利用最新的GRAIL月球重力数据和LRO地形数据，计算重力/地形导纳及其相关性。结果表明，最新的测月数据能够在球谐系数达到500阶的时候依然保持比较高的相关性，精度得到很大的提高。全月重力/地形导纳在50阶以下（波长大于~220 km），之后迅速增加，维持在110 mgal/km附近。利用Gauss-Newton迭代法计算得到全月弹性平均厚度Te=11.7 km，表明很有可能月球地形在月球早期就已经形成。
In this paper, we consider the free-air gravity model by the GRAIL (Gravity Recovery and Interior Laboratory) mission and the topographic model from the LRO (Lunar Reconnaissance Orbiter) laser altimetry. They showed high correlation up to~500 (0.8) degree. The gravity-topography admittance (the ratio of gravity to topography in spectral domain) was low for degrees below~50 (i.e., wavelength longer than~220 km), but it increased sharply and was kept at constant value of~110 mgal/km. We employed the Gauss-Newton method and simple model to estimate the elastic thickness of the Moon at 11.76 km. This thickness value is not significantly different from those found in the present Earth in spite of the smaller dimension of the Moon. This implies that the significant portion of topographic features on the Moon was formed in the early ages of the Moon, when the heat flow was comparable to that in the present Earth.
[1] Zuber M T, Smith D E, Lemoine F G, et al. The shape and internal structure of the moon from the clementine mission[J]. Science, 1994, 266(5192):1839-1843.
[2] Konopliv A S, Binder A B, Hood L L, et al. Improved gravity field of the moon from lunar prospector[J].Science,1998,281(5382):1476-1480.
[3] Namiki N, Iwata T, Matsumoto K, et al. Farside gravity field of the moon from four-way Doppler measurements of SELENE (Kaguya)[J]. Science, 2009, 323(5916):900-905.
[4] Matsumoto K, Goossens S, Ishihara Y, et al. An improved lunar gravity field model from SELENE and historical tracking data:revealing the farside gravity features[J]. Journal of Geophysical Research, 2010, 115(E6):258-273.
[5] Yan J, Goossens S, Matsumoto K, et al. CEGM02:an improved lunar gravity model using Chang' E-1 orbital tracking data[J]. Planetary and Space Science, 2012, 62(1):1-9.
[6] Araki H, Tazawa S, Noda H, et al. Lunar global shape and polar topography derived from Kaguya-LALT laser altimetry[J]. Science, 2009, 323(5916):897-900.
[7] Ping J, Huang Q, Yan J, et al. Lunar topographic model CLTM-s01 from Chang'E-1 laser altimeter[J]. Science China-physics Mechanics & Astronomy, 2009, 52(7):1105-1114.
[8] Zuber M T, Smith D E, Watkins M M, et al. Gravity field of the moon from the gravity recovery and interior laboratory(GRAIL) mission[J].Science,2013,339(6120):668-671.
[9] Simons M, Solomon S C, Hager B H, et al. Localization of gravity and topography:constraints on the tectonics and mantle dynamics of Venus[J]. Geophysical Journal International, 1997, 131(1):24-44.
[10] Watts A B. Isostasy and flexure of the lithosphere[M]. Cambridge:Cambridge University Press, 2001.
[11] Matsumoto K, Yamada R, Kikuchi F, et al. Internal structure of the moon inferred from Apollo seismic data and selenodetic data from GRAIL and LLR[J]. Geophysical Research Letters, 2015, 42(18):7351-7358.
[12] Lognonne P, Gagnepainbeyneix J, Chenet H, et al. A new seismic model of the moon:implications for structure, thermal evolution and formation of the moon[J]. Earth and Planetary Science Letters, 2003, 211(1):27-44.
[13] 袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京:科学出版社, 1999.
[14] Crosby A, Mckenzie D. Measurements of the elastic thickness under ancient lunar terrain[J]. Icarus, 2005, 173(1):100-107.
[15] Mckenzie D, Fairhead D. Estimates of the effective elastic thickness of the continental lithosphere from Bouguer and free air gravity anomalies[J]. Journal of Geophysical Research, 1997,102(B12):27523-27552.
[16] 黄倩. 基于嫦娥一号和其他探月数据的测月学研究[D]. 上海:中国科学院上海天文台, 2011.
[17] 李斐, 柯宝贵, 王文睿,等. 利用重力地形导纳估计月壳厚度[J]. 地球物理学报, 2009, 52(8):2001-2007.
[18] 钟振, 李斐, 鄢建国,等. 利用重力/地形导纳和岩石圈单一薄层模型的月球物理参数反演[J]. 武汉大学学报(信息科学版), 2014, 39(12):1487-1492.
