Inversion of lunar regolith layer thickness with CELMS data using BPNN method

Highlights

• The BPNN method is firstly employed to retrieve the lunar regolith layer thickness.

• The regolith layer thickness is related to its age if the basalt is of the same kind.

• The surface roughness strongly impacts the thickness, followed by the CELMS data in 3 GHz and the slope.

Abstract

Inversion of the lunar regolith layer thickness is one of the scientific objectives of current Moon research. In this paper, the global lunar regolith layer thickness is inversed with the back propagation neural network (BPNN) technique. First, the radiative transfer simulation is employed to study the relationship between the lunar regolith layer thickness d and the observed brightness temperature T_B׳s. The simulation results show that the parameters such as the surface roughness σ, slope θ_s and the (FeO+TiO₂) abundance S have strong influence on the observed T_B׳s. Therefore, T_B׳s, σ, θ_s and S are selected as the inputs of the BPNN network. Next, the four-layer BPNN network with seven-dimension input and two hidden layers is constructed by taking nonlinearity into account with sigmoid functions. Then, BPNN network is trained with the corresponding parameters collected in Apollo landing sites. To tackle issues introduced by the small number of the training samples, the six-dimension similarity degree is introduced to indicate similarities of the inversion results to the correspondent training samples. Thus, the output lunar regolith layer thickness is defined as the sum of the product of the similarity degree and the thickness at the corresponding landing site. Once training phase finishes, the lunar regolith layer thickness can be inversed speedily with the four-channel T_B׳s concluded from the CELMS data, σ and θ_s estimated from LOLA data and S derived from Clementine UV/vis data. the inversed thickness agrees well with the values estimated by ground-based radar data in low latitude regions. The results indicate that the thickness in the maria varies from about 0.5 m to 12 m, and the mean is about 6.52 m; while the thickness in highlands is a bit thicker than the previous estimation, where the thickness varies widely from 10 m to 31.5 m, and the mean thickness is about 16.8 m. In addition, the relation between the ages, the (FeO+TiO₂) abundance and the inversed regolith layer thicknesses in the nine main maria indicates that the regolith layer thickness is directly related to its age if the basalt is of the same kind. Furthermore, the correlation between the inversed thickness and the seven input parameters along the Moon Equator indicates that the surface roughness has the largest impact on the inversed thickness, followed by the CELMS data in 3 GHz and the slope.

Introduction

The surface of the Moon is virtually covered by a layer of fine-grained regolith that completely covers the underlying bedrock (Heiken et al., 1991). Up to now, a substantial amount of information we know about the Moon is originating from the regolith. Knowledge of the structure of the lunar regolith will provide important information to understand the geology of the Moon (Shkuratov and Bondarenko, 2001, Neal, 2009).

Inversion of the lunar regolith layer thickness is always one of the scientific objectives of current Moon research. During Apollo and Luna missions, drilling and seismic experiments at the Apollo 11, 12, and 14–17 landing sites (Watkins and Kovach, 1973, Cooper et al., 1974) and electromagnetic probing methods at the Apollo 17 landing site (Strangway et al., 1975) were carried out to yield the regolith layer thickness.

To estimate the regolith layer thickness over large area of the lunar surface, the methods based on the crater morphology were employed (Gault et al., 1966, Oberbeck and Quaide, 1968, Quaide and Oberbeck, 1968, Shoemaker and Morris, 1969, Basilevsky, 1974, Willcox et al., 2005, Bart et al., 2011). Shoemaker and Morris (1969) proposed an approximate cumulative distribution function to determine the regolith layer thickness with the frequency distribution of crater diameters. With this technique, the regolith layer thicknesses at Surveyor 7 landing site and at Luna 16, 17, 20, and 21 landing sites were estimated by Shoemaker and Morris (1969) and Basilevsky (1974), respectively. Willcox et al. (2005) improved the crater-counting method with the frequency and distribution of blocky craters to present the constraints on the thickness and the variability of the lunar regolith. Bart et al. (2011) employed the crater morphology method to reveal the global non-uniformity characteristic of the lunar regolith layer thickness. The methods based on the crater morphology could provide good first order estimation of regolith depths across large regions (tens to hundreds of kilometers), but might not clearly elucidate the variability of regolith layer thickness locally (km scale) (Willcox et al., 2005).

Using early Earth-based 70-cm Arecibo radar (Thompson, 1987), Shkuratov and Bondarenko (2001) firstly estimated the regolith layer thickness over the nearside of the Moon. Fa and Wieczorek (2012) improved the method by taking the scattering from both the lunar surface and buried rocks into account. With the data from Lunar Radar Sounder and from Laser Altimeter onboard Kaguya satellite, Kobayashi et al. (2010) also studied the regolith layer thickness in Maria Tranquillitatis, Serenitatis, Imbrium, and Oceanus Procellarum. However, the poor knowledge about the internal lunar regolith and the difficulties of the surface and volume scatterings bring challenges to estimate the regolith layer thickness with such methods (Jiang et al., 2008, Neal, 2009).

In Chinese lunar exploration project, a microwave sounder (CELMS), for the first time, was aboard the Chang׳E satellite with the purpose of measuring the lunar surface layer thickness, which operated at 3.0, 7.8, 19.35 and 37.0 GHz channels. To estimate the lunar regolith layer thickness with CELMS data, Jin et al. (2003), Lan (2004) and Meng et al. (2008) simulated the microwave emission of the regolith based on a two-layer (regolith–rock) model, where the regolith was seen as the inhomogeneous medium with the temperature and dielectric constant changing with depth. To avoid the difficulties in solving the radiative transfer equations of the lunar regolith, Fa and Jin (2010) proposed a three-layer (dust–regolith–rock) model, which treated the temperature and dielectric parameters as constants for each layer, to invert the lunar regolith layer thickness. Considering the large variation of the temperature and dielectric parameters with the depth, Wang et al. (2009) and Li et al. (2009) presented a 45-layer model to invert the regolith layer thickness. To reduce the computational complexity with 45-layer model, Zhou et al. (2011) developed an inhomogeneous multi-layer model with 36 layers, where the lunar regolith is layered according to the variation of the regolith density with depth, to investigate the lunar regolith thickness.

In addition to the different complicated regolith models, the studies on the lunar regolith parameters including the temperature profile, dielectric constant profile, particle size, buried rocks and surface roughness, which are also critical for the radiative transfer simulation, are rarely sufficient (England, 1975, Keihm, 1984, Jiang et al., 2008, Zhou et al., 2011). Moreover, the inversion of the lunar regolith layer thickness with the theoretical models is related to the solution of non-linear integer-differential equations and may lead to the so-called ‘ill-posed’ problems (Keihm, 1984, Jiang et al., 2008). That is, the same set of brightness temperatures may correspond to different sets of Moon regolith parameters, and the stability of the solution would be in doubt. How to avoid the influence from such kind of disadvantages of the microwave radiative transfer simulation and to provide a fast and efficient way to extract the lunar regolith layer thickness still remain as a crucial problem in current Moon research.

As an excellent nonlinear fit theory, the back propagation neural network (BPNN) method imitates the biological processing model and it has been widely utilizeed in the information extraction and target identification (Li et al., 2012, Hecht-Nielsen, 1989). Hornic et al. (1989) indicated that the results inversed by the BPNN method with proper input-output pairs can approach any theoretical results. Tsang et al. (1992) applied the BP type ANN method to yield the snow parameters such as the fractional volume, mean grain size and physical temperature. Based on the BPNN method, Chen (2007) classified the multi-spectral information from the lunar regolith, soil, basalt, and silicate minerals. With the BPNN methodology, Montopoli et al. (2011) numerically studied the capability of the inversion of the lunar regolith layer thickness as well as the temperature profile behavior based on the satellite onboard multi-frequency radiometer data at frequencies ranging from 1 to 24 GHz. Li et al. (2012) developed an efficient and accurate model with the BPNN method for using visible–near infrared reflectance spectra to estimate the abundance of minerals on the lunar surface. The basic idea of BPNN is to train the neural network with the input-output pairs generated by the observed data (Ishimaru et al., 1990). Once the network is trained, the desired parameters can be retrieved speedily with the inputs regardless of the aforementioned problems in radiative transfer simulation, which makes the BPNN method an appealing candidate to estimate the Moon regolith layer thickness.

In this paper, the BPNN method is selected as an attempt to invert the lunar regolith layer thickness. In Section 2, the radiative transfer simulation is employed to construct the relationship between the observed CELMS data and the regolith layer thickness. Based on this, the proper input and output parameters for the BPNN network are determined. Then the architecture of the BPNN network and the training procedure are described in Section 3. In Section 4, the CELMS data, the LOLA data and the Clementine UV/vis data are processed to obtain the brightness temperature, the surface roughness and slope, and the (FeO+TiO₂) abundance over the lunar surface, respectively. Then the lunar regolith layer thickness is retrieved using the BPNN method as shown in Section 5. The rationality of the inversed thickness is also analyzed. In Section 6, the correlations between the ages, brightness, surface roughness, slope, (FeO+TiO₂) abundance and the lunar regolith layer thickness are discussed, respectively. Finally, the conclusions are presented in Section 7.