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Application to geophysics: Challenges and some solutions Andrew Binley

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Hydrogeophysics – the drivers Characterising groundwater systems is challenging because of the (physical and chemical) complexity of the shallow subsurface and the difficulty in observing the structure of the system … Hartman et al. (2007) … and the complex response due to external loading. Robin Nimmer, Moscow, Idaho

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Hydrogeophysics – the drivers Resistivity profile and hydrogeological section, Penitencia, CA (after Zohdy, 1964). Geophysics has been widely used to support groundwater investigations for many years. However, many of the earlier approaches concentrated on using geophysics to define lithological boundaries and other subsurface structures.

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Hydrogeophysics – the drivers Tiedeman & Hsieh (2004) During the 1990s there was a rapid growth in the use of geophysics to provide quantitative information about hydrological properties and processes. Much of this was driven by: - the recognition of the importance of heterogeneity of subsurface properties that influence mass transport in groundwater systems. - the need to gain information of direct value to hydrological models, particularly given the developments of ‘data hungry’ stochastic hydrology tools.

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Hydrogeophysical approach structure (e.g. permeability maps) process (e.g. transport of solute) Kemna (2003) Dynamic imaging Static imaging Rock physics model(s) Rock physics model(s) Improved hydrogeological model Kowalsky et al. (2006)

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Hydrogeophysical approach Micro- structure Well logs Cross-borehole imaging Surface imaging Airborne Core imaging Survey scale Resolution

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Commonly used approach – static imaging A1 C2 C5 C3 C log 10 (resistivity, in m) Boise, Idaho, USA 14m Keery, Binley, Slater, Barrash and Cardiff (in prep)

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16-Mar-03 Depth (m) Distance (m) 15-Mar-03 Depth (m) Distance (m) 21-Mar-03 Depth (m) Distance (m) Depth (m) Distance (m) 24-Mar-03 Depth (m) Distance (m) 27-Mar-03 Depth (m) Distance (m) 02-Apr-03 Winship, Binley and Gomez (2006) Hatfield, UK Monitoring changes in resistivity due to tracer injection. Ultimately to understand pathways of solutes from ground surface to the aquifer. Commonly used approach – dynamic imaging H - E2 H - R2 H - R1 H - E1 H-E3 H-E4 H - I2 Tracer injected at H-I2

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But many of the hydrological challenges are at a larger scale Challenge 1: Larger scale application

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Larger scale example Elevation (m above sea level) Objective: determine potential connectivity between land surface and regional sandstone aquifer

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Electromagnetic (EM) conductivity surveys reveal variation over top 6m Larger scale example

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Current is injected between C+ and C- The voltage difference between P+ and P- is measured The voltage difference is a function of the current injected and the resistivity beneath the electrode array C+C-P+P-C+C-P+P- C+C-P+P- C+C-P+P- C+C-P+P-C+C-P+P- C+C-P+P-C+C-P+P- Electrical resistivity tomography (ERT) provides an assessment of vertical structure

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log10 (resistivity, in m) Conductivity (mS/m) stream Clayey drift Sandstone Window in the clay? Larger scale example

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Local sampling and geology Resistivity & Induced Polarisation Borehole logs Ground Conductivity GPR How do we bring all these data together to form one consistent, improved model of the system? Challenge 2: Data fusion

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Can we use other information to help constrain the inversion of geophysical data? For example, we may be able to estimate spatial covariance structure based on well log data? Linde, Binley, Tryggvason, Pedersen and Revil (2006)

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Challenge 2: Data fusion In areas where the gradients are in the same or opposite direction (or where one of the gradients is zero) will be zero (and the pixels structurally similar) We could jointly invert the two (or more) data using a structural similarity, e.g. by minimising the cross-gradients operator Gallardo (2006)

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Challenge 2: Data fusion structure (e.g. permeability maps) Static imaging Rock physics model(s) We cannot use geophysical imaging alone – we need to use geophysics to support other data (not replace it) Well log data Measurements of hydrological states

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At times there is a need to assess information content in data (this has been significantly overlooked to date) £X drilling £X geophysics Understanding the value of different information will permit appropriate resource allocation to the project and help with survey design. This is becoming more and more relevant as large hydrological projects invest in hydrogeophysical surveys. Challenge 3: Assessing information content

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Data fusion ERT Parameter resolution Spatial resolution Quantified information EM GPR Other methods Geophysical method Inversion (McMC) Output Prior information Uncertainties Mapping

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Data fusion Site represented as series of 1D models Permits practical application of Markov chain Monte Carlo (McMC) Misfit Likelihood MH sampling (accept/reject) PriorPosterior Bayes’ theorem Joint likelihood function

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Data fusion (e.g., Maurer et al., 2010) Shannon’s Entropy (Shannon, 1948) Information (Shannon’s Entropy) Increase in information as uncertainty in property reduces

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Data fusion Bayesian Maximum Entropy (BME) Serre & Christakos (1999) Expected knowledge Maximization ( Lagrange multipliers method ) G: general knowledge S: site-specific knowledge K: total knowledge Predicted pdf BMELIB (http://www.unc.edu/depts/case/BMELIB/)http://www.unc.edu/depts/case/BMELIB/ Christakos (2000) Prediction Hard data (Information >2) Soft data (Information <2)

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Data fusion JafarGandomi & Binley (in review) 1D synthetic example showing how different data provides constraint to resistivity structure

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Distance (m) Example data fusion on quasi 2D profile from Trecate, Italy Data fusion

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Coupled hydrogeophysical inversion Hydrological model, e.g. permeability structure Geophysical surveys ? Hydrological model Inversion (assumed known) Rock physics model(s) And, if so, then we should use this in our inversion Surely we know something about the hydrology?

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Scholer, Irving, Binley and Holliger (2011) Coupled hydrogeophysical inversion Do we need to invert geophysical data? We have been exploring the potential of using geophysical data (not images) as a means of constraining hydrological models in an McMC framework.

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Scholer, Irving, Binley and Holliger (2011) Coupled hydrogeophysical inversion Prior distribution for the 4 hydrological model parameters Posterior distribution for the 4 hydrological model parameters for each of the 4 layers

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Summary Deterministic inversion of 3D geophysical data is now relatively common, although the assessment of uncertainty is lacking. We need to develop ways of combining multiple data (multiple scales). Attempts have been made to use geophysical data within a hydrological model inversion. So far these have been limited to relatively low dimensional models. These fusion approaches must allow some assessment of information value, particularly as we look at new survey designs (for future data). Attempts have been made to jointly invert geophysical data, although most of these have been done in 2D.

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