1. Abstract 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. State of the Art 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. Forward Modeling, Validation, Calibration and Shape-based Inversion for Geophysics Problem He (Sophia) Zhan, Carey M. Rappaport, Mohammad Farid, Akram N. Alshawabkeh, Eric L. Miller, Harold Raemer Department of Electrical Engineering, Northeastern University, MA 02115 This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging systems, under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC- 9986821) Value added to CenSSIS R1 Fundamental Science Fundamental Science Validating TestBEDs Validating TestBEDs L1 L2 L3 R3 S1 S4 S3 S5 Bio-MedEnviro-Civil S2 R2 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. 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 Problem Description Objective Half-space Scattered Field with Born Approximation The scattered field as a function of source location, receiver location and source frequency, involves a sensor transfer function (dyadic Green’s function and background field ) and the perturbation of object function. For 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 where is the wave number; is the complex permittivity and is the complex permeability; is the source. Plane wave decomposition Fresnel reflection for each plane wave at interface Integration for angles far into evanescent range Half-Space Lossy Green’s Function Model Air Soil Transmitter Receiver position 00  0 (  ’ - j  /  0 ) Half space FDFD % error |E x | |E y | |E z | Validation: Air/Sand Half-Space Model vs. Finite Difference Freq. Domain (FDFD) Pilot-scale (1/100) of CWR imaging 8 transmitters / 8 receivers Positioned on a circle of radius 6” Antenna specifically developed for CWR Good wideband (0.5 ~ 2.2GHz) coupling to dry/wet sand Fabricated for repeated insertion in PVC boreholes Cross-Well Radar Sensing Setup Sensor Independent Transformation: Channel Transfer Function (CTF) 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 The three cascaded two-port junctions with unknowns is matching to the one two- port junction obtained via experiments. Since the soil is lossy, the reflection coefficient at soil junction can be neglected. The magnitude of CTF is solved as: S 21 = Transmission measurements S 11 = Reflection measurements  0 (f) = phase offset The assumption in solving the CTF could affect the phase of the CTF, a progression analysis is conducted to find the appropriate offset amount to the phase. Microwave junction matching method for CTF Source depth is 20  below interface in z-direction and centered in xy plane; observation plane is 20  apart from source, where at f=1GHz; The relative dielectric of the lossy media is 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 where Calibration results for soil parameters Relative dielectric constantLoss target Experiment vs. Model  Network analyzer measurements  Half-Space Lossy Green’s Function, initial soil calibration  Optimal soil selection T/R Separation is 12” Depth of T/R is 9”/13” Depth of T/R is 13”/13” T/R Separation is 8.5” Shape-based Inversion 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 Numerical Experiment 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 (l x,l y and l z ) Geometry function Use Levenberg-Marquardt Method Compute Jacobian matrix analytically Ground truth: [xo,yo,zo, lx, ly, lz] = [4.764452 4.764452 0.400000 4.168896 4.1688960 0.2500000]cm Estimated result: [xo,yo,zo, lx, ly, lz] = [4.764460 4.764484 0.400014 4.168896 4.1688959 0.2500099]cm 1)M. 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Karbeyaz, “Reduced Complexity Geometry-Based Born Inversion for Frequency Domain Ultrasonic Monitoring of Cancer Treatment”, Ph.D thesis, Sept., 2005 References Future Works 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 Initial guess volume Reconstructed volume 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. Publications Acknowledging NSF Support