月球阿波罗盆地叶状陡坎雷达散射特性与应力场研究

彭嫚; 胡文敏; 李熙健; 王敏娜; 邸凯昌

doi:10.12000/JR25189

月球阿波罗盆地叶状陡坎雷达散射特性与应力场研究

DOI: 10.12000/JR25189 CSTR: 32380.14.JR25189

彭嫚¹,
胡文敏²,
李熙健^{1, 3},
王敏娜⁴,
邸凯昌^1, ,

1.
中国科学院空天信息创新研究院遥感与数字地球全国重点实验室, 北京 100101
2.
中国矿业大学矿山互联网应用技术国家地方联合工程实验室徐州 221116
3.
国科学院大学北京 100049
4.
中国矿业大学环境与测绘学院徐州 221116

基金项目: 国家重点研发计划(2022YFF0503100)，福建省自然科学基金面上项目(2025J01859)，行星科学与超算联合实验室开放课题基金(CDCSZX-QT-2026-01)

详细信息

作者简介:
彭　嫚，副研究员，主要研究方向为行星摄影测量与遥感

胡文敏，副研究员，主要研究方向为摄影测量与遥感、高分影像处理及应用

李熙健，博士生，主要研究方向为行星遥感与制图

王敏娜，硕士生，主要研究方向为行星科学、构造模拟

邸凯昌，研究员，主要研究方向为行星摄影测量、行星遥感、行星科学和视觉导航定位

通讯作者:
邸凯昌 dikc@aircas.ac.cn

责任主编：徐丰 Corresponding Editor: XU Feng

中图分类号: P691
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出版历程
- 收稿日期: 2025-09-26

Radar Scattering Characteristics and Stress Field of Lobate Scarps in the Apollo Basin on the Moon

PENG Man¹,
HU Wenmin²,
LI Xijian^{1, 3},
WANG Minna⁴,
DI Kaichang^{1
, ,}

1.
State Key Laboratory of Remote Sensing and Digital Earth, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China
2.
The National Joint Engineering Laboratory of Internet Applied Technology of Mines, China University of Mining and Technology, Xuzhou, 221116, China
3.
University of Chinese Academy of Sciences, Beijing 100049, China
4.
School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China

Funds: National Key Research and Development Program of China (No. 2022YFF0503100), The Fujian Provincial Natural Science Foundation of China (2025J01859), The Opening Project of Joint Laboratory for Planetary Science and Supercomputing, funded by Chengdu University of Technology and the National Supercomputing Center in Chengdu(CDCSZX-QT-2026-01)

More Information

Corresponding author: DI Kaichang, dikc@aircas.ac.cn

摘要

摘要: 月球叶状陡坎是月表浅层逆冲断层活动形成的小型线性构造，其空间分布与应力特征为揭示月球晚期构造演化提供了关键线索。目前，叶状陡坎的应力特征与雷达散射响应间的关联机制尚不明确。该研究以阿波罗盆地叶状陡坎为研究对象，利用Mini-RF影像提取散射特性参数；然后基于高分辨率数字高程模型采用库仑软件反演区域应力场分布特征；在此基础上，从统计关联角度分析雷达散射特征与应力之间的对应关系，揭示其构造活动性与表面物质响应的关联机制。主要结论如下：(1) 断层附近应变显著高于外围，最大剪应变集中于断层倾向方向，体应变显示断层上盘体积膨胀，两端及滑动面中心呈现体积收缩。(2) 陡坎面与上盘区域在圆极化比与部分极化分解参数上表现出更强的散射响应，表明这些区域可能存在更高的破碎度、块石暴露或结构复杂性，然而散射差异同时受到表面粗糙度、入射几何条件和后期改造过程的综合影响。(3)基于多元线性回归和随机森林算法进行了散射参数与应力场的回归分析，说明散射特征与应力之间的关联更可能是受地形条件、表面粗糙度及局部构造等共同作用的非线性关系。总体而言，该研究建立了一个面向阿波罗盆地叶状陡坎的雷达—地形联合探索性分析框架，用于评估散射特征与应力指标之间是否存在可量化的统计对应关系，并为相似地质背景下的浅层构造活动研究提供参考。
- SAR散射特性 /
- 叶状陡坎 /
- 应力场关联 /
- 形变机理 /
- 阿波罗盆地 /
- 雷达反演
Abstract: Lunar lobate scarps are small-scale linear structures formed by shallow thrust fault activity on the lunar surface, and their spatial distribution and stress characteristics provide essential clues for understanding the late-stage tectonic evolution of the Moon. At present, the correlation mechanism between the stress characteristics of lobate scarps and their radar scattering response remains unclear. In this study, lobate scarps in the Apollo Basin are considered as the research focus, and scattering characteristic parameters are extracted from Mini-RF images. Subsequently, the Coulomb software is used to invert the distribution characteristics of the regional stress field based on high-resolution digital elevation models. On this basis, the correspondence between radar scattering characteristics and stress is analyzed using statistical correlation methods, revealing the underlying relationship between tectonic activity and surface material response. The main conclusions are as follows. (1) The strain near the fault is markedly higher than that in the surrounding areas, with the maximum shear strain concentrated in the fault dip direction. Volumetric strain indicates volume expansion within the fault hanging wall, whereas volume contraction is observed at both ends and at the center of the sliding surface. (2) The scarp face and hanging wall regions exhibit stronger scattering responses in terms of the circular polarization ratio and partial polarization decomposition parameters, suggesting higher degrees of fragmentation, boulder exposure, or structural complexity in these areas. However, the scattering differences are also influenced by the combined effects of surface roughness, incidence geometry, and subsequent modification processes. (3) The regression analysis of scattering parameters and stress fields, based on multiple linear regression and random forest algorithms, indicates that the correlation between scattering characteristics and stress is likely nonlinear, governed by the combined effects of topographic conditions, surface roughness, and local structures. Overall, this study develops an exploratory radar-topography joint analysis framework for lobate scarps in the Apollo Basin to evaluate whether a quantifiable statistical correspondence exists between scattering features and stress indicators, as well as to provide supplementary evidence for studies of shallow tectonic activity under similar geological settings.
- SAR backscatter /
- lobate scarp /
- stress–scattering association /
- deformation mechanisms /
- Apollo Basin /
- radar inversion

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图 1 阿波罗盆地西北叶状陡坎的分布^[15]

Figure 1. The distribution of lobate scarps at western rim of the Apollo basin ^[15]

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图 2 叶状陡坎逆冲断层位错模型示意图^[5]

Figure 2. Schematic diagram of the dislocation model for lobate scarp thrust fault^[5]

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图 3 CPR图叠加叶状陡坎(编号与表1一致)

Figure 3. CPR overlaid with lobate scarps (numbered consistently with Table 1)

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图 4 叶状陡坎的陡坎面

Figure 4. Scarp face of lobate scarps

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图 5 叶状陡坎DEM结果和LROC NAC图像叠加^[15]

Figure 5. Overlay of DEMs and LROC NAC images^[15]

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图 6 叶状陡坎库仑应力分布图.

Figure 6. Coulomb Stress distribution map of lobate scarps. .

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图 7 撞击坑壁9#叶状陡坎库仑应力分布图

Figure 7. Coulomb stress distribution map of lobate scarp #9 on the crater wall

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图 8 断层附近水平应变场与垂直应变场(LS07)

Figure 8. Horizontal and vertical strain fields near the fault (LS07)

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图 9 断层附近的应变场(LS07)

Figure 9. Strain field near the fault (LS07)

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图 10 K-means聚类算法应力分层结果

Figure 10. Stress layering results based on K-means clustering algorithm

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图 11 基于 ($\Delta $CFS=0) 的物理阈值分区结果

Figure 11. Partitioning results based on the physical threshold of $\Delta $CFS = 0

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图 12 不同E参数下的库仑应力分布

Figure 12. Coulomb stress distribution under different E parameters

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图 13 不同摩擦系数条件下的库仑应力分布

Figure 13. Coulomb stress distribution under different $\mu' $ parameters

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图 14 不同泊松比参数对应的库仑应力分布

Figure 14. Coulomb stress distribution under different v parameters

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表 1 研究区域叶状陡坎面散射特性的统计结果

Table 1. Statistical results of surface scattering characteristics of lobate scarps in the study area

陡坎 ID	S₀均值	CPR均值	m均值	χ均值
1	0.069	0.479	0.355	26.561
2	0.074	0.490	0.436	40.267
3	0.081	0.451	0.526	41.073
4	0.090	0.546	0.448	39.420
5	0.089	0.427	0.549	37.492
6	0.069	0.480	0.467	37.789
7	0.074	0.541	0.451	37.452
8	0.060	0.612	0.449	36.708
9	0.191	0.389	0.557	38.395
10	0.058	0.867	0.413	33.714
11	0.060	0.718	0.400	30.893
12	0.071	0.656	0.439	33.451
13	0.073	0.637	0.394	28.003
14	0.094	0.879	0.386	17.771
均值	0.083	0.583	0.448	34.213

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表 2 研究区域叶状陡坎上盘和下盘散射特性的统计结果

Table 2. Statistical results of hanging wall and foot wall scattering characteristics of lobate scarps in the study area

陡坎 ID	部位	S₀均值	CPR均值	m均值	χ均值
1	下盘	0.077	0.506	0.489	38.918
2	上盘	0.057	0.469	0.342	37.813
2	下盘	0.075	0.439	0.528	44.549
3	上盘	0.065	0.564	0.452	36.077
3	下盘	0.075	0.432	0.503	42.140
4	上盘	0.074	0.512	0.469	39.509
4	下盘	0.106	0.392	0.554	40.286
5	上盘	0.102	0.370	0.543	38.980
5	下盘	0.126	0.502	0.544	43.609
6	上盘	0.087	0.449	0.518	37.791
6	下盘	0.089	0.379	0.572	39.166
7	上盘	0.069	0.534	0.459	39.438
7	下盘	0.079	0.186	0.533	38.118
8	上盘	0.064	0.593	0.425	34.996
8	下盘	0.175	0.438	0.550	32.211
9	上盘	0.094	0.398	0.544	38.526
9	下盘	0.116	0.406	0.559	36.884
10	上盘	0.052	0.758	0.369	30.306
10	下盘	0.071	0.579	0.427	35.291
11	上盘	0.065	0.732	0.377	27.730
11	下盘	0.071	0.671	0.410	31.471
12	上盘	0.086	0.571	0.449	34.133
12	下盘	0.080	0.618	0.430	33.592
13	上盘	0.089	0.594	0.439	34.137
13	下盘	0.095	0.644	0.405	32.008
14	上盘	0.065	0.887	0.348	17.569
14	下盘	0.064	0.910	0.327	18.737
均值	上盘	0.073	0.572	0.441	34.385
均值	下盘	0.090	0.507	0.488	36.212

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表 3 研究区域叶状陡坎形态参数与库仑应力统计结果

Table 3. Statistical results of morphological parameters and Coulomb stress of lobate scarps in the study area

陡坎 ID	经度(°)	纬度(°)	长度(m)	深度(m)	起伏度(m)	库仑应力均值(MPa)
1	–160.877	–34.090	2266.73	804.68	13.33	0.383
2	–160.872	–34.094	685.12	222.56	7.69	1.308
3	–160.951	–34.142	866.58	296.90	13.57	0.755
4	–160.970	–34.204	5677.90	1892.46	18.81	0.270
5	–160.999	–34.298	563.50	183.68	7.56	–0.100
6	–161.007	–34.321	1970.36	645.48	7.98	–0.106
7	–161.013	–34.341	1300.02	440.93	8.41	0.073
8	–161.083	–34.395	672.92	219.58	7.64	0.001
9	–161.089	–34.659	1886.88	613.50	78.77	–0.241
10	–161.350	–34.789	652.72	220.84	13.86	0.093
11	–161.380	–34.830	1184.92	399.35	3.42	0.401
12	–161.425	–34.853	1715.37	596.13	28.13	0.570
13	–161.466	–34.890	1440.30	489.98	35.52	1.120
14	–161.622	–35.035	954.18	303.57	7.38	–0.202

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表 4 对象内验证下模型性能对比

Table 4. Within-object validation model performance comparison

模型	多元线性回归	随机森林
MAE	0.231	0.136
RMSE	0.410	0.256
R²	0.569	0.832
Spearman ρ	0.809	0.916

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表 5 5折GroupKFold交叉验证下模型泛化能力对比

Table 5. Model generalization performance comparison under 5-Fold groupkfold cross-validation

模型	多元线性回归	随机森林
各折测试集 R²范围	–0.715～–0.084	–0.776 ～–0.114
平均折间指标 (MAE/RMSE/R²)	0.472/0.623/–0.427	0.486/0.635/–0.491
OOF总体指标 (MAE/RMSE/R²)	0.464/0.665/0.132	0.478/0.674/0.165

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表 6 Leave-One-Group-Out交叉验证下模型泛化能力对比

Table 6. Model generalization performance comparison under leave-one-group-out cross-validation

模型	多元线性回归	随机森林
MAE	0.467	0.474
RMSE	0.658	0.661
R²	–0.109	–0.120

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表 7 剔除#9后对象内验证下模型性能对比

Table 7. Within-object validation model performance comparison after excluding #9

模型	多元线性回归	随机森林
MAE	0.235	0.139
RMSE	0.415	0.260
R²	0.568	0.831

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表 9 剔除#9后Leave-One-Group-Out交叉验证下模型泛化能力对比

Table 9. Model generalization performance comparison under leave-one-group-out cross-validation after excluding #9

模型	多元线性回归	随机森林
MAE	0.475	0.481
RMSE	0.666	0.668
R²	-0.112	-0.117

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表 8 剔除#9后5折GroupKFold交叉验证下模型泛化能力对比

Table 8. Model generalization performance comparison under 5-Fold groupkfold cross-validation after excluding #9

模型	多元线性回归	随机森林
平均折间指标 (MAE/RMSE/R²)	0.496/0.642/-0.503	0.510/0.653/-0.567
OOF总体指标 (MAE/RMSE/R²)	0.477/0.676/-0.143	0.491/0.685/-0.175

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参考文献(31)

[1]	WATTERS T R, ROBINSON M S, COLLINS G C, et al. Global thrust faulting on the Moon and the influence of tidal stresses[J]. Geology, 2015, 43(10): 851–854. doi: 10.1130/G37120.1.
[2]	BINDER A B and GUNGA H C. Young thrust-fault scarps in the highlands: Evidence for an initially totally molten moon[J]. Icarus, 1985, 63(3): 421–441. doi: 10.1016/0019-1035(85)90055-7.
[3]	BANKS M E, WATTERS T R, ROBINSON M S, et al. Morphometric analysis of small-scale lobate scarps on the Moon using data from the Lunar Reconnaissance Orbiter[J]. Journal of Geophysical Research: Planets, 2012, 117(E12): E00H11. doi: 10.1029/2011JE003907.
[4]	WILLIAMS N R, WATTERS T R, PRITCHARD M E, et al. Fault dislocation modeled structure of lobate scarps from Lunar Reconnaissance Orbiter Camera digital terrain models[J]. Journal of Geophysical Research: Planets, 2013, 118(2): 224–233. doi: 10.1002/jgre.20051.
[5]	CLARK J D, HURTADO JR J M, HIESINGER H, et al. Investigation of newly discovered lobate scarps: Implications for the tectonic and thermal evolution of the Moon[J]. Icarus, 2017, 298: 78–88. doi: 10.1016/j.icarus.2017.08.017.
[6]	ROGGON L, HETZEL R, HIESINGER H, et al. Length-displacement scaling of thrust faults on the Moon and the formation of uphill-facing scarps[J]. Icarus, 2017, 292: 111–124. doi: 10.1016/j.icarus.2016.12.034.
[7]	KUMAR P S, MOHANTY R, LAKSHMI K J P, et al. The seismically active lobate scarps and coseismic lunar boulder avalanches triggered by 3 January 1975 (M_W 4.1) shallow moonquake[J]. Geophysical Research Letters, 2019, 46(14): 7972–7981. doi: 10.1029/2019GL083580.
[8]	MISHRA A and SENTHIL KUMAR P. Spatial and temporal distribution of lobate scarps in the lunar south polar region: Evidence for latitudinal variation of scarp geometry, kinematics and formation ages, neo-tectonic activity and sources of potential seismic risks at the artemis candidate landing regions[J]. Geophysical Research Letters, 2022, 49(18): e2022GL098505. doi: 10.1029/2022GL098505.
[9]	WILLIAMS J G and BOGGS D H. Tides on the Moon: Theory and determination of dissipation[J]. Journal of Geophysical Research: Planets, 2015, 120(4): 689–724. doi: 10.1002/2014JE004755.
[10]	WATTERS T R, WEBER R C, COLLINS G C, et al. Shallow seismic activity and young thrust faults on the moon[J]. Nature Geoscience, 2019, 12(6): 411–417. doi: 10.1038/s41561-019-0362-2.
[11]	WILLIAMS N R, BELL III J F, WATTERS T R, et al. Evidence for recent and ancient faulting at Mare Frigoris and implications for lunar tectonic evolution[J]. Icarus, 2019, 326: 151–161. doi: 10.1016/j.icarus.2019.03.002.
[12]	FRUEH T, HETZEL R, WATTERS T R, et al. Extensional structures at lunar lobate scarps[J]. Icarus, 2025, 432: 116493. doi: 10.1016/j.icarus.2025.116493.
[13]	SCHULTZ R A. Localization of bedding plane slip and backthrust faults above blind thrust faults: Keys to wrinkle ridge structure[J]. Journal of Geophysical Research: Planets, 2000, 105(E5): 12035–12052. doi: 10.1029/1999JE001212.
[14]	CLARK J D. CLARK J D. Characterization of thrust faults on the moon using fault dynamics and three-dimensional visualizations[D]. [Ph.D. dissertation], University of Texas, 2012.
[15]	LI Xijian, YUE Zongyu, PENG Man, et al. Characterization of lobate scarps at the western rim of the Apollo basin using high-resolution DEMs generated using generative adversarial network (GAN) based approach[J]. Icarus, 2025, 435: 116562. doi: 10.1016/j.icarus.2025.116562.
[16]	OKADA Y. Internal deformation due to shear and tensile faults in a half-space[J]. Bulletin of the Seismological Society of America, 1992, 82(2): 1018–1040. doi: 10.1785/BSSA08200210180.
[17]	李长圣. 基于离散元的褶皱冲断带构造变形定量分析与模拟[D]. [博士论文], 南京大学, 2019. LI Changsheng. Quantitative analysis and simulation of structural deformation in the fold and thrust belt based on discrete element method[D]. [Ph.D. dissertation], Nanjing University, 2019.
[18]	卢菁琛. 基于精细地壳和断层结构的青藏高原东部构造应力演化数值模拟研究[D]. [硕士论文], 中南大学, 2023. doi: 10.27661/d.cnki.gzhnu.2023.003968. LU Jingchen. Numerical simulation of tectonic stress evolution in eastern Tibetan based on a refined model in crust and fault structure[D]. [Master dissertation], Central South University, 2023. doi: 10.27661/d.cnki.gzhnu.2023.003968.
[19]	RANEY R K, CAHILL J T S, PATTERSON G W, et al. The m-chi decomposition of hybrid dual-polarimetric radar data with application to lunar craters[J]. Journal of Geophysical Research: Planets, 2012, 117(E12): E00H21. doi: 10.1029/2011JE003986.
[20]	CAHILL J T S, THOMSON B J, PATTERSON G W, et al. The Miniature Radio Frequency instrument’s (Mini-RF) global observations of Earth’s Moon[J]. Icarus, 2014, 243: 173–190. doi: 10.1016/j.icarus.2014.07.018.
[21]	BELL S W, THOMSON B J, DYAR M D, et al. Dating small fresh lunar craters with Mini-RF radar observations of ejecta blankets[J]. Journal of Geophysical Research: Planets, 2012, 117(E12): E00H30. doi: 10.1029/2011JE004007.
[22]	NYPAVER C A, THOMSON B J, FASSETT C I, et al. Prolonged rock exhumation at the rims of kilometer-scale lunar craters[J]. Journal of Geophysical Research: Planets, 2021, 126(7): e2021JE006897. doi: 10.1029/2021JE006897.
[23]	郭弟均, 刘建忠, HEAD W J, 等. 月球阿波罗盆地区域月壳结构及光谱特征[J]. 深空探测学报, 2018, 5(5): 488–494. doi: 10.15982/j.issn.2095-7777.2018.05.013. GUO Dijun, LIU Jianzhong, HEAD W J, et al. Crustal structure and spectral features of lunar apollo basin region[J]. Journal of Deep Space Exploration, 2018, 5(5): 488–494. doi: 10.15982/j.issn.2095-7777.2018.05.013.
[24]	LIU Yang, WANG Yexin, DI Kaichang, et al. A generative adversarial network for pixel-scale lunar DEM generation from high-resolution monocular imagery and low-resolution DEM[J]. Remote Sensing, 2022, 14(21): 5420. doi: 10.3390/rs14215420.
[25]	MUKHERJEE S and SINGH P. Identification of tectonic deformations on the south polar surface of the moon[J]. Planetary and Space Science, 2015, 112: 46–52. doi: 10.1016/j.pss.2015.04.010.
[26]	TODA S, STEIN R S, SEVILGEN V, et al. Coulomb 3.3 graphic-rich deformation and stress-change software for earthquake, tectonic, and volcano research and teaching—user guide[R]. U.S. Geological Survey Open-File Report 2011–1060, 2011: 1–63.
[27]	KING G C P, STEIN R S, and LIN Jian. Static stress changes and the triggering of earthquakes[J]. Bulletin of the Seismological Society of America, 1994, 84(3): 935–953. doi: 10.1785/BSSA0840030935.
[28]	RICE J R. Fault stress states, pore pressure distributions, and the weakness of the San Andreas fault[J]. International Geophysics, 1992, 51: 475–503. doi: 10.1016/S0074-6142(08)62835-1.
[29]	SHEN Xiang, LIU Bin, and LI Qingquan. Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2017, 125: 125–131. doi: 10.1016/j.isprsjprs.2017.01.007.
[30]	DRAPER N R and SMITH H. Applied Regression Analysis[M] 3rd ed. New York: Wiley, 1998. 473–504.
[31]	WATTERS T R and SCHULTZ R A. The fault geometry of planetary lobate scarps: Listric versus planar[C]. Lunar and Planetary Science XXXIII. Houston, TX, 2002: 1668.