IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 12, NO. 1, JANUARY 2015 73

Application of m-χ Decomposition Techniqueon Mini-SAR Data to Understand Crater

and Ejecta MorphologySaumitra Mukherjee and Priyadarshini Singh

Abstract—Miniature Synthetic Aperture Radar (Mini-SAR)data conveniently reveals the unique morphological characteris-tics associated with crater ejecta blankets. Various surface andsubsurface features in and around shadowed polar regions canbe inferred using this data to explain the newly formed topog-raphy after impact events. A group of three craters lying northof Cabeus. A crater have unique ejecta morphology when m-χdecomposition technique is applied on mini-SAR data. The volumescattering observed for the region describes the relative slope ofthe terrain around and within crater walls. Alternately, Wapowskicrater, which lies at the southern rim of Scott crater, has a differentejecta morphology indicative of it being relatively young. The highcircular polarization ratio (CPR) calculated inside and outsideWapowski crater rim suggests that the presence of water ice withinthe shadowed portion of the crater is highly unlikely. The highCPR therefore is obtained due to the fresh blocky proximal ejectablanket formed post impact. Volume scattering in m-χ decom-position image also corresponds to the region having high CPR.m-χ decomposition technique also shows that the proximal ejectablanket is asymmetrically distributed around the crater rim. Thistechnique therefore helps to study the process of impact crateringand the features generated thereafter.

Index Terms—Circular polarization ratio (CPR), ejecta, m-χdecomposition, Miniature Synthetic Aperture Radar (Mini-SAR),Wapowski crater.

I. INTRODUCTION

M ICROWAVE sensors have been used to observe manysurface and subsurface features along varying terrains

otherwise not visible from simple optical data [1]. The Minia-ture Synthetic Aperture Radar (Mini-SAR), an active imagingradar onboard CHANDRAYAAN-1 mission, conveniently re-veals various crater features in completely or partially shad-owed regions of the lunar poles. This microwave data is used toinfer morphological details present on the shadowed lunar sur-face as well as underneath the regolith even in the illuminatedregions of the lunar surface [1]–[3].

Distinct morphological features such as extent and symmetryof proximal ejecta blanket, crater morphology, etc. found withinand around crater rims can be viewed using mini-SAR data

Manuscript received April 20, 2014; revised May 8, 2014; accepted May 9,2014. This research work has been funded by Indian Space Research Organiza-tion, Department of Space, Govt. of India.

The authors are with the School of Environmental Sciences, JawaharlalNehru University, New Delhi 110 067, India (e-mail: saumitramukherjee3@gmail.com; saumitra@mail.jnu.ac.in; ps.sesjnu@gmail.com).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LGRS.2014.2326420

[1]. Parameters such as circular polarization ratio (CPR) anddegree of polarization (m) derived from Mini-SAR data signifyvarying degrees of surface roughness as well as scatteringproperties linked to presence of planetary ice in permanentlyshadowed regions of polar craters [3]–[5]. The CPR gives theratio of the same sense backscatter power received as emittedover opposite sense backscatter power received as emitted [6].High CPR values (> 1) are obtained either due to highlyrough surfaces or from volumetric water-ice reflections fromice crystals mixed within the regolith [7]–[9]. Also, favorableconditions for predicting the presence of water ice are when theCPR values are high (> 1) within the crater rim in the shadowedparts and low (< 1) outside the rim which is illuminatedby the sun [9]. Further, if the regions inside the shadowedcraters show low values for degree of polarization (m) andrelative LH-LV phase (δ), then water ice crystals might existmixed with the rocky debris within the lunar regolith [8]–[11].

To further understand the degree of surface roughness, m-χdecomposition images with false color composite showing“blue” for surface scattering, “red” for double bounce scatteringand “green” for volume/diffuse scattering are made [12]–[15].The images obtained are subsequently analyzed along withCPR maps and optical images to demarcate areas having highsurface roughness. The signatures obtained are then studiedto infer characteristics of geological features present over theshadowed polar surface within and around the craters.

II. STUDY AREA AND DATA SETS

Two craters having shadowed interiors have been selected tostudy and compare their ejecta blanket morphology, both lyingin the south polar region. The first area is a group of threeimpact craters centered along 81◦28′54′′ S and 43◦16′39′′ Wlying North of Cabeus A crater [Fig. 1(a)]. This group of cratershas shadowed interiors with two smaller craters lying side byside at the northeastern rim of the largest of the three craters.The study area is unique as it is difficult to view the boundariesof the individual craters in the group when viewed on opticalWide Angle Camera (WAC) image from Lunar ReconnaissanceOrbiter Camera (LROC).

This group of craters is compared with another region cen-tered on Wapowski crater. Wapowski crater is a small impactcrater located at the southern rim of Scott crater. It is centered atapproximately 83◦3′11′′ S and 53◦45′17′′ E and has a diameterof around 11.6 km [Fig. 1(b)].

The Mini-SAR data strips each having four bands weredownloaded from NASA Planetary Data system (PDS) node.

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74 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 12, NO. 1, JANUARY 2015

Fig. 1. (a) Study area 1—Crater group lying north of Cabeus A crater.(b) Study area 2—Wapowski crater region.

The S-band mini-SAR radar data has a resolution of150 m/pixel [11]. The relevant data strips were projected andmosaicked using ISIS software. Each pixel in an image stripconsists of 16 bytes data in four channels of 4 bytes each as|LH|2, |LV |2, Real (LH LV ∗), and Imaginary (LH LV ∗).The first two channels represent the intensity images of the“horizontal” and “vertical” receive, respectively. The last twochannels represent the real and imaginary components, respec-tively of the complex value for the cross power intensity imagebetween “horizontal” and “vertical” receive [2]. This data wasthen used for deriving Stokes vectors.

III. METHODOLOGY

Mini-SAR data has a phase shift of 45◦ in the anticlockwisedirection which exaggerates the number of pixels showingvolume backscattering [1]. Therefore, phase calibration wasdone for Band 3 and Band 4 using the following band mathequations on ENVI software:

Re(LH LV ∗)calib =Re(LH LV ∗) cos 45◦

− lm(LH LV ∗) sin 45◦ (1)

lm(LH LV ∗)calib =Re(LH LV ∗) sin 45◦

+ lm(LH LV ∗) cos 45◦. (2)

Stokes Parameters (S0, S1, S2, S3) were calculated usingBands 1 and 2 and phase calibrated Bands 3 and 4 for eachdata strip using the equations in (3) as described in [6]

S =

⎡⎢⎢⎢⎣S0 =

⟨|ELH |2 + |ELV |2

⟩S1 =

⟨|ELH |2 − |ELV |2

⟩S2 = 2�e 〈ELH .E∗

LV 〉S3 = −2�m 〈ELH .E∗

LV 〉

⎤⎥⎥⎥⎦ (3)

where ELH and ELV are the electric fields for the horizontaland vertical linear polarizations received, respectively, and theaverages are time or spatial averages and ∗ represents theconjugate of the complex number.

Reference [2] equations were used to calculate the degree ofpolarization (m) and CPR. References [12] and [13] were usedto calculate the degree of circularity (χ) and m-χ scattering

Fig. 2. WAC image of study area 1. White boundary marks the region of theejecta melt better visible on m-χ decomposition in Fig. 3.

contributions for each pixel on ENVI software. The equationsused are as follows:

m =

√{(S1)2 + (S2)2 + (S3)2}

S0(4)

CPR =(S0 − S3)

(S0 + S3)(5)

Sin 2χ =−S3

(m∗S0)(6)

B =

√{(S0)∗m∗ [1− sin(2χ)]}

2(7)

G =√{(S0)∗(1−m)} (8)

R =

√{(S0)∗m∗ [1 + sin(2χ)]}

2. (9)

Here, blue (B) in (7) indicates single-bounce (Bragg) backscat-tering, green (G) in (8) represents the randomly polarizedconstituent or volume scattering and red (R) in (9) correspondsto double-bounce scattering.

The images obtained along with optical data (Wide AngleCamera with 100 m/pixel resolution from LROC) and LROCWAC color-shaded relief was used to study the surface featuresin and around the identified craters within the South PolarRegion of the moon.

IV. RESULTS AND DISCUSSION

A. Study Area 1

In this region, the individual crater boundaries are not visibleon optical images (Fig. 2). After applying m-χ decompositiontechnique however, it becomes easier to view the individualcrater boundaries (Fig. 3).

Fig. 3 shows that the ejecta from the smaller of the threecraters has draped down along the northern outer crater wall.The draping of the ejecta is such that it indicates that the outercrater wall of this region does not have a steep slope. Furtherwest of the crater group, the ejecta blanket again shows highervolume scattering on the outer wall of the largest of the threecraters. This draping of the ejecta indicates that the steepness ofthe slope of the crater wall in this region is comparatively high.

It is also observed that the m-χ decomposition image showshow the ejecta melt has draped onto another smaller crater lyingnorth of the group of craters in the study region (Fig. 4—region

MUKHERJEE AND SINGH: APPLICATION OF m-χ DECOMPOSITION TECHNIQUE ON MINI-SAR DATA 75

Fig. 3. m-χ decomposition of the study area 1. White boundary marks theejecta blanket sloping down the outer walls of craters. This ejecta blanket isfaintly visible on wide angle camera optical image (Fig. 2).

Fig. 4. m-χ decomposition image of study area 1. Image on the right is azoomed in view of the region with white boundary showing where the ejectablanket has draped halfway onto an adjacent crater. Yellow box zoomed in viewbelow shows the degraded rim.

marked with white boundary). This helps to estimate the rela-tive time of the impact events forming the craters. The largestof the three craters has a degraded crater rim as seen on them-χ decomposition image. Smaller impacts over the rim havecaused the debris to slide down inside the crater (Fig. 4—regionmarked with yellow boundary). This phenomenon suggests thatthe largest crater of the three is the oldest of the group.

B. Study Area 2—Wapowski Crater Region

1) Circular Polarization Ratio: CPR values > 1 suggest thepresence of highly rough surfaces [6], [7]. CPR values of pixelsaround and inside Wapowski rim are relatively high (∼0.1–2)suggesting the presence of rough surfaces possibly due to fea-tures such as blocky lava flow or fresh blocky ejecta [Fig. 6(a)].The CPR values were found to be uniformly high within andoutside the crater rim [Fig. 5]. Therefore, this suggests thatthe high CPR values are due to presence of rough surfacesprimarily [6].

Alternatively, since the range of CPR values inside and out-side the crater rim is relatively high and quantitatively similar

Fig. 5. Plot of CPR versus relative number of pixels for region inside theWapowski crater (red curve) and outside the crater (blue curve).

both in the shadowed as well as the region illuminated by thesun, the presence of water ice within the shadowed part of thecrater is highly unlikely. The high CPR values can thereforebe attributed to surface roughness caused by ejecta debris [6].Also, since the CPR values are quantitatively similar withinand outside the Wapowski rim, this crater can be termed as arelatively “fresh” crater [6]. Reference [6] includes a similarstudy of a Copernican age fresh crater, Main L (14 km diameter,81.2◦ N, 22.7◦ E), displaying high CPR both inside and outsidethe rim. The histogram plot of the CPR was reported to havebeen caused by the “enhanced degrees of wavelength-scalesurface roughness” associated with blocky ejecta blanket [6].Also, the CPR distributions of such type of craters have a highlypeaked (high kurtosis) also observed for the CPR histogram plotof Wapowski crater.

Alternatively, another small polar anomalous crater withinthe floor of the large crater Rozhdestvensky (85.2 N, 155.4 W)has a different and distinct distribution of the CPR histogram[6]. It has a low kurtosis (relatively flattened distribution) andhigh CPR values inside the rim (region of permanent shadow)but low CPR outside the rim. The elevated CPR, therefore, insuch cases can be associated with the presence of water ice inthe permanently shadowed crater interior [6].

2) m-χ Decomposition: m-χ decomposition images weremade to show the presence of mainly diffuse [calculated from(6)] and double bounce [calculated from (5)] scattering contri-butions at the region having rough surfaces within and aroundthe crater rim [Fig. 6(b)]. m-χ decomposition images also showthat the high CPR values correspond to the diffuse backscat-tering regions showing the extent and asymmetric nature of therough proximal ejecta blanket.

The asymmetric nature of the ejecta blanket aroundWapowski rim can be further understood using the LROC colorshaded relief overlain on WAC image of the region [Fig. 7(b)].The elevation on the northern side of Wapowski rim is loweras compared to the remaining sides. The depression is causedsince the northern outer wall of Wapowski overlaps with thewall of the adjacent Scott crater. Therefore, the ejecta on impactseems to have spread out and draped more toward the inner wallof Scott crater due to the steep slope of the inner wall.

High CPR values as well as diffuse scattering can thereforebe seen to a larger extent in this region. Alternately, the ejectablanket on the remaining edges of Wapowski rim has spreadless owing to the higher relative elevation compared to thenorthern side. Therefore, the extent of volume scattering pixelsseen on m-χ decomposition image in these regions is also less.

76 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 12, NO. 1, JANUARY 2015

Fig. 6. (a) CPR map of Wapowski crater region derived from mini-SAR data.(b) m-χ decomposition of Wapowski crater region.

Fig. 7. (a) WAC image of Wapowski crater region. (b) LROC WAC color-shaded relief of Wapowski crater region. Turquoise color depicts the region ofdepression; green and yellow colors depict relatively elevated terrain.

Fig. 8. WAC image of Wapowski region. Chain of secondary craters markedwith black boundary zoomed in on the right.

3) Presence of Secondary Crater Chain: Optical images ofthe region from Wide angle camera (WAC) show the presenceof a chain of secondary craters possibly formed by the impactof smaller pieces of debris released after the larger impact(Fig. 8). m-χ decomposition images further substantiate thepresence of the chain of secondary craters. This secondarycrater chain shows volume scattering on m- χ decompositionimage [Fig. 6(b)].

V. CONCLUSION

The crater ejecta blanket can be conveniently seen on m-χdecomposition images derived from Stokes vectors and degreeof polarization using mini-SAR data.

Study Area 1 lying north of Cabeus A crater has ejectablanket draped on the northern outer wall of the craters. The twosmaller crater impacts are relatively younger as compared to thelargest of the three impact craters since the ejecta blanket ofthe largest crater cannot be seen on m-χ decomposition image.

Also, the inner rim of the largest crater has been degradedfrom all sides due to smaller impacts around its rim. The ejectablanket is not spread out as much as compared to the ejectablanket of Wapowski crater.

The possibility for the presence of water ice within theshadowed part of Wapowski crater is highly unlikely. High CPRvalues ranging from ∼0.1–2 were found within and outsidethe crater rim. Therefore, the reason behind the high CPRvalues can be attributed to the rough and rugged inner wallsof the crater. The extended blocky ejecta blanket around the rimformed post impact is inferred to be the cause of high CPR valuecalculated outside the crater rim. Also, since the CPR values aresimilar inside and outside the crater rim, Wapowski crater canbe termed as a relatively fresh impact crater.

WAC images and m-χ decomposition shows the presenceof a chain of secondary craters lying further east from theWapowski rim. These have possibly formed from the impactof the debris released after the primary impact.

ACKNOWLEDGMENT

The authors are thankful to Dr. A. Das and Mr. S. Saranat Space Application Centre, Ahmedabad, India for providingCHANDRAYAAN-1 Mini-SAR data.

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