HR: 1340h
AN: H13C-1345    [Abstracts]
TI: Geostatistically Constrained Inversion and Uncertainty Estimation
AU: * Johnson, T C
EM: tcj@cgiss.boisestate.edu
AF: Center for Geophysical Investigation of the Shallow Subsurface, Department of Geosciences, Boise State University, 1910 University Drive, Boise, ID 83725 United States
AU: Routh, P S
EM: routh@cgiss.boisestate.edu
AF: Center for Geophysical Investigation of the Shallow Subsurface, Department of Geosciences, Boise State University, 1910 University Drive, Boise, ID 83725 United States
AU: Clemo, T
EM: tomc@cgiss.boisestate.edu
AF: Center for Geophysical Investigation of the Shallow Subsurface, Department of Geosciences, Boise State University, 1910 University Drive, Boise, ID 83725 United States
AU: Barrash, W
EM: wb@cgiss.boisestate.edu
AF: Center for Geophysical Investigation of the Shallow Subsurface, Department of Geosciences, Boise State University, 1910 University Drive, Boise, ID 83725 United States
AU: Clement, W P
EM: billc@cgiss.boisestate.edu
AF: Center for Geophysical Investigation of the Shallow Subsurface, Department of Geosciences, Boise State University, 1910 University Drive, Boise, ID 83725 United States
AB: Geophysical inverse problems are typically non-unique and additional constraints are used to remove the ill-posedness of the inverse problem. Smoothness constraints are commonly placed on the inverse solution in order to obtain simple models that can explain the data. These constraints are often applied in the form of a regularization operator. Although these simple solutions identify large scale geologic features, they do not provide details that are important for understanding processes in the subsurface. For example, tomography studies of alluvial aquifers show large-scale layering. However, we know from well logs and exposed quarry faces that fine-scaled structure exists in the subsurface sampled by the tomography experiment. How do we include these fine-scale features into our model and how can we estimate the probability that such features exist? We show how geostatistical information can be used to constrain the solution space to those models that are geostatistically accurate. We find models that simultaneously fit the observations and satisfy some geostatistical structure as specified by one or more semivariograms. A geostatistical operator is formulated to minimize the misfit between the "measured" and the predicted semivariogram values at each lag (or bin). In other words, the semivariogram values are used as data that the model must fit at all scales. By beginning the inversion with different, random starting models, we sample the constrained solution space and build an ensemble of possible solutions. These individual solutions contain some features which are required by the observations and other details which are not. The required features are in the activated model space. The optional details are in the null space of the data. The geostatistical operator adds to the solution those null vectors that cause each solution to satisfy the semivariogram(s). These solutions are used to estimate conditional ensemble statistics. The ensemble captures the variability of solutions fully consistent with both the observations and the geostatistics. We demonstrate geostatistically constrained inversion using a synthetic and a field example of ground-penetrating radar travel time tomography conducted at the Boise Hydrogeophysical Research Site.
UR: http://cgiss.boisestate.edu/~tcj/
DE: 3245 Probabilistic forecasting (3238)
DE: 3252 Spatial analysis (0500)
DE: 3260 Inverse theory
DE: 3265 Stochastic processes (3235, 4468, 4475, 7857)
DE: 3275 Uncertainty quantification (1873)
SC: Hydrology [H]
MN: Fall Meeting 2005