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Modeling Surface and Subsurface Scattering from Saline Soils

A. Freeman, Tom Farr Jet Propulsion Laboratory, California Institute of Technology

4800 Oak Grove Drive, Pasadena, CA 91109 Philippe Paillou, Astronomical Observatory of Bordeaux Yanick Lasne, Astronomical Observatory of Bordeaux

Bruce Campbell, National Aerospace and Science Museum

ABSTRACT Smooth surface and subsurface layers are modeled as lossy dielectric materials. The Small Perturbation Model is used to estimate the relative amplitude and phase of polarimetric radar backscatter returns from each layer, and interactions at the air-surface interface are addressed using the complex amplitude Fresnel transmission coefficients for a lossy dielectric. The model is shown to be in good agreement with NASA/JPL AIRSAR polarimetric SAR data obtained over Death Valley. Anomalous HH-VV phase differences and HH/VV amplitude ratios are consistent with surface scattering from a salt pan, consisting of salt mixed with a highly saline brine solution to form the surface dielectric material. 1. INTRODUCTION The motivation behind the work presented in this paper is to better understand polarimetric scattering from non-vegetated surfaces on Earth and then Mars. In an earlier paper [1], we developed a model for surface-subsurface scattering and showed how the two were independent of each other. Intriguing and unique HH-VV phase signatures that possibly originate from buried interfaces were recently identified in Lasne et al [2]. Is there information in the HH-VV phase difference in areas where we expect subsurface scattering? The Pyla dunes results from Phillippe Paillou’s group suggest this. In this paper, the intent is to further our understanding of these phenomena through modeling of phase signatures from surface or subsurface lossy dielectrics, in particular those of saline soils. 2. SCATTERING MODEL As shown in Figure 1, a rough interface is buried beneath a low-loss dielectric layer at a shallow depth z (few m’s). Surface and subsurface scattering terms arrive back at the radar simultaneously from locations Q and P (not Q and O as in [2]). In what follows we will ignore scattering in the dielectric layer (incl. volume). Equation (1) below represents the scattering model from the 2 layers. M is the measured scattering matrix. The 1st term on the right-hand side is the surface return (from position P). The 2nd term on the right is the subsurface return (from position Q). The β-terms represent attenuation due to propagation through air-dielectric interface and the dielectric medium

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Figure 1: Illustration of the geometry of scattering from 2 layers. 2. OBSERVATIONS The AIRSAR images of Death Valley in Figure 2 exhibit unusual phase signatures, similar to those observed at the Pyla Dunes site. Some very large phase signatures are observed in the data, up to 180 degrees, while the valley floor generally has phase differences significantly different from zero. In [1] we showed that the presence of azimuth ambiguities in the data can explain some of the larger phase difference values observed, particularly at C-Band. This is illustrated in Figure 3. For odd-numbered azimuth ambiguities, the approach to acquiring quad-pol data used by most polarimetric SAR systems causes the HH and VV phase to be offset by 180 degrees. Data acquisition involves collecting HH, HV and then VH, VV returns from separate, interleaved pulses, then resampling one pair of data samples to lie on top of the other. The resampling causes the odd-numbered ambiguities in the VV and VH channels to be offset by +/- π. This is visible in the corner reflector signature in Figure 3, and in the detail shown from the Death Valley data at C-Band. The presence of azimuth ambiguities cannot explain all of the unusual phase signatures visible in Figures 2 and 4, however, as recent analysis of SIR-C data has shown. In addition, similar phase difference values appear in AIRSAR data obtained over other sites, as seen in the example from an area with saline soils in Kerang, Australia in Figure 5.

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Figure 2: HH-VV Phase Differences from AIRSAR data of the Death Valley floor: From left to right – C-, L-, and P-Band.

Figure 3: Manifestation of odd-numbered azimuth ambiguities in HH-VV Phase Differences. Corner reflector signature from Rosamond Dry lake Bed (left); detail from Figure 1 in Center showing offset ambiguity signatures. The azimuth offset of ambiguities is predictable based on the formula given to the right of the figure, evaluated for C-, L- and P-Band in the table at bottom right.

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4. INTERPRETATION The question we are trying to answer is: are the unusual phase signatures seen in the Death Valley data due to surface or subsurface features? Analyzing each of the terms in our model for combined surface and subsurface scattering, we find that significant phase differences between HH and VV are possible for:

(1) Surface scatter using the Small Perturbation Model (SPM) [3]

(2) Surface scatter using the Kirchhoff model [4] (3) 2-way transmission through the air-dielectric

interface, modeled using the Fresnel transmission coefficients

In each case, we find that the HH-VV phase difference is only significant for relatively large incidence angles (θi > 40 degrees), and when the imaginary part of the dielectric constant is significant. This is illustrated in Figure 6. The Kischhoff model is essentially a facet model, that uses the Fresnel reflection coefficients to determine the phase and amplitude ratios between the H and V polarizations. It forms the basis of the IEM model and, in particular, produces the relative phase behavior we would expect from IEM. Our model also predicts that there is little or no contribution to the HH-VV phase difference from the following mechanisms:

(4) Propagation through the dielectric medium (5) Subsurface scatter using either SPM or the

Kirchhoff model The reason that the subsurface contribution to the HH-VV phase difference turns out to be minimal, is because of the shallow angle of incidence due to refraction – neither the SPM or Kirchhoff scattering models yield significant phase differences at small incidence angles. A possible exception to this could occur when the subsurface scattering plane is tilted, changing the effective angle of incidence – a possible explanation for the Pyla Dunes result. Analyzing the Death Valley data, we find that the high HH-VV phase differences for the salt pan (Fig. 4) are best explained by Kirchhoff scattering at C-Band and SPM at P-Band. The P-Band phase values are also consistent with 2-way transmission through the air-dielectric interface, but further examination of the HH/VV amplitude ratio confirms that surface

scattering using SPM is the better fit to the data. The Kerang phase difference results are also consistent with Kirchoff scattering, but the HH/VV amplitude ratios are not. [The HH/VV amplitude ratios for Death Valley and Kerang are not shown here to keep the paper concise, but can be found in the presentation slides.] 5. SUMMARY AND NEXT STEPS • Surface scattering alone explains some of the

Death Valley results - though some are due to azimuth ambiguities and others remain unaccounted for.

• Need to invoke Kirchhoff scattering for C-Band, SPM for L- and P-Band.

• Expect to resolve remaining issues in field studies in Spring ’07.

• Verify dielectric constant values used in model • Kerang, Australia results not explained by this

model (HH/VV amplitude ratio is too high @ -2 dB) - possible multiple scattering effects, e.g. from vegetation?

• For Pyla Dunes data, scattering off inclined subsurface layers could give rise to significant HH-VV phase difference (because of large incidence angle).

Acknowledgments Part of the research described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. References [1] The 2-layer scattering problem, Freeman, A. and Campbell, B. C., IGARSS 2006 [2] Y. Lasne et al, A Phase Signature for Detecting Wet Subsurface Structures Using Polarimetric L-Band SAR, IEEE TGRS, VOL. 42, NO. 8, AUG. 2004. [3] Guissard, A. , Phase Calibration of Polarimetric Radars from Slightly Rough Surfaces, IEEE TGRS, Vol. 32, No. 3, May 1994 [4] Microwave Remote Sensing Vol II, Ulaby, Fung and Moore, publ. Addison-Wesley, 1982, p943

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Figure 4: P-band and C-Band HH, HV and HH-VV phase signatures extracted from a transect across the salt pan on the floor of Death Valley

Figure 5: AIRSAR L-Band HH-VV Phase difference signatures for the Kerang, Australia test site

Figure 6: Modeled HH-VV phase differences as a function of incidence angle for Kirchhoff surface scattering for a variety of dielectric constants (left); Modeled HH-VV phase differences as a function of incidence angle due to Fresnel reflection, SPM, and 2-way transmission through the air-surface interface, for a dielectric constant of ε = 3+ 8i.