The document discusses image distortion effects in subsurface synthetic aperture radar (SAR) imaging of deserts and proposes an iterative corrective approach. It summarizes that subsurface SAR can map subsurface topography under sand but images are distorted due to geometric distortion and defocusing. It then proposes using dual-frequency SAR, with VHF penetrating sand and Ka imaging the surface, along with an iterative algorithm using the surface data to correct the VHF image and retrieve accurate subsurface heights. Simulation results showed the approach improved height resolution and coherence by 20-40% compared to conventional SAR.

1. Image Distortion Effects in Subsurface SAR Imaging of Deserts and Their Correction Technique Adel Elsherbini and Kamal Sarabandi Radiation Laboratory, University of Michigan – Ann Arbor 1

2. Outline Motivation Subsurface InSAR Operation Scattering Phenomena Processing Technique Image Distortion Effects Proposed Iterative Corrective Approach Simulation Results Verification using Scaled Model Conclusion & Future Work 2

3. Motivation Deserts cover ~ 20% of the earth’s land surface. Estimation of the subsurface topography and the top sand layer thickness is very useful in: Oil fields and ground water explorations Study of sand dunes formation & migration Planetary explorations Deep mine fields detection Archaeological surveys …. etc. Current technology is GPR Sand dunes advancing towards the city of Nouakchott, the capital of Mauritania*. Sand dunes on Proctor Crater on Mars ** 3

4. High Cost Would not penetrate through the sand Low Vertical Accuracy The Proposed Technique Common Fast Top Surface Height Retrieval Techniques* 4 (*) Richards, M.A.; , "A Beginner's Guide to Interferometric SAR Concepts and Signal Processing [AESS Tutorial IV]," Aerospace and Electronic Systems Magazine, IEEE , vol.22, no.9, pp.5-29, Sept. 2007

5. Background:Conventional InSAR SAR Image 1 (Master) Phase Interferogram ~(R1 – R2) Prop. Path Noise Fringes Coregister the two images and generate the phase difference R2 R1 SAR Image 2 (Slave) Unwrapped Interferogram Ref. Points => Heights 5

6. Scattering Phenomena for Sand Covered Bedrock Sand Layer Roughness ~few mm Surface and volume scattering negligible up to ~1GHz Low propagation loss at VHF (~150 MHz) Bedrock Layer Roughness ~few cm Higher backscattering Low Frequency InSAR (150 MHz) High Frequency InSAR (35 GHz) Sand Layer Bedrock 6

8. Different propagation velocity7

10. Worse azimuth resolution

11. Conventional 2D Phase Unwrapping

12. Use the same techniques as conventional InSAR

13. Top Surface Height information from KaInSAR is used together with the VHF InSAR data to obtain the correct subsurface height using a new inversion algorithm (*).(*) A. Elsherbini, and K. Sarabandi, “Mapping of Sand Layer Thickness in Deserts Using SAR Interferometry”, TGRS 2010. 8

14. 3D Top Surfaces Top sand surface is not flat. Need to verify the performance for 3D surfaces A new subsurface SAR simulator is developed. Inputs: Top Surface Target(s) Locations Radar Path Output: Raw SAR Image Range to target Amplitude change due to attenuation Requires solution of nonlinear equations for each target and radar combination (Very time consuming) New acceleration technique is developed using 3D interpolation*. Radar Target 9 (*) Presented by the authors at IGARSS 2010

15. Actual Height (-5m) Targets Height Example:Barchan Dune Simulation Path 2 Proposed Algorithm Path 1 Targets Height Geometric Distortion Generating the phase difference and Applying the proposed Algorithm Conventional InSAR Targets Height 10

16. Subsurface Image Distortions Geometric Distortion SAR Image Defocusing Full aperture Best resolution Quick defocusing as the target gets deeper (small depth of focus) Partial aperture Worse resolution Long depth of focus Subsurface focusing can be used if we know the target height. To know the height, we need to focus ! Iterative Focusing Algorithm 11

17. Subsurface Correction Algorithm Iter. #1 Iter. #3 Conventional Subsurface Height Focusing Surface 12

18. Experimental Verification 10 GHz scaled model measurements in the Lab 10 GHz Horn Antennas 2.5 m 25 cm NWA Flat sand with rough metallic horizontal bedrock Corner reflectors for calibration 13

19. Experimental Verification Azimuth Sections Different azimuth sections are shown aside. Height errors conventional InSAR processing: 40% Artificial slope Using the proposed algorithm, the measured R.M.S error is 4mm (0.3m in the actual model) and the mean error ~1-2mm. About 20% improvement in the coherence is also obtained. 14 Iter. Approach. Conventional

20. Conclusion Subsurface InSAR Importance and Operation. Image distortion effects include: Geometric Distortion Azimuth Defocusing Image distortion limits the use of subsurface InSAR in many applications New Iterative Image Correction Algorithm. Order of magnitude improvement in the resolution. 20-40% Improvement in coherence. Verification using Simulation and Scaled Model Measurements 15

21. Future Work Multiple Look Angles Allows inversion for the sand dielectric constant in addition to the subsurface height Can enable height retrieval under inhomogeneous sand layer. Can be used to detect and correct some layover effects. Multiple operating frequencies Scattering from both top and bottom surface at some frequencies. Allows estimation of the subsurface roughness. Scattering from Dense Random Media (Sand): Used semi-empirical formulas to estimate the backscattering at Ka band. More rigorous approach is desired. 16

22. Thank you Question ? 17

23. Thank you Question ? 18

24. Thank you Question ? 19

26. L-band radar reveals previously unknown faults covered by sand.

27. 200 x 190 Km area in northern Sudan.

28. L-Band radar could penetrate the superficial sand layers up to several metersOptical Image Optical Image Radar Image Radar Image (*) Paillou, P.; Rosenqvist, A.; , "A JERS-1 radar mosaic for subsurface geology mapping in East Sahara," Geoscience and Remote Sensing Symposium, 2003. IGARSS '03. Proceedings. 2003 IEEE International , vol.3, no., pp. 1870- 1872, 21-25 July 2003 20

29. Current Technique for Subsurface Topography Estimation GPR: Ground Penetrating Radar Operation Disadvantages Ground Based Very Labor Intensive Very Time Consuming for mapping large areas A new remote sensing technique is required ! 21

31. Only a portion of the synthetic aperture can be used to avoid defocusing

32. Worse ground resolution

33. Conventional 2D Phase Unwrapping

34. Subsurface height at the ground control points is obtained using GPR.

35. Use the same techniques as conventional InSAR

36. Top Surface Height information is used together with the VHF InSAR data to obtain the correct subsurface height using a new inversion algorithm22

37. VHF InSAR Phase Interferogram [Rad] Inversion Algorithm Based on: Geometrical Optics Uses: Ka-InSAR top surface map VHF-InSAR Interferogram Generates: The bedrock height map Knowns: Phase Interferogram (VHF) Electrical Range to Bedrock (VHF) Flight Paths (VHF) Top surface map (Ka-InSAR) Unknowns: Radar look angle Bedrock Height Iterative approach is used Azimuth [Km] Electrical Range [Km] 23

38. Future Work:Investigation of Ka band backscattering models for the sand volume scattering. Current techniques: Wave Approach Very complex and requires certain simplifying approximations. Some of these approximations are not valid for sand. Radiative Transfer Theory (RT) Calculating the phase and extinction matrices for sand is not straight forward Possible Approach: Hybrid Numerical-RT Model Use of the previously developed packing algorithm to calculate the pair distribution function. A numerical technique is used to compute the effective permitivity of the dense medium using Monte-Carlo simulations as well as phase and extinction matrices. Examine the interaction between volume scattering and surface scattering for natural sand surfaces. 24

39. Future WorkAntenna design for near ground operation Antenna will be placed closed to a dielectric half space Using dielectric filling of the waveguide. Artificial dielectrics to reduce the weight. 25

40. Sensitivity Analysis The effect of each of the following on the estimated subsurface height error was analyzed: Range Resolution Need good range resolution BW >~ 60 MHZ (40% @ 150MHz, UWB) Interferogram phase error Very sensitive for small baselines Baseline has to be > ~100 m Two path interferometry Sand Height & Slope (from Ka-InSAR) Relatively sensitive but within the achievable accuracies using Ka-InSAR Sand Dielectric Constant Not sensitive to moderate variations Baseline Distance 26

41. Doppler History 27

42. Coherence Improvement 28

43. Caustic Effects 29

44. Subsurface Height Estimation Using Conventional InSAR Sample Scenario Assumed low frequency to penetrate the top layer. Conventional InSAR height estimation does not account for propagation through the top layer: Surface undulations is transferred to the estimated bedrock height Calculated height is incorrect. A new subsurface height estimation system is required ! Sand Bedrock Estimated Height using Conventional InSAR 30

45. Algorithm Results Simulated several sand and bedrock scenarios The algorithm was found to converge within a few iterations (~5 iterations). 31