A Reduced-Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography
Yeh, Tian-Chyi J.
Illman, Walter A.
AffiliationUniv Arizona, Dept Hydrol & Atmospher Sci
geostatistical inverse modeling
MetadataShow full item record
PublisherAMER GEOPHYSICAL UNION
CitationZha, Y., Yeh, T.‐C. J., Illman, W. A., Zeng, W., Zhang, Y., Sun, F., et al. (2018). A reduced‐order successive linear estimator for geostatistical inversion and its application in hydraulic tomography. Water Resources Research, 54, 1616–1632. https://doi.org/10.1002/2017WR021884
JournalWATER RESOURCES RESEARCH
Rights© 2018. American Geophysical Union. All Rights Reserved.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractHydraulic tomography (HT) is a recently developed technology for characterizing high-resolution, site-specific heterogeneity using hydraulic data (n(d)) from a series of cross-hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (n(y)), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (n(y) x n(y)) in these models are prodigious for large-scale 3-D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (n(y) forward runs). Although employment of the adjoint method can reduce the cost to n(d) forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced-Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen-Loeve Expansion (KLE) truncated to n(kl) order, and it calculates the directional sensitivities (in the directions of n(kl) eigenvectors) to form the covariance and cross-covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3-D transient HT analysis of data from a highly heterogeneous field site.
Note6 month embargo; published online: 16 February 2018
VersionFinal published version
SponsorsNational Natural Science Foundation of China [51779179, 51609173, 51479144, 51522904]; CRDF [DAA2-15-61224-1]; Tianjin Normal University from the Thousand Talents Plan of Tianjin City; Special Fund for Public Industry Research from Ministry of Land and Resources of China