head and tracer data and geochemical heterogeneity identification.