GISMO Simulation Study Objective Key instrument and geometry

GISMO Simulation Study • • • Objective Key instrument and geometry parameters Surface and base DEMs Ice mass reflection and refraction modeling Algorithms used for space-borne phase history data simulation • Data processing steps • Results analysis • Modifications for airborne simulation

Objective • to perform analysis to validate the interferometric ice sounding technique for measuring the ice mass thickness in polar areas using a P-band spaceborne SAR • Analysis approach – Generate phase history data – Process the data into SLC data and interferograms – Band pass filtering to extract the basal contribution and to derive the ice thickness from both surface and base interferogram

Key instrument and geometry parameters • • Platform Height: 600 km Center Frequency: 430 MHz Chirp Bandwidth: 6 MHz Pulse Length: 20 us PRF: 2 k. Hz Antenna Length: 12. 5 m Antenna Boresight Angle: 1. 5 o Baseline: 45 m

Surface and base DEMs (Greenland) 200 km Surface DEM Base DEM

Ice mass reflection and refraction modeling S s H 1 n 1=1 A h 2 D B xb xs surface DEM C n 2 =1. 8 ice mass d n 3 =3 (for rocks) Fig. 1 ice mass reflection and refraction model basal DEM (land or water)

Space-borne SAR phase history data simulation • Reflectivity map calculation for both reference and slave antennas • Phase history data generation

Reflectivity map calculation S 2 (sensor) All quantities: slant range, incidence angle, refraction angle and reflection coefficients, are calculated at each ground range grid. A slant range grid will lie between two neighboring ground range grids. The reflectivity coefficient for each slant range grid is calculated through interpolation of these two neighboring ground range bins. When calculating the reflection from the basal, we still start from the ground range grid on the surface. The refraction vector may not hit exactly the ground range grids. Bilinear interpolation is therefore used to calculate the refraction pointing vector from each surface ground grid to the basal. At each surface ground range grid the basal reflection coefficient and the slant range from the sensor to the basal are calculated. S (sensor) B (baseline) All the calculations for the second orbit are the same as for the reference orbit except the interferometric phase, which is the result of the non-zero baseline and DEMs, is added to the secondary reflectivity map for both surface and basal calculations. 1 surface DEM (n 1) A C 2 ice mass (n 2) B ground range grids basal DEM (n 3: land or sea water) Fig. 2 Implementation of reflectivity map calculation

Phase history simulation • Inverse chirp scaling Phase history data HSAR(f) Reflectivity map H-1 SAR(f) SLC data Phase history data

Data Processing • SAR processor (Vexcel’s FOCUS) SLC data • IFSAR processor (Vexcel’s RAMS 2) Interferograms • Interferometric ice sounding processing – Band-pass filtering to extract the basal interferogram – Derive surface and base topography

Results Analysis • Interferogram with both surface and basal contributions • Interferogram spectrum analysis • Extracted basal interferogram using band-pass filter • Comparison between the true and derived ice mass thickness

Results Analysis …… • DEMS in slant range geometry 148. 8 km (ground range) 148. 8 km echo delay caused by the ice thickness at nadir 137. 5 km (a) surface DEM (b) basal DEM

Results Analysis …… • Amplitude images of the phase history data

Results Analysis …… • Amplitude images of the SLC data

Results Analysis …… Slant range 11. 8 km ( ground range 70 km ) • 80 -azimuth-look interferogram 2 Azimuth (130 km) 0

Results Analysis …… • Interferogram range spectrum The peak at 0 frequency represents the surface contribution and the peaks at the right side are from base contribution.

Results Analysis …… Slant range 11. 8 km ( ground range 70 km ) • Band-pass filtered interferogram 2 Azimuth (130 km) 0

Results Analysis …… ground range 70 km +2500 m 2850 m +2137 m 1714 m Comparison between the true and derived ice mass thickness

Results Analysis …… • Comparison between true and extracted basal interferograms true basal interferogram extracted basal interferogram from band-pass filtering

Modifications for airborne simulation • • Airborne platform with air turbulence Varying PRF Interferometric mode with 2+ receiving antennas Inverse chirp-scaling modifications for varying PRF and sensor velocity • Airborne SAR processor

Air Turbulence Simulation • Along track: x = xa • sin(2 fxat + xa) + xe • sin(2 fxet + xe) • Horizontal: y = ya • sin(2 fyat + ya) + ye • sin(2 fyet + ye) • Vertical: z = za • sin(2 fzat + za) + ze • sin(2 fzet + ze)

Varying PRF Simulation • PRF = PRFn + PRF • sin(2 f. PRFt + PRF)

Interferometric mode with 2+ receiving antennas • Current space-borne Scatter: repeat pass mode • Future airborne Scatter: – Repeat pass mode – Single pass mode • One transmitting/receiving with others receiving • Ping-Pong mode ?

Inverse chirp-scaling for varying PRF and varying sensor speed • The phase history data created from the inverse chirp scaling algorithm apply to a staright line path and uniform along track spacing. • The data need to be interpolated for a curved path, varying PRF and sensor speed

Airborne SAR processor • Modify Vexcel’s current fast-back-projection space-borne spotlight SAR processor to be able to process the simulated airborne strip. Map SAR data

SAR Tomography Potentials of GISMO • • SAR tomography background SAR tomography simulation Results of E-SAR tomography tests GISMO potentials for SAR tomography applications

SAR Tomography Background • Conventional SAR Imaging Idealized Straight Flight Paths Ground Reference Point

Multi-Pass SAR Imaging re tic the tu per A n Sy Ground Reference Point Synthetic Elevation Aperture

Simulated Results • Straight & Parallel Paths 19. 2 m Illumination Image Formation Plane

Simulated Results Illumination • Straight & Parallel Paths 19. 2 m Image Formation Plane Backprojection Plane Coherent Sum

Vexcel’s tomography research Classified

Tomography results from E-SAR • • • L-band Nominal orbit altitude: Number of flights: Total vertical aperture: Vertical resolution: 3600 m 14 280 m 3. 5 m

E-SAR Height/azimuth slice tomogram

E-SAR Height/azimuth slice tomograms Using MUltiple SIgnal Classification algorithm (MUSIC) with pre-assumed one or five scatterers

GISMO’s Potentials for Tomography Applications Baseline • One flight track 2 – track altitude : 10 km – 4 ~ 6 receiving antenna elements H 1 (flight height) – total aperture: 20 m • Multiple flights – Assume 10 or more flights – Total 40 ~ 60 measuremes – total aperture: 400 m D (ice thickness)

GISMO’s Potentials for airborne case Total Baseline / Angular resolution : 20 m / 2 o (single pass) 400 m / 0. 1 o (repeat pass) Angular separations between the surface and base return Ground range (look angle) 0 km 1 km 2 km 3 km 4 km Ice thickness 100 m (0 o) (5. 7 o) (11. 3 o) (16. 7 o) (21. 8 o) 10. 8 o 6. 4 o 4. 2 o 3. 0 o 2. 3 o 500 m 23. 4 o 18. 3 o 14. 4 o 11. 5 o 9. 4 o 1000 m 32. 0 o 26. 7 o 22. 3 o 18. 6 o 15. 7 o 2000 m 42. 6 o 37. 2 o 32. 3 o 28. 1 o 24. 4 o

GISMO’s Potentials for space-borne case with 600 km orbit Total Baseline / Angular resolution : 45 m / 0. 89 o (single pass) 1000 m / 0. 04 o (repeat pass) Angular separations between the surface and base return Ground range (look angle) 10 km 30 km 50 km 75 km 100 km Ice thickness 100 m (0. 95 o) (2. 86 o) (4. 76 o) (7. 12 o) (9. 46 o) 0. 74 o 0. 33 o 0. 2 o 0. 14 o 0. 1 o 500 m 2. 3 o 1. 38 o 0. 93 o 0. 66 o 0. 5 o 1000 m 3. 5 o 2. 41 o 1. 73 o 1. 26 o 0. 97 o 2000 m 5. 4 o 4. 0 o 3. 09 o 2. 34 o 1. 85 o

SAR Tomographic Ice Sounding • Would repeat pass SAR tomographic ice sounding WORK ? ? ? • Probably basal returns are still correlated even though the surface returns may corrupt the surface components of the tomogram.