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Lunar gravity anomaly and its computational method
Abstract
The lunar gravity anomaly is the basis of the studies followed such as the lunar internal structure and density imaging. Thus, based on the perspective of the physical meaning, we tried to give a reasonable method of lunar gravity anomaly calculation and then analyzed the related influencing factors. Finally, the lunar global Bouguer gravity anomalies with a clear physical meaning were obtai`ned and the preliminary geological interpretation was given for the results.
... Since reference ellipsoid of the Moon is assumed to be a sphere, it could be considered 0. Moreover, because zero term and first term are omitted in the spherical harmonic synthesis, the coefficients of lunar normal field are not considered in Eq. (1) (Du et al., 2012;Š prlák et al., 2020). ...
The Lunar Radar Sounder (LRS) performed global soundings and detected possible subsurface echoes at the nearside maria. This paper examines the relationship between the distribution of the detected subsurface echoes and the surface ages in the western nearside maria. Continuous subsurface reflectors are clearly detected only in a few areas consisting of about 10% of the western nearside maria at apparent depths from hundreds to more than a thousand meters. These reflectors are not generally the basements of the mare but are the interface between different basaltic rock facies. Comparison between the distribution of the detected subsurface boundaries and the surface ages suggests that most of the detected subsurface reflectors were formed more than 3.4 billion years ago. Based on the strong connection between the accumulation rate of regolith and the absolute age, the detected subsurface boundaries appear to be relatively thick regolith layers accumulated during the depositional hiatuses of basaltic lavas.
We present an approach of the inverse gravimetric problem that allows the gravity to be directly related to the deviatoric stresses without any rheological assumptions. In this approach a new set of parameters is considered: (1) the density variations over equipotential surfaces and the height of interfaces above the corresponding equipotential surfaces and (2) the stress difference. The method is applied to lunar topographic and gravimetric data that are interpreted in term of transversally isotropic deviatoric stress within the Moon. It also provides inference on density and crustal thickness variations. The estimated lateral variation in deviatoric stress is about 500 bars within the crust and upper mantle. In the crust, because of topography, the strongest stress differences take place on the far side, with large lateral compressions beneath the south pole-Aitken basin. Vertical compression under the mascons of the nearside is the main feature within the upper mantle.
By lowering the altitude of Lunar Prospector to about 10-20 km the spacecraft will provide measures of the Moon's gravity field at very high resolution, enabling us to derive a spherical harmonic representation that includes harmonics of degree 360 and demanding precise calculation of the gravity field of the topography at such low altitudes. We present a method to determine the gravity field of the topography at low altitudes, which is very efficient even for higher degree harmonics and is also applicable for topography with laterally and radially varying density. The method is applied to three simple models; namely, an unfilled basin, a basin with mare filling, and a topography specified by a tesseral harmonic of degree 60 and order 30, before applying it to the actual topography of the Moon. It is shown that the gravity of the topography calculated by the surface-mass density approximation (a conventional method) is sufficient for harmonics of degree up to about 100 but becomes increasingly inadequate as the degree of the harmonics increases. The method is also applied to internal density interfaces, such as a possible Moho undulation, and it is concluded that the surface-mass density approximation becomes less appropriate once the degree of the harmonics exceeds about 20. We also calculate the free air gravity anomaly of the lunar topography at 10 km altitude using this method and the available 90 degree spherical harmonic model of the topography. Although the surface topography of Venus has been expanded in terms of the spherical harmonics of degree up to 360 [Rappaport and Plaut, 1994], its gravity field is measured at altitudes greater than 150 km [Sjogren et al., 1997], which is much larger than the surface topography or possible undulation of the crust-mantle boundary. The results of our method and the conventional method may not differ significantly for Venus.
Using multiple step least squares fitting method and 0.25° gridded altimetry data (http://pds-geophys.wustl.edu/pds) from Clementine, a lunar topography model, NLT180A, is determined complete to spherical harmone degree (n) 180 This model is compared with the GLTM2 model (70x70) and shows good agreement for the long-wavelength component (longer than n=70).Other important parameters, including the offset between the center of figure (COF) and the center of mass (COM) of the Moon, and the topographical flattening of the Moon, have also been estimated. The estimates are similar to those obtained by other researchers. Possibility to obtain higher (than n=180) degree spherical harmonic model from the Clementine gridded data is discussed.Based on NLT180A, the lunar Moho topography and crustal thickness are estimated by assuming a traditional single layered crust on the top of Moho. The method used in this article will benefit the research of the future lunar mission, SELENE (SELenological and ENgineering Explorer).
Density models for the Moon, including the effects of temperature and pressure, can satisfy the mass and moment of inertia of the Moon and the presence of a low density crust indicated by the seismic refraction results only if the lunar mantle is chemically or mineralogically inhomogeneous. IfC/MR
2 exceeds 0.400, the inferred density of the upper mantle must be greater than that of the lower mantle at similar conditions by at least 0.1 g cm–3 for any of the temperature profiles proposed for the lunar interior. The average mantle density lies between 3.4 and 3.5 g cm–3, though the density of the upper mantle may be greater. The suggested density inversion is gravitationally unstable, but the implied deviatoric stresses in the mantle need be no larger than those associated with lunar gravity anomalies. UsingC/MR
3=0.400 and the recent seismic evidence suggesting a thin, high density zone beneath the crust and a partially molten core, successful density models can be found for a range of temperature profiles. Temperature distributions as cool as several inferred from the lunar electrical conductivity profile would be excluded. The density and probable seismic velocity for the bulk of the mantle are consistent with a pyroxenite composition and a 100 MgO/(MgO+FeO) molecular ratio of less than 80.
The main goal of this paper is to estimate the chemical composition of the lunar upper mantle as well as the bulk composition of the silicate portion of the Moon based on a method of thermodynamic modeling (phase equilibrium calculations in the CaOFeOMgOAl2O3SiO2 system) and geophysical observations including the seismic data, moment of inertia and mass of the Moon. It has been found that the upper mantle is chemically uniform and may be composed of pyroxenite containing 0.5–2 mol.% of free silica. The calculated lunar bulk silicate composition (mantle + crust) as well as the bulk composition of the entire lunar mantle generated by the geophysical data suggest that the concentrations of FeO, SiO2 and refractory elements (Ca, Al) are significantly higher than those in the Earth's upper mantle. The atomic ratio is equal to 0.18 for the silicate portion of the Moon and 0.22 for the Moon as a whole (crust + mantle + core); the latter value is the lowest known ratio of any object in the solar system. Phase changes in any model considered in the dry CFMAS system are not able to explain the nature of the 270 km and 500 km discontinuities; it is concluded that the lunar mantle is chemically stratified. Thermodynamic modeling and geophysical observations allow some constraints on the internal density distribution and suggest the presence of a lunar core: 480 km in radius for the FeS-core and 310 km for the Fe-core. As compared with the Moon, an allowed range of the Fe-core and FeS-core radius for Io is estimated to be 300–680 km and 450–1050 km, respectively. Without specifying a mechanism for the origin of the Moon, we may conclude that the Earth and its satellite formed from compositionally different materials. Composition of the Moon remains unusual in comparison with the Earth and chondrites.