1. Application to geophysics: Challenges and some solutions
Andrew Binley

2. 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

3. Hydrogeophysics – the drivers
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.
Resistivity profile and hydrogeological section, Penitencia, CA (after Zohdy, 1964).

4. Hydrogeophysics – the drivers
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.
Tiedeman & Hsieh (2004)

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

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

7. Commonly used approach – static imaging
Boise, Idaho , USA
14m
log10 (resistivity, in Wm)
2.3
3.2
Keery, Binley, Slater, Barrash and Cardiff (in prep)

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

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

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

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

12. Larger scale example
Electrical resistivity tomography (ERT) provides an assessment of vertical structure 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-
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

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

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

15. Challenge 2: Data fusion
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)

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

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

18. Challenge 3: Assessing information content
At times there is a need to assess information content in data (this has been significantly overlooked to date)
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. £X
drilling £X
geophysics

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

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

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

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

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

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

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

26. 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.
Scholer, Irving, Binley and Holliger (2011)

27. 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
Scholer, Irving, Binley and Holliger (2011)

28. Summary
Deterministic inversion of 3D geophysical data is now relatively common, although the assessment of uncertainty is lacking.
Attempts have been made to jointly invert geophysical data, although most of these have been done in 2D.
We need to develop ways of combining multiple data (multiple scales).
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 use geophysical data within a hydrological model inversion. So far these have been limited to relatively low dimensional models.