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

Application to geophysics:Challenges and some solutions

Andrew BinleyEmail: [email protected]

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


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.


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.

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)


Improved hydrogeological model

Kowalsky et al. (2006)

Hydrogeophysical approach

Micro-structure

Well logs

Cross-boreholeimaging

Surface imaging

Airborne

Coreimaging

Survey scale

Reso

lutio

n

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)

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

)


Dep

th (m

)


24-Mar-03

Dep

th (m

)


27-Mar-03

Dep

th (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

But many of the hydrological challenges are at a larger scale

Challenge 1: Larger scale application

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

7 9 11 13 15

Conductivity (mS/m)

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



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

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?


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


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)


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)


structure(e.g. permeability maps)

Static imaging


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

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

Data fusion

ERT

Parameter resolution

Spatial resolution

Quantifiedinformation

EM

GPR

Other methods

Geophysical method

Inversion(McMC)

Output

Prior information Uncertainties

Mapping

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

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

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)

http://www.unc.edu/depts/case/BMELIB/

http://www.unc.edu/depts/case/BMELIB/

Data fusion

JafarGandomi & Binley (in review)

1D synthetic example showing how different data provides constraint to resistivity structure

Distance (m)

Example data fusion on quasi 2D profile from Trecate, Italy

Data fusion

Coupled hydrogeophysical inversion

Hydrological model,e.g. permeability structure

Geophysical surveys

?Hydrological model

Inversion

(assumed known)


And, if so, then we should use this in our

inversion

Surely we know something about the hydrology?

Scholer, Irving, Binley and Holliger (2011)


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)


Prior distribution for the 4 hydrological model parameters

Posterior distribution for the 4 hydrological model parameters for each of the 4 layers

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.

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

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