Research by Jim Yeh Ph.D

Electrical Resistivity
Hydraulic Tomography
Adaptive Fusion of Stochastic Information for Imaging Fractured Vadose Zones

Funded by NSF ITR-Information Integration program SEI(EAR) program

Hydraulic Tomography | Stochastic Fusion | ERT inversion | VSAFT2

Adaptive Fusion of Stochastic Information for Imaging Fractured Vadose Zones

Adaptive Fusion of Stochastic Information for Imaging Fractured Vadose Zones (Yeh, Lee, Hsue, et al., 2008, Ni and Yeh, 2008, Hao et al, 2008, Yeh et al., 2008, Yeh and Zhu, 2007) A stochastic information fusion methodology is developed to assimilate electrical resistivity tomography, high-frequency ground penetrating radar, mid-range-frequency radar, pneumatic/gas tracer tomography, and hydraulic/tracer tomography to image fractures, characterize hydrogeophysical properties, and monitor natural processes in the vadose zone. The information technology research will develop: (1) mechanisms and algorithms for fusion of large data volumes; (2) parallel adaptive computational engines supporting parallel adaptive algorithms and multi-physics/multi-model computations; (3) adaptive runtime mechanisms for proactive and reactive runtime adaptation and optimization of geophysical and hydrological models of the subsurface; and (4) technologies and infrastructure for remote (pervasive) and collaborative access to computational capabilities for monitoring subsurface processes through interactive visualization tools. The combination of the stochastic fusion approach and information technology can lead to a new level of capability for both hydrologists and geophysicists enabling them to "see" into the earth at greater depths and resolutions than is possible today. Furthermore, the new computing strategies will make high resolution and large-scale hydrological and geophysical modeling feasible for the private sector, scientists, and engineers who are unable to access supercomputers, i.e., it is an effective paradigm for technology transfer.

Hydraulic Tomography

Hydraulic tomography (Yeh and Liu, 2000 and Liu, Yeh and Gardner, 2000) is a recently developed method for analyzing aquifers using several pumping and monitoring locations. The concept of hydraulic tomography is similar to that used in any tomographic investigation (ERT or CAT scans, etc.). Hydraulic tomography can be used to discern the anisotropy and heterogeneity inherent in the hydraulic parameters at a site, while 'textbook' pumping test solutions (i.e. Theis or Cooper-Jacob) assume homogeneity implicitly.

Currently my research group is working on transient hydraulic tomography which will use both steady-state and early time drawdown observations to estimate the 3-D distribution of hydraulic conductivity and specific storage throughout the aquifer.

See some synthetic examples of both steady-state and transient hydraulic tomography on this page, and see this poster for an example using hydraulic tomography with data collected at a field site in Italy.

True K distribution for 3D HT. Click graphic for animation.

Work done jointly with Water Management Consultants, Tucson AZ

Results of ERT inversion process, only using measurements from surface resistivity survey.

Results of ERT inversion process, using both surface and downhole resistivity survey results.

Electrical Resistivity Tomography (ERT)

Stochastic Fusion of Information

View a brief introduction to ERT

My research group is currently exploring the power of the ‘Stochastic Fusion’ (Yeh and Simunek, 2002) of different types of data in variably saturated geologic media utilizing a newly developed Sequential Successive Linear Estimator (SSLE) (Vargas-Guzman and Yeh, 2002 and Yeh et. al, 2002) approach. The main point of the stochastic infusion process is to include as many types of different information in the inversion process simultaneously. The process can benefit from including both geophysical (i.e. ERT, GPR and other standard or emerging geophysical technologies) and hydrological data (ie. pumping and tracer test results) to iteratively solve anisotropic and heterogeneous problems. Using the SSLE to invert the results of hydraulic tomography (Yeh and Liu, 2000), coupled with any geophysical survey, can yield astonishing detail and heterogeneity, for relatively large areas, while providing a measure of the uncertainty in the estimate as well.

You can explore the results of this unique ERT inversion process (that inverts the resistivity solution in 3 dimensions - no pseudo-sections), for a medium-scale synthetic problem, through the sequence of four steps illustrated in the next section.

The figures to the left lead to animations illustrating the marked difference in the estimated resistivity field, for a medium-scale site, when downhole resistivity survey data are added to the basic surface survey results. The addition of the downhole data reveals the presence of a large, high-resistivity zone near the base of the domain. The addition of different types of data can greatly enhance the resolution.

3D ERT Inversion of Heap Leaching Data

This figure illustrates some results from our powerful SSLE inversion method for estimating the 3D distribution of resistivity anomalies from resistivity data. These anomalies in resistivity can often be related to anomalies in water content or the concentration of dissolved species in the pore water. More details about this problem can be found on here (including the evolution of these distributions over time). These results were obtained directly from the measured voltages from a resistivity survey, without the use of apparent resistivity or pseudo sections.

Work done jointly with Water Management Consultants, Tucson AZ

Synthetic 3D ERT Example The following four figures illustrate the components of one of my 3 dimensional electrical resistivity tomography inversion examples. The first figure shows the true resistivity field, used for the forward ERT survey simulations, the second shows the finite element mesh used for the simulation and inversion, while the third graphic displays the results of the inversions process. The final frame shows the resulting uncertainty associated with the estimated resistivity in the third frame. This inversion algorithm no only is able to take full advantage of 3D data (see home page for real-world example), but it quantifies the distribution of uncertainty associated with the estimate. Click the images for larger graphics with detailed explanations.
True Resistivity Field	Electrode Network	Inverted Resistivity Field	Uncertainty of Estimate

Work supported: by Water Management Consultants, Tucson AZ

Results of joint ERT inversion process, using 4 ERT survey lines, and no pseudo-sections.

Joint ERT Inversion

My research group is currently focused on the modernization and improvement of variably saturated flow and transport modeling; we are exploring the use of the latest computational techniques (adaptive finite element mesh refinement and discrete event time domain methods) to maximize computational power with our available resources.

The SSLE is an efficient inverse solution technique that can take ERT survey line data, and invert it to 3-D domains of the size shown here (tens of thousands of computational nodes) without using pseudo-sections. The sequential approach to the inversion allows use to invert large domains in only a few days on an single off-the-shelf Windows PC. We are currently in the process of parallelizing different portions of both the forward (including the resistivity simulation and Kriging process) and inverse (sequential parameter estimation process) portions of the model using MPI, and already these inversion model runs are executing in a fraction of the time.

VSAFT2: Flow, Transport and Inversion

We are making available our powerful variably saturated two and three dimensional flow and transport models with user-friendly Graphical User Interfaces (GUIs). The GUI will allow a broader group of people to take advantage of the powerful forward and inverse modeling tools we have developed. This powerful program combines a proven finite element method for solving the steady-state or transient flow problem with the modified method of characteristics to solve the transport equations in variably saturated media. VSAFT2 then goes to the next step and also incorporates our powerful inversion method to facilitate the inversion of flow and transport models, as well as hydraulic tomography.

The GUI makes model setup a simpler, and error-free process, rather than a tedious job of editing text input files by hand. The program also interfaces with the top of the line graphics software package Tecplot. New features include inverse modeling and hydraulic tomography, built-in geostatistical modeling features, random field generation, a triangular or rectangular finite element mesh and the ability to import a background image (map) for model setup. VSAFT2 is currently available on the downloads page, and the powerful 3-dimensional modeling tool VSAFT3 will be available soon.

The latest version of VSAFT2 can also be used for river stage tomography, which is explained in the following poster.

VSAFT2 doing hydraulic tomography inversion

Future Goals for Research

The ‘infusion’ of different types of data into the inversion process will be expanding beyond traditional geophysical modeling to include other data types, including natural stimuli tomography. Uncertainty can be reduced significantly when other, independent information is used to constrain the flow and transport system. Tracer and isotope studies can provide additional data as a ‘reality check’ on the results from the hydrologic and geophysical inversion process. In the future, we are intending to take advantage of stimuli that nature provides freely to us (gravitational tides, storm events, earthquakes and even lightning) that can be used to refine existing parameter inversions continuously, as data is received. This technology can dramatically increase the amount of data available for calibration, while relying less on costly invasive techniques like borehole drilling.