application to geophysics: challenges and some solutions andrew binley email:...
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![Page 2: Application to geophysics: Challenges and some solutions Andrew Binley Email: a.binley@lancaster.ac.uk](https://reader030.vdocuments.us/reader030/viewer/2022032701/56649c755503460f94929a27/html5/thumbnails/2.jpg)
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
0
10
20
z (m
)
2 0 3 0 4 0 5 0 6 0 7 0 8 0x ( m )
structure(e.g. permeability maps)
process(e.g. transport of solute)
Kemna (2003)
Dynamic imagingStatic imaging
Rock physicsmodel(s)
Rock physicsmodel(s)
Improved hydrogeological model
Kowalsky et al. (2006)
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Hydrogeophysical approach
Micro-structure
Well logs
Cross-boreholeimaging
Surface imaging
Airborne
Coreimaging
Survey scale
Reso
lutio
n
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Commonly used approach – static imaging
A1 C2C5 C3C4
2.3 3.2
log10 (resistivity, in Wm)
Boise, Idaho , USA 14m
Keery, Binley, Slater, Barrash and Cardiff (in prep)
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16-Mar-03
Dep
th (m
)
Distance (m)Distance (m)
15-Mar-03
Dep
th (m
)Distance (m)
Distance (m)
21-Mar-03
Dep
th (m
)
Distance (m)Distance (m)
Dep
th (m
)
Distance (m)Distance (m)
24-Mar-03
Dep
th (m
)
Distance (m)Distance (m)
27-Mar-03
Dep
th (m
)
Distance (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 imagingH
-E2
H-R
2
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
30
40
50
60
70
80
90
Elevation (m above sea level)
Objective: determine potential connectivity between land surface and regional sandstone aquifer
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7 9 11 13 15
Conductivity (mS/m)
Electromagnetic (EM) conductivity surveys reveal variation over top 6m
Larger scale example
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Larger scale example
Current is injected between C+ and C-The voltage difference between P+ and P- is measured
The voltage difference is a function of the currentinjected 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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1.6 1.8 2 2.2 2.4
log10 (resistivity, in Wm)
0 20 40 60 80 100 120 140 160 180
Distance (m)
-20
0D
epth
(m)
0 20 40 60 80Distance (m)
-20
-10
0
Dep
th (m
)
0 20 40 60 80Distance (m)
-20
-10
0
Dep
th (m
)
10 30 50 70 90
Distance (m)
-20
-10
0
Dep
th (m
)
7 9 11 13 15
Conductivity (mS/m)
stream
Clayey driftSandstone
Window in the clay?
Larger scale example
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Local sampling and geology
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0- 1 0
- 5
0
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0- 1 0
- 5
0
Resistivity & Induced Polarisation
Boreholelogs
0 1 0 2 0 3 0 4 0 5 0 6 00
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 1
2 2
2 3
2 4
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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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)
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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) t 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 physicsmodel(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
£Xgeophysics
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
Quantifiedinformation
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 modelsPermits practical application ofMarkov chain Monte Carlo (McMC)
mmm CL
21
2211
112
2
1
1
21 2
1
2
1exp
2
1εεεεm TT
nnnnL
Misfit
Likelihood
MH sampling(accept/reject)
Prior Posterior
Bayes’ theorem
Joint likelihood function
m m
mL
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Data fusion
x
xxxxx dEntcI log)(
mmm ,; IEJ (e.g., Maurer et al., 2010)
Shannon’s Entropy (Shannon, 1948)
Info
rmati
on(S
hann
on’s
Entr
opy)
Increase in information as uncertainty in property reduces
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Data fusion
mapmapGmapGmap dfffEntropy log
mapmapG gZf exp
SGK
Bayesian Maximum Entropy (BME)Serre & Christakos (1999)
Expected knowledge
Maximization (Lagrange multipliers method)
G: general knowledgeS: site-specific knowledgeK: total knowledge
Predicted pdf
BMELIB (http://www.unc.edu/depts/case/BMELIB/)
Christakos (2000)
softsoftSsofthardG
softsoftSksofthardG
softSmapkkdff
dffff
,
,,,|
ksofthardmap ,,
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 physicsmodel(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.