Abstract

1
Abstract
Numerical Experiment
Half-Space Lossy Greens Function Model
Microwave junction matching method for CTF

• frequency 1.5GHz Additive Gaussian
  noise SNR 20dB
• Region of interest is 9cm x 9cm x 0.75cm
  (15x15x15)
• ?x ?y ? 6mm ?z ? 0.5mm
• ?sand 20 0.14j ?obj 2.6 0.001j
• Linear array of T/R -- 7 vertical locations and 4
  corner positioning
• Levenberg-Marquardt method

The sensing and detection of dense non-aqueous
phase liquid (DNAPL) contaminations in soil has
significant geo-environmental benefits and it is
challenging because the background media is
uncertain, wave characteristics of media may be
hard to determine, and wave scattering of
non-ideal volumes in non-uniform backgrounds is
difficult. Sensing the subsurface volume between
boreholes using cross-well radar (CWR) is less
expensive and saves effort, but has not been
investigated satisfactorily. In this work, we
developed an analytical model to approximate CWR
sensing in infinite half-space lossy media in
frequency domain. Half-space dyadic Green's
function due to a vertical polarized dipole
source is introduced. Integration for angles gets
far into evanescent range. Born approximation is
employed as a linear model for a shape-based
inversion that is developed to localize the
object assuming its contrast to the lossy
background is a priori information. This forward
model is validated via CWR experiment. Soil
parameters (relative dielectric constant and loss
tangent) variance with frequency is represented
by a quadratic polynomial. Calibration for soil
parameters is conducted with CWR data using an
iterative low-order parameterized optimization
technique involving both magnitude and phase
information. The validated forward model can
predict for CWR sensing experiments in a broad
frequency range very well. Localization and
reconstruction of the object is performed as a
non-linear least square optimization problem by
minimizing a cost function that calculates the
misfit between the predicted numerical simulation
and experimental observation. The proposed
inversion method is validated by numerical
experiments, and it gives promising preliminary
results.

• Plane wave decomposition
• Fresnel reflection for each plane wave at
  interface
• Integration for angles far into evanescent range

Calibration via CWR Experiments

• Analysis
• Loss tangent variance will only affect the
  magnitude of the electric field
• Relative dielectric constant change affects both
  the magnitude and the phase
• Assumptions
• Quadratic polynomial as a function of frequency
  is sufficient to describe the parameter variances
  with frequency
• Approach
• Minimize a cost function in the sense of
  nonlinear least square error
• Obtain optimal polynomial coefficients using
  Lavenberg-Marquardt Method

Validation Air/Sand Half-Space Model vs.
Finite Difference Freq. Domain (FDFD)
Initial guess volume Reconstructed volume
Ex Ey Ez
Half space
State of the Art
Source depth is 20? below interface in
z-direction and centered in xy plane observation
plane is 20? apart from source, where
at f1GHz The relative dielectric of
the lossy media is
where
There are different detection techniques
implemented in the field, such as Direct Push
Probe Technologies (DPT), In-Situ Tracers (IST),
Geophysical Methods (GM). GM methods are the most
non-invasive ones to locate subsurface DNAPLs
avoiding the risk of additional vertical
migration of pooled DNAPL. Of course, GPR is the
least non-invasive, but has depth limitation.
Thus, CWR has been chosen to study in this
research. The prospective algorithms in solving
the pool characterization problem are based upon
multi-scale image formation and shape-based
inversion methods for localizing parameterized
pollution pools.
Ground truth xo,yo,zo, lx, ly, lz 4.764452
4.764452 0.400000 4.168896 4.1688960
0.2500000cm Estimated result xo,yo,zo, lx,
ly, lz 4.764460 4.764484 0.400014
4.168896 4.1688959 0.2500099cm
Calibration results for soil parameters
FDFD

error
Future Works
Problem Description
Value added to CenSSIS

• Segmentation of region of interest with
  non-uniform voxel to better match the shape of
  the object while preserving good resolution
• Experiment vs. model comparison with DNAPL
• Inversion using multi-frequency information
• Inversion algorithm validation with CWR data

Cross-Well Radar Sensing Setup

• Dense non-aqueous phase liquid (DNAPL)
  contaminants
• ? ? ?0 (2.6 0.001j)
• Object is wide and thin (pool)
• Side width to thickness ration is bigger than 10
  typically
• relative dielectric constant and loss tangent)
  are frequency dependent
• Saturated sandy soil (lossy medium)
• ? ? ?0 ( 21 0.08j)
• Reconstruct and detect the location and the size
  of the anomaly

Experiment vs. Model
Publications Acknowledging NSF Support
1) Zhan, H., Farid, M., Rappaport, C. M and
Alshawabkeh, A. N., Born Approximation Modeling
of Lossy Soil Half-Spaces for Cross-Well Radar
Sensing of Contaminants with Low-Order Parameter
Optimization, in submission 2) Farid, M. ,
Zhan, H., Alshawabkeh, A. N, and Rappaport, C.
M., Cross Well Radar II Comparison and
Validation of Experimentation and Modeling
Validation using Channel Transfer Function, in
submission 3) Zhan, H., Rappaport, C., Farid,
M., Akram, A. and Raemer, H., Lossy Halfspace
Born Approximation Modeling of Electromagnetic
Wave Source and Scattering in Soil by Cross Well
Radar, ASCE Geo-frontiers, Austin, TX, Jan.
2005, electronic CD 4) Farid, M., Akram, A.,
Zhan, H. and Rappaport, C., Challenges and
Validation of Cross Tomography Experimentation
for Inverse Scattering Problems in Soil, ASCE
Geo-frontiers, Austin, TX, Jan. 2005, electronic
CD 5) Farid, M. et al. (2003), "Experimental
DNAPL Detection Using Cross-Well Radar", SAGEEP,
San Antonio, TX. USA, Electronic
Proceeding 6) Farid, M. et al. (2003), "Modeling
Borehole Dipole Antenna Patterns for Cross-Well
Radar DNAPL Imaging", Soil-Rock Conference, MIT,
Boston, MA. USA, proceeding, pp. 261-267 7) Farid
M. et al. (2002), "DNAPL Detection Using
Cross-Well Radar", Environmental Geotechnics, 4th
ICEG, pp. 465-470 8) M. Farid, A. Alshawabkeh, C.
Rappaport (2003) Experimental DNAPL Detection
Using Cross-Well Radar", SAGEEP, St. Antonio, TX.
Objective
Develop and verify innovative computational tools
for real time efficient, non-invasive,
cost-effective and reliable monitoring,
delineation and characterization of DNAPLs using
Ultra-Wideband Cross-Well Radar.
Sensor Independent Transformation Channel
Transfer Function (CTF)
Half-space Scattered Field with Born Approximation

• In cross-well-radar experiment, coupling between
  monopole antenna and soil varies with frequency
• In forward modeling, wave propagation that is
  independent of the sensor is studied
• CTF is introduced to translate the real
  experimental data to the form that is compatible
  to the simulation by forward model

• Electric field for 3D electromagnetic problems in
  frequency domain
• vector Helmholtz equation
• Assumption object and homogeneous background are
  additive
• Scattered E-field with first order Born
  Approximation

References
1) M. L. Brewster and A. P. Annan, GPR
Monitoring of a Controlled NAPLRelease 200 MHZ
Radar, Geophysics, Vol. 59, No. 8, August
1994 2) L. Tsang, J.A. Kong and R. R. Shin,
Theory of Microwave Remote Sensing, JOHN WILEY
SONS, 1985 3) C. Balanis, Antenna Theory
Analysis and Design, Harper Row, 1982 4) J.
Hipp, Soil Electromagnetic Parameters as
Functions of Frequency, Soil Density, and Soil
Moisture, Proc IEEE, Vol. 62, pp. 98-103, Jan.
1974. 5) C. R. Vogel, Computational Methods for
Inverse Problems,SIAM,2002 6) R. E. Collin,
Foundations for Microwave Engineering,2nd ed.,
1992 7) Misha E. Kilmer, Eric L. Miller, Alethea
Barbaro and David Boas, Three-dimensional
shped-based imaging of aborpton perturbation for
diffuse optical tomography, Applied Optics
(2003), 42, 3129 3144 8) Basak, U. Karbeyaz,
Reduced Complexity Geometry-Based Born Inversion
for Frequency Domain Ultrasonic Monitoring of
Cancer Treatment, Ph.D thesis, Sept., 2005
Shape-based Inversion

• Find a geometry function such that the voxels
  have value 1 inside the ellipsoid, 0 elsewhere
  8
• Ellipsoid formulation
• Entries of diagonal matrix D are the inverse of
  the lengths of the semi-axes (lx,ly and lz)
• Geometry function
• Use Levenberg-Marquardt Method
• Compute Jacobian matrix analytically

The scattered field as a function of source
location, receiver location and source frequency,
involves a sensor transfer function (dyadic
Greens function and background field ) and the
perturbation of object function.