When
Where
Available in person in Harshbarger 110 and via zoom (see email link)
Abstract
Geological formations have multi-scale heterogeneities, ranging from grain size variations to clusters, layers, formations, and structures. Spatial/temporal variations in processes that excite the formations are also multi-scale. Besides, the scales of our observations, interests, and theories vary. For these reasons, uncertainties exist in our observations, interpretations, and analyses at different scales.
Over the past decades, scientists have employed stochastic representations of aquifer property spatial heterogeneity at sample scales (core samples, local hydraulic tests, and others). The representations assume that the samples' mean, variance, and spatial correlation scales (i.e., average dimensions) characterize their spatial variabilities statistically. Physically, these quantities describe the most likely values, spatial variations, and spatial relationships between samples (geological structures) in a field. Scientists based on these representations have developed mathematical theories to investigate the effects of local-scale heterogeneity on large-scale flow and solute transport in fields (Gelhar, 1986). These studies have led to the concepts of effective hydraulic properties, anisotropy, macrodispersion concepts, and uncertainty analyses in the prediction based on these concepts.
Wu et al. (1996) questioned the traditional pumping test in the field as comparing apples and oranges. They pointed out the scale inconsistency between our observation and the estimation theories (Theis solution). Their criticisms led to the development of Hydraulic Tomography (HT, Yeh and Liu, 2000). While tomography is common sense and has been widely applied in medical, geophysical, and other fields, hydrogeologists rarely pay attention to scanning the aquifer by pumping at different locations. Difficulties in the interpretation of HT results were likely the barrier. Yeh and his group developed the successive linear estimator (SLE) based on stochastic concepts to estimate the most likely property fields that agree with local sample values and observed responses for the HT (conditioning) and retain the heterogeneity statistics. SLE further addresses the estimates' uncertainty--stochastic information fusion.
This fusion technology has been widely validated and tested in the field and extended to fuse pieces of different information (e.g., tracers, geophysics, gravity, and others) to map other properties of aquifers. Recently developed machine learning (e.g., graph neural network (GNN) embedded with a heat kernel (HK) model) is similar to SLE. Perhaps SLE is better since it conditions the outcome with the observed hard and soft data and addresses uncertainty.
More importantly, many have extended the HT technology to characterize basin-scale aquifers and geological formations, using observed responses of the aquifer due to spatiotemporal variations of the river stages or artificially triggered lightning because of their powers. Moreover, HT has been applied to investigate aquifer remediations, slope stability, leakage from earth dames, and other geological engineering projects.
While the technologies remain to be improved, this talk's message to the audience is that combining the merits of AI and SLE may be the future of information fusion technology and, more importantly, developing cost-effective means (such as HT) to collecting high-resolution data sets and stochastically fusing them is the key to advancing our sciences. High-level math or computer skills are essential, but exercising common sense and innovation are the key!
Bio
Dr. Jim Yeh is a Professor in the Department of Hydrology and Atmospheric Sciences at the University of Arizona. His research focuses on stochastic/numerical analysis and laboratory/field investigations, as applied to heterogeneity effects on flow and solute transport in the saturated and unsaturated geologic media. Dr. Yeh also focuses on development of rapid methods for characterizing transport properties of multi-phase flow and of cost-effective imaging tools for characterizing geological media and monitoring evolutions of water, oil, and contaminants in the subsurface using hydro/geophysical techniques.