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2019年1月3日嫦娥四号着陆器与巡视器玉兔二号成功地于月球背面(远离地球的一侧)软着陆[10]。玉兔二号目前已经正常工作至第八个月昼,搭载的红外成像光谱仪已经获取了大量的月球原位高光谱数据。红外成像光谱仪的相关参数见表1。红外成像光谱仪包括两个通道,短波红外SWIR通道和可见近红外VNIS通道,其中SWIR所探测的区域为VNIS所探测区域的中间偏左侧内部的圆形区域。由于光谱由两个光谱通道观测范围不一致,所以需要对二者进行统一。该研究对VNIS范围内与SWIR观测范围一致部分进行平均,对于原始数据去噪、平滑以及二者的整合等预处理参照参考文献[11]和[12]。由于在小于530 nm的短波范围内光谱的信噪比较低,而在大于2 200 nm的长波范围内受热辐射影响较大,故该研究只采用530~2 200 nm波长范围内的光谱数据。
表 1 嫦娥四号,玉兔二号红外成像光谱仪技术参数
Table 1. Parameters of the CE-4, Yutu-2 visible and near-IR imaging spectrometer (VNIS) and short-wave infrared (SWIR) spectrometer
Parameters VNIS SWIR Wavelength/nm 450-950 900-2 400 Band resolution/nm 2-10 3-12 View field/(°) 8.5×8.5 ф3.58 Numbers of valid pixel ≥256×256 1 Detective distance/m 0.7-1.3 Detective time/min ~2 在嫦娥四号的观测点中,第三个月昼共获得了十个点位的光谱数据(点12~点21)。为了研究嫦娥四号登陆点附近的月壤太空风化情况,选取了两个观测点的光谱数据。通过可见光近红外成像光谱仪的影像以及短波红外的光谱数据研究发现,嫦娥四号登录后的第三月昼的所探测的点15的光谱为岩石光谱(见图1)。尚未风化的岩石表面的SMFe含量为0[7],如果得到其他点的月壤SMFe含量与该点的差值,便可以得到相应光谱对应月壤的SMFe含量。为了得到可以代表SMFe原位赋存状态的光谱,该研究筛选掉了玉兔二号车轮碾压过的月壤光谱以及表面碎石较多或者太阳斜度较大造成表面阴影较为严重的光谱,最终选取点20的光谱(图2)。由于记录的角度信息均为假设被拍摄面为水平面,而点15为岩石的侧上方,故该研究重新估算了点15的几何角度,点15与点20光谱的几何信息见表2。
图 1 嫦娥四号15号观测点影像及其光谱。(a)成像数据(450~945 nm),红色圆圈为短波红外数据探测范围;(b) 红圈范围内光谱
Figure 1. Image and spectra of site 15 of Chang'e-4. (a) Imaging data (450−945 nm), red circle is the scope of the SWIR data; (b) spectra inside the red circle scope
图 2 嫦娥四号20号观测点影像及其光谱。(a)成像数据(450~945 nm),红色圆圈为短波红外数据探测范围;(b) 红圈范围内光谱
Figure 2. Image and spectra of site 20 of Chang'e-4. (a) Imaging data (450−945 nm), red circle is the scope of the SWIR data; (b) spectra inside the red circle scope
表 2 玉兔二号获取的点15与点20光谱的几何信息
Table 2. Data acquisition conditions of Site 15 and Site 20 by Yutu-2
Parameters Point 15 Point 20 Local time 08:32:00 15:35:00 Distance to the Sun/(AU) 0.989 146 37 0.991 539 51 View angle/(°) 17 46.26 Incident angle/(°) 70.5 64.54 View azimuth angle/(°) 143.32 83.03 Incident azimuth angle/(°) 61.48 296.66 Phase angle/(°) 65.48 104.24 -
基于辐射传输理论的二相性反射传输模式的Hapke模型,主要表达被研究物质成分、颗粒大小以及观测几何角度的光学特性等方面的内容[1],其公式如下:
$$\begin{split}{{REFF}} = \;&\frac{{{\omega _{{\rm{ave}}}}}}{{4({\mu _0} + \mu )}}* \\ &\left\{ {\left[ {1 + B(g)} \right]P(g) + H({\mu _0},{\omega _{{\rm{ave}}}})H(\mu ,{\omega _{{\rm{ave}}}}) - 1} \right\}\end{split}$$ (1) 式中:g为观测相位角;μ0为入射角i的余弦;μ为观测角e的余弦;B(g)为后向散射函数,
$$ B(g) = \frac{{{B_0}}}{{1 + (1/h)\tan (g/2)}} $$ (2) 式中:B0为后向效应幅度,可以近似为1[13];h为后向效应的宽度参数,与颗粒的粒径、介质的填充因子等相关,其表达式为:
$$ h = - \frac{3}{8}\ln (1 - \varphi ) $$ (3) 式中:φ为填充因子,月壤可以约等于0.41[14]。P(g)为单个粒子的相函数,可以由以拉格朗日多项式来定义:
$$ P(g) = 1 + b\cos (g) + c(1.5{\cos ^2}(g) - 0.5) $$ (4) 式中:b=–0.4,c=0.25[15]。ωave为所有成分的平均单次散射反照率(average Single Scattering Albedo,SSA)。其表达式如下:
$$ {\omega _{{\rm{ave}}}} = {S_e} + (1 - {S_e})\frac{{(1 - {S_i})\Theta }}{{1 - {S_i}\Theta }} $$ (5) $${S_e} = \frac{{{{({n_h} - 1)}^2} + k_h^2}}{{{{({n_h} + 1)}^2} + k_h^2}} + 0.05 \approx \frac{{{{({n_h} - 1)}^2}}}{{{{({n_h} + 1)}^2}}} + 0.05 $$ (6) $$ {S_i} = 1.014 - \frac{4}{{{n_h}{{({n_h} + 1)}^2}}} $$ (7) $$\varTheta = {e^{ - {\alpha _w} < D > }} $$ (8) 式中:nh和kh分别为基质折射率指数(refractive index)的实部(即折射率)和虚部(即消光系数),月壤的折射率nh为1.7[3],而消光系数kh则由模型反演得到;αω为吸收系数(absorption coefficient),其大小为4πnk/λ,λ为波长;<D>为光在颗粒内部的平均路径长度,在月壤中约为30 μm[16]。H(μ, ωave)为各向同性散射函数[5]:
$$ \begin{split} H(\mu ,{\omega _{{\rm{ave}}}}) =\;& \left\{1 - \left( {1 - \sqrt {1 - {\omega _{{\rm{ave}}}}} } \right)*\right.\\ &\left. \mu \left[ {{r_0} + \left( {1 - \frac{{{r_0}}}{2} - {r_0}\mu } \right)\ln \frac{{1 + \mu }}{\mu }} \right]\right\}^{ - 1} \end{split} $$ (9) 其中,
$$ {r_0} = \frac{2}{{1 + \sqrt {1 - {\omega _{{\rm{ave}}}}} }} - 1 $$ (10) 空间风化的光谱效应是计算吸收系数α的因素[4]:
$$ \alpha = \frac{{4\pi {n_h}{k_h}}}{\lambda } + \frac{{36\pi zf{\rho _h}}}{{\lambda {\rho _{{\rm{Fe}}}}}} $$ (11) 其中,
$$ z = \frac{{n_h^3{n_{{\rm{Fe}}}}{k_{{\rm{Fe}}}}}}{{{{(n_h^2 - k_{{\rm{Fe}}}^2 + 2n_h^2)}^2} + {{(2{n_{{\rm{Fe}}}}{k_{{\rm{Fe}}}})}^2}}} $$ (12) 该研究中铁的光学常数为Paquin[17]实验数据。ρh,ρFe则分别代表基体和铁单质的密度,基体的密度本章假定为1.6 g/cm3[18];铁的密度为7.87 g/cm3[19];f为SMFe在月壤颗粒表面的质量比例。
在该研究中,首先利用Hapke模型反演得到尚未风化的岩石矿物光谱(即点15的光谱)对应的光谱消光系数k,此时输入该光谱对应的各种观测角度,而吸收系数以4πnk/λ计算。然后利用计算所得的波长范围内k值在其他光谱(即点20的光谱)测定时的测光角度信息等模拟计算,此时,吸收系数α增加空间风化因子。从0逐步增加SMFe的含量,计算模拟光谱与点20光谱的光谱角,当二者最为相等或者接近时的f便是点20月壤的SMFe含量。
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经过模型反演,当未风化的岩石光谱(点15光谱)增加SMFe含量为0.048 wt.%时,与点20的光谱拟合结果达到最佳(见图3)。由于点15的SMFe含量为0,故点20的SMFe含量为0.048 wt.%。利用Morris[5]的公式(4)定义的成熟度为:
$$ ({I_s}/FeO) = f/(3.2*{10^{ - 4}}*FeO) $$ (13) 结合该点的FeO含量13 wt.%[20],可以得出该点的成熟度为11.5,可能属于不成熟月壤。
图 3 模拟光谱与所选取光谱的(a)原始数据与(b)在1 100 nm波长处归一化后的对照图
Figure 3. (a) Original and (b) the normalized diagram at 1 100 nm wavelength of the modeled spectra and the selected spectra
需要说明的是,该研究中假定岩石矿物的表面SMFe含量为0。而事实上,岩石在风化前表面也可能存在包浆并不为0,所以反演的SMFe含量可能与实际相比偏低。利用Hapke模型反演得到的亚微观铁粒径范围为不大于50 nm,而Morris模型中采用的核磁共振敏感的亚微观铁范围仅为4~33 nm,这就使得在反演成熟度时,结果会偏高,这在一定程度上缓解了上述假设的偏差。
前人的研究目前主要是月球正面月海的研究,而对月球背面月海高地过渡区的相关参数是否需要调整仍需进一步研究与分析。
Study on space weathering of Chang´e-4 landing site by in situ spectra
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摘要: 月球表面没有大气层的保护,岩石矿物长期在太空风化的作用下,逐渐演化为月壤。太空风化过程是月壤产生、成熟的过程,由于物质形态结构的改变,导致月表光谱特征产生变化。因而,作为风化产物的月壤的光谱特性,包含了月表的太空风化信息。月壤成熟度,是描述太空风化程度的重要指标,利用高光谱遥感数据进行亚微观铁(SMFe)的反演进而获取月壤成熟度,是目前研究月表太空风化的主要手段。原位探测数据,由于没有受到其他因素的干扰,获得的反演结果相对更加准确、可靠。我国嫦娥四号(CE-4)玉兔二号巡视器搭载了能直接获取月表原位高光谱数据(450~2395 nm)的科学载荷红外成像光谱仪,为研究月表的太空风化提供了很好的机会。选取了CE-4卫星着陆器登陆点附近的两处光谱数据,采用Hapke模型和光谱角匹配法对CE-4卫星登陆点附近月壤的SMFe进行了反演。根据Morris模型和FeO含量进一步反演CE-4卫星登陆点附近月壤的成熟度。结果表明,该处月壤成熟度为11.5,较大概率为不成熟月壤。Abstract: Without atmosphere, the lunar surface is gradually evolved into lunar soil by the space weathering. The space weathering generates lunar soil and matures it. This progress changes the morphological structure and the spectral characteristics. Thus the spectral characteristics of lunar soil contains information about the space weathering of the moon's surface. Lunar soil maturity is an important indicator to describe the degree of the space weathering. Using hyperspectral data to produce the submicroscopic metallic iron (SMFe) and to obtain lunar maturity is an important method for studying the space weathering. Since the in situ detection data is not disturbed, the results obtained are relatively more accurate and reliable. Therefore, the Chang'e-4 (CE-4) Yutu-2 rover was equipped with a detection instrument that directly obtained the in situ hyperspectral data (450-2395 nm) of the lunar surface, which provided a good opportunity for studying the lunar weathering. Two spectral data near the landing site of the CE-4 lander were selected, using the Hapke model and the spectral angle matching method, SMFe content was produced. The maturity of the lunar soil near the landing site of the CE-4 was further inferred based on the Morris model and FeO content. The results show that the lunar soil's maturity is 11.5, indicating that it may be immature lunar soil.
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Key words:
- lunar hyperspectra /
- Hapke model /
- Chang'e-4 /
- SMFe /
- maturity
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表 1 嫦娥四号,玉兔二号红外成像光谱仪技术参数
Table 1. Parameters of the CE-4, Yutu-2 visible and near-IR imaging spectrometer (VNIS) and short-wave infrared (SWIR) spectrometer
Parameters VNIS SWIR Wavelength/nm 450-950 900-2 400 Band resolution/nm 2-10 3-12 View field/(°) 8.5×8.5 ф3.58 Numbers of valid pixel ≥256×256 1 Detective distance/m 0.7-1.3 Detective time/min ~2 表 2 玉兔二号获取的点15与点20光谱的几何信息
Table 2. Data acquisition conditions of Site 15 and Site 20 by Yutu-2
Parameters Point 15 Point 20 Local time 08:32:00 15:35:00 Distance to the Sun/(AU) 0.989 146 37 0.991 539 51 View angle/(°) 17 46.26 Incident angle/(°) 70.5 64.54 View azimuth angle/(°) 143.32 83.03 Incident azimuth angle/(°) 61.48 296.66 Phase angle/(°) 65.48 104.24 -
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