Reconstruction of martian methane's spatial density distribution

The exploration of martian methane (CH₄) is the important way to search life on the Mars. The determination of the source region of CH₄ provides an appropriate target location that explorer the possible lives on the Mars. So it requires us to know the spatial density distribution of CH₄, thus the densest source region of CH₄ can be identified. In deep space exploration, there is long history for scientists to detect the characteristic spectrum from resonance scattering of the gas molecular as a result of solar radiation. For example, in 1995, the European Space Agency detected the 3.3 nm fluorescence from CH₄ through Space Telescope. At present, the project team is trying to study the possibility of exploration of the CH₄ resonance scattering on Mars, which is the base for this paper. Since the gas of CH₄ is very thin, and the rescattering can be negligible, so it can be approximated as an optically thin layer, and the measured brightness is proportional to the column abundance of the CH₄ along the lines of imager radiation corresponding to each pixel. This process is very similar with the emission computed tomography (ECT), so the computed tomography (CT) can be used to calculate the CH₄ spatial density distribution when the data could be collected from various angles. In the strict sense, the accurate reconstruction needs the projection data satisfy the Tuy-Smith sufficiency condition. But this condition is very difficult for the satellite. In 2006, Sidky et al developed an algebraic reconstruction technique (ART) based on the minimization of the image total variation (TV) that applies to insufficient data problems. Therefore, this method is adopted to solve our problems. In order to verify our formulas for the CH₄ density, in this paper, a three dimensional (3D) model for the density distribution of the CH₄ is established based on the Mars' atmosphere distribution law, which may not consistent with the truth, but it is enough for verify the formulas. Through the numerical simulation, the density distribution is reconstructed and compared with the 3D model. It is shown that the reconstruction results are in agreement with the model. Especially, it can distinguish the densest region of CH₄, hence, to define the source region of the CH₄ on the Mars' surface. So the CT method can be used to calculate the density of CH₄ from the image data. But there are still some problems. Firstly, the results have certain deviation which can be improved by increasing the projection data. For example, reduce the time interval of sampling, change the orbit of the satellite. Additionally, the spatial resolution of the results requires to be improved which is controlled by the one of the detector. According to the detector developed by the project team, the best resolution, both vertical and horizontal, is 50 km, which is too low for the reconstruction. How to improve the resolution of the detector is the problem that the project team is trying to solve. Moreover, the assumption of the steady-state condition for CH₄ is supposed in this work. We ignore the CH₄ motion during taking all the pictures by the Imager, but in fact, this assumption is unreasonable and unacceptable. The recent research showed that the density of CH₄ should vary with time because of the motion of the neutral wind. All these difficulties will be further studied in our future work.