Figure 1: Position of tomography-wells in the Moreppen research field.
Here, we present GPR time lapse tomography results from a
natural infiltration event: the melting of snow during the spring of
2005 at the Gardermoen aquifer. Three datasets were collected
before, during and after snowmelt. From the GPR images we
observe focusing and defocusing of water flow. We reproduce
these effects by inverse modeling of the flow parameters. This
result is a strong argument for taking focusing and defocusing of
unsaturated flow into consideration in vulnerability analysis of
groundwater resources.
In this project we combined borehole ground penetrating radar
data (GPR) with soil physics and flow modeling. We used ray
tracing and electromagnetic travel time tomography to derive
spatially continuous images at different times during a complete
snowmelt event. The purpose of this study was to derive robust
parameters for unsaturated flow modeling: How much additional
information do we get from GPR borehole tomography compared
to only observations of soil moisture and groundwater level?
Motivation
Cross-well Ground Penetrating Radar (GPR) datasets from
three adjacent wells were collected near Oslo’s
Gardermoen airport (Norway) before, during and after
snowmelt in 2005. Velocity images from the GPR data,
obtained using ray tracing and travel time tomography,
provide a time dependent 2D picture of the vadose zone.
The electromagnetic (EM) velocity images show two
distinct units: delta topset and foreset layers. These results
are consistent with GPR surface reflection data, core data,
as well as knowledge of local sedimentary geology.
Through petrophysical relations (Topp et al. 1980) the
EM-velocities were converted to soil water content, which
we used as input observations for inverse modeling of
unsaturated flow parameters. Two innovative procedures
were implemented in this project: (i) optimization of
geological geometry and (ii) computation of estimation
weights based on ray coverage. Using this method we
were able to demonstrate focusing and de-focusing of
water infiltration after snow-melt. Focusing of infiltration
implies a faster flow than previous predictions.
Defocusing implies that smaller volumes of the
unsaturated zone take an active part in transport of
contaminants. Both focusing and defocusing effects means
reduced remediation capacity in the unsaturated zone. By
imaging focusing and defocusing of water flow, GPRtomography can be used to evaluate vulnerability of
groundwater resources to contamination from surface
infiltration.
Abstract
22 April 2005
1 April 2005
22 March 2005
Soil water content
First-arrival travel time picks for source at depth 2.2m in
cross-well k14-k16.
Travel time tomography
Infiltration history
derived form snowpillow data from NVE
and meteorological
observations from
met.no, and
groundwater table from
Bioforsk.
Images of soil water
content derived from
GPR-tomography
and soil physics
(Farmani et al.,
2007)
Curved raytracing
improve EM-velocity
estimates.
22.04. after snowmelt.
01.04. during snowmelt.
22.03. before snowmelt.
High quality data from
NGI’s step frequency
radar with borehole
antennas.
Good fit
Compare the output with
observations
Bad fit
Flow sheet indicate principles for inverse modeling. Images at
left is observations derived from GPR tomograms at different
time steps. Images at right is corresponding images from flow
simulations. Optimal parameters are obtained by minimizing
difference between observed at the same time as the geological
geometry is optimized. Geometrical optimizations are achieved
by introducing moveable control points (g1, g2, …).
Final estimates of the flow
parameters
Change the value of the flow
parameters
Boundary conditions and initial guesses of
flow parameters are made
Inverse modeling procedure
Difference between dry and wet conditions indicate
focusing of water flow above permeability barrier.
Below the barrier there are no observed difference in
water content which means that this part of the
unsaturated zone does not take part of water
transport.
Difference in θ between the third and first survey
Focusing and dede-focusing of water flow
WesternGeco, Oslo Technology Center, Sølbraveien 23, 1372 Asker, Norway.
3
Institute for Agricultural and Environmental Research, Frederik A. Dahls vei 20, 1432 Ås, Norway.
Department of Geosciences, University of Oslo, 1022 Blindern, 0315 Oslo, Norway.
2
1 Norwegian
Nils-Otto Kitterød1 , M. Bagher Farmani2, Henk Keers3
22 March 2005
Cross validation
Misfit reduction
22 April 2005
1 April 2005
k14
k16
Soil water content estimates by GPR
Inverse modeling
Forward model
Infiltration history
Misfit Reduction
Soil water content estimates by flow model
k18
Application of methodology to field data
Inverse modeling of unsaturated flow parameters - what can we learn from GPR tomography?
N
j =1 k = 1
nt
- 2*
jk
*
jk
(
))2
Topp, G.C., Davis, J.L., and A.P. Annan. 1980.
Electromagnetic determination of soil water content:
measurements in coaxial transmission lines. Wat. Resour. Res.
16:574-582.
Farmani, M.B., Keers, H. and Kitterød, N.-O., 2007, TimeLapse GPR Tomography of Unsaturated Water Flow in an IceContact Delta, Vadose Zone Journal, Vol. 6, No. 4, November
2007, doi:10.2136/vzj2006.0132
Farmani, M.B., Kitterød, N.-O., and Keers, H., 2008, Inverse
modeling of unsaturated flow parameters using dynamic
geological structure conditioned by GPR tomography, Water
Resour. Res., 44, W08401, doi:10.1029/2007WR00625
References
Thanks to Professor Per Aagaard at Department of geosciences,
University of Oslo for financial and scientific supports; Dr. Fan
Nian Kong at Norwegian Geotechnical Institute for software
supports and letting us use NGI step-frequency radar; Dr. Hervé
Colleuille and Frode Kvernhaugen at the Norwegian Water and
Energy Directorate; and Ole Einar Tveito (Meteorological
Survey).
Acknowledgement
• Weights derived from ray coverage improve the inverse
modeling results.
• Sensitivity analysis demonstrates the sensitivity of geological
geometry to the flow parameters.
• Inverse flow modeling estimates the flow parameters in the
vadose zone and reproduces the main characteristics of
groundwater recharge and independent tracer tests.
• The use of curved ray paths (ray tracing) rather than straight
lines improves the quality of the images.
• GPR travel time tomography, when combined with soil physics,
gives quantitative volumetric soil water content estimates.
• Time laps tomography images preferential flow paths.
• Travel time tomography images geological structures.
Topp’s model error variance
weighted with tomographic
ray coverage
− θ jk p1 , p2 ,..., p M , g 1 ,K , g Q
Differences between GPR
water content estimates and
flow model estimates
-2
σ -2*
jk = W jk σTopp
∑∑ σ (θ
Conclusions
F=
Objective function