THE METHOD OF MOONQUAKES SELENOPHYSICAL PARAMETERS ANALYSIS

Abstract

The purpose of the present study is to apply the new methods of multi-parametric analysis to moonquakes. It should be noted such physical phenomena as moonquakes are some kinds of complex systems. As the works in which analysis of moonquakes observations is conducted have shown, lunar seismophysics is much more complex process than Earth's geophysics. This is why to study the physical nature of moonquakes and their parameters it is necessary to use methods of statistical physics and robust estimates. Currently, there are some attempts to study the lunar internal structure based on moonquakes using different seismic methods, such as signal's passage time analysis, tomography techniques, seismic interferometry waves for deep moonquakes in order to conduct backward reflection on "Apollo" mission stations. Based on simulation of tidal lunar parameters which have been improved during the recent space missions, such as GRAIL (gravity), LRO (shape), and LLR (rotation), the presence of lunar internal layer with low viscosity coinciding with the areas where deep moonquakes take place is assumed. The method of moonquakes database analyzing is developed using the author's time series analysis introduced for the Earth's seismics studies based on space observations. The software applications to quantitatively describe parameters of moonquakes dynamic features are developed. A theoretical model for analyzing correlation with the lunar pole dynamics is developed for deep moonquakes. The connection of lunar poles motion dynamics and their uneven rotation with seismic activity has been tested. When developing numerical algorithms and software for moonquakes time series data processing, the modern methods of non-equilibrium statistical physics allowing obtaining a set of statistical parameters and information measures to study the statistical memory effects, periodic patterns, non-stationarity and dynamic intermittency effects, alignment and/or misalignment effects, frequency-phase synchronization from time signals have been used.

Headnote

ABSTRACT

The purpose of the present study is to apply the new methods of multi-parametric analysis to moonquakes. It should be noted such physical phenomena as moonquakes are some kinds of complex systems. As the works in which analysis of moonquakes observations is conducted have shown, lunar seismophysics is much more complex process than Earth's geophysics. This is why to study the physical nature of moonquakes and their parameters it is necessary to use methods of statistical physics and robust estimates. Currently, there are some attempts to study the lunar internal structure based on moonquakes using different seismic methods, such as signal's passage time analysis, tomography techniques, seismic interferometry waves for deep moonquakes in order to conduct backward reflection on "Apollo" mission stations. Based on simulation of tidal lunar parameters which have been improved during the recent space missions, such as GRAIL (gravity), LRO (shape), and LLR (rotation), the presence of lunar internal layer with low viscosity coinciding with the areas where deep moonquakes take place is assumed. The method of moonquakes database analyzing is developed using the author's time series analysis introduced for the Earth's seismics studies based on space observations. The software applications to quantitatively describe parameters of moonquakes dynamic features are developed. A theoretical model for analyzing correlation with the lunar pole dynamics is developed for deep moonquakes. The connection of lunar poles motion dynamics and their uneven rotation with seismic activity has been tested. When developing numerical algorithms and software for moonquakes time series data processing, the modern methods of non-equilibrium statistical physics allowing obtaining a set of statistical parameters and information measures to study the statistical memory effects, periodic patterns, non-stationarity and dynamic intermittency effects, alignment and/or misalignment effects, frequency-phase synchronization from time signals have been used.

Keywords: space astrometry, selenodesy, moonquakes, lunar seismophysics, space mission

INTRODUCTION

The studies of the Earth's and Moon's seismic processes showed there were the same causes for both of them [1]. Analysis of data on more than 200000 earthquakes by International Seismological Catalog showed:

1) Seismic activity at the Poles and polar ice caps was almost absent;

2) In the middle latitudes of both hemispheres there was maximum activity;

3) Near the equator there was a stable minimum of seismic activity.

Epicenters of earthquakes in most cases for large geographical latitudes are located at depths less than 20 km. As they come to middle latitudes, epicenters are gradually achieving depths from 20 up to 60 km. Near the equator earthquakes epicenters are located at depths 100-240 km or deeper than 500 km.

Analysis of "Apollo" mission's Moonquakes data (1971-1974) showed the lunar seismic activity was very similar to the processes taking place on the Earth. The lunar activity was also less at the Poles and polar ice cap of the Moon, achieved maximum value in middle latitudes of both hemispheres, and had a stable minimum near the equator. Shallow moonquakes have their epicenters at depths of 100-300 km and usually take place in latitudes of 30°-40° of both lunar hemispheres. Deep moonquakes (at depths of 800-1100 km) have their epicenters near the equator in lunar latitudes of 10°-30°. Thus, distribution of seismic processes for both celestial bodies is equal for latitudes and very similar for depths. Therefore, there is a fundamental connection between seismic processes and certain physical phenomena which are equal for both the Earth and Moon. In the work [1] it is assumed that seismic events on the Earth and Moon depend on tidal impacts from the Sun. That theory enables to explain the similarity of earthquakes and moonquakes quantity distribution for latitudes. The main cause of earthquakes is considered to be tectonic processes [2]. The main cause of moonquakes is considered to be the Earth's gravity. However, those theories cannot explain the same for the Earth and Moon distribution of seismic activity for latitudes.

On the other hand, in the work [3] based on the analysis of 1000 tidal moonquakes with energies up to 109 Erg, magnitudes 0,3-1,3, periodicity of 13, 27 (lunar month), 206 days, and 6 years, it was found that periodicity of moonquakes correlate with dynamic parameters of the Moon's orbital motion around the Earth and Sun. 60 tidal moonquakes epicenters were studied and it was found that forms of signals for all the tidal moonquakes repeated during the entire observation period. Tidal moonquakes epicenters are usually located in territories of lunar basaltic seas and fall into 4 global seismic belts. Lengths of those belts are 1000-2500 km, widths are 100-300 km, and depths are 800-1000 km.

SEISMIC LUNAR OBSERVATIONS DATA

Seismic lunar observations include all the seismic data recorded by 5 out of 6 ALSEP (The Apollo Lunar Surface Experiments Package) stations. Those stations were adjusted by the American astronauts during the "Apollo" space missions in 1969-1972 and kept operating until 1977.

The least number of moonquakes are located in the territory of Southwestern area on the Moon, where a lot of meteorite craters are situated. In the West the line of moonquakes crosses Mare Serenitatis and goes slightly north of Mare Crisium. In the North the line of moonquakes passes through the middle of Mare Imbrium and almost reaches the Northern Pole. In the South the line of moonquakes goes through the middle of Mare Cognitum and Mare Humorum and almost approaches the Southern Pole of the Moon.

ANALYSIS OF THE LUNAR INTERNAL STRUCTURE BASED ON MOONQUAKES

Density of the Moon is 3340 kg/m3, which is similar to the Earth's mantle. The seismographs of the "Apollo" space mission have shown that moonquakes occurs permanently, however, they are significantly different compared with earthquakes. There were installed 4 seismometers on the surface of the Moon [4]. The data from the "Apollo" space mission was used to simulate the lunar internal structure for its depth areas up to 400 km. The structure near the center of the Moon was not determined. In some studies there were attempts to identify seismic waves reflected on the borders between liquid and solid layers of the Moon by the analysis of noise signals [5], but significant differences between the models of deep moonquake areas were found.

In the work [2] it was found that numerous inhomogeneous moonquakes occurred repeatedly in special source-areas located at depths 700-1200 km [6]. A small amount of minor earthquakes caused by meteoroids and artificial moonquakes were found, though.

In the work [7] it was concluded there was partially molten layer inside the lunar sphere. It was determined low viscosity of about 106 Pa at the bottom part of the lunar mantle could be the result of significant amount of molten substance and even certain critical state. In the paper [8] it was found that high content of water could explain the lunar dissipation without considering partial melting of the mantle. Nevertheless, existence of partially molten layer is not yet proven.

THE METHOD OF DETERMINING THE LONG-PERIODIC GEODYNAMICAL COMPONENTS FROM ASTRONOMICAL OBSERVATIONS

One of the methods of analyzing moonquakes can be the method of determining the long-periodic geodynamical components from astronomical observations, which was approved by us for the case of earthquakes.

To study geodynamical activity we analyzed slow (long-periodic) component of mean geographical latitude change [1-2]. Thus, we analyzed some large territory.

In Fig.1 and Fig.2 we see long-periodic variations of mean latitude non-polar changes in EAO latitude: Fig.1 corresponds to the period of 1959-1970, Fig.2 (irregular line) corresponds to the period of 1978-1994. In the Fig.2 all the periodic components were excluded for polar and non-polar variations. That was performed using the special linear transformation for latitudes smoothing. The data in the Fig.1 and Fig.2 is plotted with a step of 0.1 year. In the Fig.1 and Fig.2 X-axis corresponds to time (in years), while Yaxis corresponds to change of mean latitude.

For excluding random observation errors single values of latitude were grouped into normal points. Averaging was performed for 5 to 20 days intervals depending on density of observations. The mean value of averaging period was 14.7 days. Each normal point contains from 7 to 22 single values of latitude, which had been plotted in the Fig.1 and Fig.2. The mean square error of a single mean latitude determining fluctuated within ± 0.0008"- 0.0022". The mean latitude of EAO was taken as 20.318". Variations of latitude were calculated by the Pole's coordinates. The data on the Pole's coordinates (X and Y) were taken from monthly bulletins of International Earth Rotation and Reference Systems Service and Federal Agency on Technical Regulation and Metrology of the Russian Federation.

Based on the given figures it may be concluded that the Earth's crustal motions occur permanently and unevenly. Deviations from the mean value of latitude, which turn out to be 0.02" - 0.04", are significant and cannot be explained by any measurement errors.

It should also be noted that significant changes of the mean latitude up to 0.1" occurred during the period of 1959-1962, while after that there were no observed changes of the mean latitude until the year 1980. In the middle of the year 1980 the mean latitude started increasing and reached the maximum value in 1981. The next fluctuation of the mean latitude occurred in 1984. The most significant changes of the mean latitude took place in 1987-1988. Those changes were of a wrong and wavelike nature. But for some time periods there was a notable linear trend.

Based on the data from the Fig.1 and Fig.2 we may conclude that geodynamical activity turns out to be very significant. The Earth's crust and the subcortical substance are permanently moving and their activity is manifesting in a wide frequency range and with different periods of change covering large in size territories. This method may be successfully applied for analyzing lunar geodynamics.

CONCLUSION

During the "Apollo" space mission more than 8000 moonquakes were recorded including tidal moonquakes, tectonic tremors, fall of meteorites, impacts by spent spacecrafts' stages. Based on the analysis of lunar seismic waves the lunar internal structure was studied. At depth of a half the lunar radius there is the lunar lithosphere, in which seismic waves do not weaken. Deeper than the lithosphere there is the asthenosphere (lunar liquid core), through which transverse seismic waves cannot go. In the area of lithosphere-asthenosphere transition there are tidal moonquakes epicenters. Based on the analysis of moonquakes in the lithosphere one may distinguish basaltanorthosite crust and peridotite mantle. The border between the crust and the mantle at depth of 60 km is sharp.

Along with tidal moonquakes the lunar seismic stations recorded tectonic pushes. They were observed at depths up to 300 km. 25 tectonic pushes, which had been much more intensive than tidal ones ( value of magnitude: 4-5), were noted. There was no periodicity found in the tectonic pushes, but they coincided in time with the strongest tidal moonquakes. Epicenters of tectonic pushes are located near the borders of global seismic belts. Convection velocity in the bowels of the Moon is much less than on the Earth, that is why moonquakes energy (1018 Erg) is million times less than the Earth's one.

However, the discovered general regularities between earthquakes and moonquakes are based on small number of observations. Nevertheless, the existing theories, according to which the main cause of moonquakes is tidal forces, while in case of earthquakes the main cause is tectonic processes, cannot explain the results of space observations.

Currently, there is a project of installing 10-12 seismometers for collecting data during 3 to 5 years. According to the researchers, this work is essential to find the safest areas for spacecraft landing. In the future the results of the present project are going to be applied to other celestial bodies [9]. It will be taken into account that there is very few information on the Poles of the Moon [10], while this is especially important, since it is planned to place manned lunar bases at the lunar Poles.

ACKNOWLEDGEMENTS

The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University. This work was partially supported by the Russian Foundation for Basic Research, grant nos. 15-02-01638-a, 16-32-60071-mol_a_dk (N.D.).

References

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