PPS03-01

Room:A03

Time:May 28 14:15-14:30

On low-velocity zone at the bottom of the lunar mantle
MATSUMOTO, Koji1∗ ; YAMADA, Ryuhei1 ; KIKUCHI, Fuyuhiko1 ; KAMATA, Shunichi2 ; ISHIHARA, Yoshiaki3 ;IWATA, Takahiro3 ; HANADA, Hideo1 ; SASAKI, Sho4
1

RISE Project Office, National Astronomical Observatory of Japan, 2 Hokkaido University, 3 JAXA, 4 Osaka Univresity

Introduction: The knowledge of internal structure of the Moon is a key to understand the origin and the evolution of ournearest celestial body. Some analyses of the Apollo seismic data have indicated the existence of low-velocity zone (LVZ) at thebottom of the lunar mantle, e.g., [1], [2], but some models do not include the LVZ, e.g., [3]. The recent Gravity Recovery andInterior Laboratory (GRAIL) mission has provided a degree-2 potential Love number k2 accurate to 1% [4], [5]. This level of k2
accuracy has a potential to better characterize the lunar deep interior [6]. One of the recent studies which used the GRAIL-derived
k2 indicates the existence of the LVZ [7].
Data and inversion: In order to infer the deep structure of the Moon, we employed four selenodetically observed data ofmean radius (R), mass (M), normalized mean solid moment of inertia (Is /MR2 ), and the GRAIL-derived k2 which are recently
summarized by [8], together with the seismic travel time data which are selected by [9], i.e., 318 data (183 P-wave and 135
S-wave) from 59 sources (24 deep quakes, 8 shallow quakes, 19 meteoroid impacts, and 8 artificial impacts). The Love number
k2 is corrected for the anelastic contributions following [7]. We used Markov chain Monte Carlo (MCMC) algorithm to infer theparameters of the lunar internal structure. The solutions of the parameters and their uncertainties are obtained from the posterior
distribution which is sampled by the MCMC algorithm.
Results: The inferred mean crustal and mantle structures are basically consistent with previous studies (e.g., [2], [3], [10]).
Our model, however, has larger lower-mantle density. P and S wave velocities in the LVZ are estimated to be 6.9 +0.9/-0.5 km/s
and 2.6 ± 1.4 km/s, respectively. A two-dimensional posterior probability function clearly shows a negative correlation between
the outer core size and the LVZ thickness; a smaller outer core should be accompanied by a thick LVZ and vice versa. The outer
core radius is estimated to be 310 +90/-200 km. The thickness of the LVZ is inferred as 220 ± 170 km, so provided that theanelastic correction is appropriate, the LVZ is required from the observations. The plausible inference from the existence of the
LVZ is that the LVZ is partially molten where viscosity is also low and most of the tidal dissipation occurs [11, 7]. Although
the uncertainty is large, the estimated LVZ density at the pressure near the core mantle boundary (∼4.5 GPa) indicates that thiszone is typically high-Ti basalt which might have originated black glass with TiO2 content ∼16 wt% [12]. The deep Ti-richcomposition is consistent with a lunar evolution model involving lunar mantle overturn in which ilmenite-bearing cumulate layersank with trapped incompatible heat-producing elements [13]. The above discussions support the idea that both tidal heating andradiogenic heating have maintained the partially molten region up until the present.
References: [1] Nakamura Y. (2005) JGR, 110, E01001. [2] Weber R. C. et al. (2011) Science, 331, 309-312. [3] Garcia R.
F. et al. (2011) PEPI, 188, 96-113. [4] Konopliv A. S. et al. (2013) JGR, 118, 1415-1434. [5] Lemoine F. G. et al. (2013) JGR,
118, 1676-1698. [6] Yamada R. et al. (2014) PEPI, 231, 56-64. [7] Khan A. et al. (2014) JGR, 119, 2197-2221. [8] Williams J.
G. et al. (2014) JGR, 119, 1546-1578. [9] Lognonne P. et al. (2003) EPSL, 211, 27-44. [10] Wieczorek et al. (2013) Science,
339, 671-675. [11] Harada Y. et al. (2014) Nat. Geosci., 7, 569-572. [12] Sakamaki T. et al. (2010) EPSL, 299, 293-297. [13]Hess P. C. and Parmentier E. M. (1995) EPSL, 134, 501-514.
Keywords: Moon, low-velocity zone, energy dissipation, Love number, internal structure

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PPS03-02

Room:A03

Time:May 28 14:30-14:45

Strong tidal heating inside an ultralow-viscosity zone over the lunar core-mantle boundary
HARADA, Yuji1∗ ; GOOSSENS, Sander2 ; MATSUMOTO, Koji3 ; YAN, Jianguo4 ; PING, Jinsong5 ;NODA, Hirotomo3 ; HARUYAMA, Junichi6
1

SSI, MUST, 2 CRESST, UMBC, 3 NAOJ, NINS, 4 LIESMARS, WHU, 5 NAOC, CAS, 6 ISAS, JAXA

Tidal heating due to viscous dissipation in a planetary body is an important energy conversion process, depending on its internal structure, and connected to its thermal and orbital states. Our moon is not an exception. Previous studies have calculated thetidal response including dependence of the dissipation on the lunar interior structure, but these studies did not completely explain
the geodetically-observed dependence of the dissipation on the lunar tidal period. One possibility to interpret this frequencydependence is a low-viscosity layer inside the mantle as a natural consequence of the strong seismic attenuation zone, becausesuch a viscosity contrast affects this dependence. However, previous studies have not considered its potential impact. Here
we show that the explicit influence of the low-viscosity zone successfully provides the frequency-dependent dissipation on theMoon consistent with the geodetic observables. We found that the above-mentioned high attenuation zone is equivalent to the
low-viscosity layer. Furthermore, we also found that the resultant viscosity value is remarkably low, signifying a relaxation timeclose to the tidal period. This ultralow viscosity implies partial melting as formerly suggested. Our result demonstrates that themost effective dissipation is localised to this layer, indicating a blanket effect on the core. We anticipate that such tidal heating,balanced against convective cooling, maintains this layer over the course of the lunar tidal history.
Keywords: the Moon, core-mantle boundary, low-viscosity zone, tidal heating

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PPS03-03

Room:A03

Time:May 28 14:45-15:00

Precession, nutation, pole motion and variations of LOD of the Earth and the Moon
BARKIN, Yury1∗ ; HANADA, Hideo2 ; BARKIN, Mikhail3
1

Sternberg Astronomical Institute, Moscow, Russia, 2 National Astronomical Observatory of Japan, Mizusawa, Japan, 3 Bauman
Moscow State Technical University, Moscow, Russia
The theories of precession, nutation, pole motion and variations of LOD of the Earth and the Moon are developed on the baseof unified approach. The Earth and the Moon are modeled as non-spherical bodies with ellipsoidal liquid core.
The base of studies is the Hamiltonian formalism with application of Andoyer’s and Poincare’s variables.
New analytical theory of Earth’s rotation. The theory of non-spherical Earth’s rotation with an elastic mantle, with variable
outer shell and with ellipsoidal liquid core in the gravitational field of the Moon, the Sun and planets are developed. As thebase the equations of motion have been used equations in Andoyer’s variables. We take into account the second harmonic of
the geopotential for high-precision orbital description of the motion of the Earth and the Moon. We take into account variationsof the components of the inertia tensor of the Earth. They are based on the modern satellite data about secular, annual andsemi-annual variations of geopotential. An approximate solution of the problem of the rotation of the Earth is constructed using
the small parameter method in Andoyer variables, as well as projections of the angular velocity of rotation of the Earth and its
core. It is assumed that the core is an ideal fluid undergoing a simple Poincare’s motion. As unperturbed rotational motion of
the Earth is taken no axial rotation (rotation around the polar axis of inertia of the planet), and a conical Eulerian ? Chandler
motion (Barkin Yu., Barkin M., 2014). The tables of precession, nutation, polar oscillations axis of rotation of the Earth andothers perturbations of the Earth rotation have been constracted. They show the good agreement between the developed theory
and previously developed theories of the Earth’s rotation (Kinoshita, 1977; Getino, Ferrandiz, 2001 et al.).
New analytical theory of lunar rotation. In our work the analytical theory of lunar physical libration based on its two-layer
model consisting of a non- spherical solid mantle and of the ellipsoidal liquid core has been developed. On the base of analyticalsolution for two layers model (the Moon with liquid core) and empirical theory of the Moon’s rotation (Rambaux, Williams,
2011), we have identified period, amplitude, and the initial phase of the forth mode of free libration of the Moon, caused byliquid ellipsoidal core. The plans for future studies of the Moon rotation are discussed. On the base of two layers model ofthe Moon we have fulfilled systematic studies of the Moon physical librations. And in first we have presented a solution of the
problem in components of vector of angular velocity of the Moon. An analytical presentation of LOD of the Moon with highaccuracy in form of trigonometric series has here the progressive value. In first we have determined the fourth mode of freelibration of the Moon caused by the influence of the liquid core oscillations of pole axis of rotation of the Moon (its mantle), witha long period in 205.7 yr, with an amplitude of 0?0395 and the initial phase of -134 o (for the initial epoch 2000.0). The estimates
for the dynamic (meridional) oblatenesses of the ellipsoidal liquid core of the Moon: 0.000442 and 0.000283 have been obtained(Barkin et al., 2014).
Keywords: Moon rotation, free libration, liquid core, solid core

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PPS03-04

Room:A03

Time:May 28 15:00-15:15

Improvement of the Earth rotation theory: recent advances and prospects
FERRANDIZ, Jose M.1∗ ; GETINO, Juan2 ; ESCAPA, Alberto1 ; BARKIN, Yuri V.3 ; NAVARRO, Juan F.1
1

University of Alicante, Spain, 2 University of Valladolid, Spain, 3 SAI, Moscow State University, Russia

Earth rotation is considered as one of the three pillars of modern Geodesy and is presently a very active field of research, due
to the very stringent demands of accuracy resulting from a broad set of applications to various fields. The most stringent ones
are those related with the monitoring of sea level, which is tightly linked to the climate change and related prevention policies,
having both a big economic and social impact.
In 2013 the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) approved the creationof an IAU/IAG Joint Working Group on Theory of Earth Rotation (JWG ThER) chaired by the first author. This group has asingular structure since comprises 3 sub-working groups. Its purpose is promoting the development of theories of Earth rotationthat are fully consistent and that agree with observations and provide predictions of the Earth orientation parameters (EOP) withthe accuracy required to meet the needs of the near future as recommended by GGOS, the Global Geodetic Observing System ofIAG. Such accuracy is of the order of 1 mm in position, measured on the Earth surface, which corresponds roughly to an angleof 30 micro arc seconds from the Earth’s centre.
Those extreme requirements of accuracy challenge all of the theories that have been devised and used up to the date anddemand their improvement, paying especial attention to the achievement of a level of consistency appropriate to the pursued
accuracy not only in the internal construction of theories but in the realization of the celestial and terrestrial frames related towhich the EOP are referred.
This presentation emphasizes the recent advances in the Hamiltonian approach to Earth rotation developed by the authors,since they provide a systematic and consistent way of treating a variety of Earth models and physical second order effects andderive accurate enough mathematical solutions, mainly by means of analytical perturbation methods.

Keywords: Earth orientation parameters, precession, nutation, second-order effects

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PPS03-05

Room:A03

Time:May 28 15:15-15:30

Nature of contrasting changes in sea level in the northern and southern hemispheres of the
Earth
BARKIN, Yury1∗
1

Sternberg Astronomical Institute, Moscow, Russia

S/N oceanic secular tide. South-north a ocean secular tide in the present epoch has been found in 2007 and was analyticallydescribed the quasi-static approximation by the author (Barkin, 2011). This tide of a different nature compared with the lunarsolar tides. It is caused by the gravitational attraction of Earth’s core shifting to the north.
Displacement of the core (and as consequence of the center of mass of the Earth) relative to its mantle generates a slow tideof oceanic and atmospheric masses from the southern hemisphere to the northern (Barkin, 2011). Similar phenomena are also
observed on Mars, Titan and other bodies of the solar system. Along with the fundamental core of the tide, we studied otherphenomena that determine the secular changes in sea level. Deformation changes the Earth’s surface that are installed on the
GPS satellite observations. The role of the asymmetric arrangement of the continents in relation to the northern and southernhemisphere. The modern thermal factors of the ocean volume and its thermal expansion. All these factors, taken together, madeit possible to explain the observed increase in global average sea level. The result revealed contrasting changes its average levelsin the northern and southern hemispheres. In the northern hemisphere the average sea level increases at a rate of about 2.45 ±0.32 mm / year, and in the southern hemisphere, the average sea level rises with a much lower average rate of 0.67 ± 0.30 mm /yr (Barkin, 2011). I.e. the contrast change NS levels of ocean is 1.78 mm / year.
Confirmation of S/N tide. Revealed asymmetric ocean tide towards south-north also has obtained a clear confirmation inmodern observations on the coastal tidal stations in the past 30 years (Evreeva et al., 2007). The theoretical value of the rateof rise of the global sea level was 1.61 ± 0.36 mm / yr (Barkin, 2011). This value agrees well with the modern determinationsof its characteristic obtained from the coastal tidal observations at stations including taking into account the vertical geodetic
displacements of coastal tide stations. In a recent paper Woppelman et al. (2014), this effect was more evidence. Contrast rates
of change mean sea level over the past 100 years was approximately 0.9 mm / year. The authors used data from tide gauges
and GPS data to identify the vertical displacements of coastal stations themselves. As a result, by strict selection criteria havebeen studied in detail data on 76 stations. Estimates of the average velocity change in sea level have been obtained for the entire
20th century. For the northern and southern hemispheres, they amounted to (2.0 ± 0.2) mm / year and (1.1 ± 0.2) mm / year
(Woppelmann et al., 2014). In my work in 2007 were received related values (2.45 ± 0.30) mm / year and (0.67 ± 0.30) mm /yr (Barkin, 2011). This match could be more expressive if the studies undertaken to take into account data on some tidal stations
located at higher latitudes 60 - 90o in the southern and northern hemisphere. In the paper (Barkin, 2011) we have considereda shorter time interval of about 30 years, at which the contrast of mean sea levels in S/N hemispheres is represented by more
expressive. We also note that according to our research post glassial rebound effects and the effects of vertical displacement
observation stations (in average sense) do not provide a significant contribution to the parameters studied changes in sea level(Shen et al., 2015). Studies of South - northern secular tide require additional intensive research. The work was accepted by
grant of RFBR N 15-05-07590 A.
Keywords: sea level increase, Southern-northern secular ocean tide, moving core

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PPS03-06

Room:A03

Time:May 28 15:30-15:45

Software development for precise LLR data analysis and initial results of parameter estimation for lunar motion
NAGASAWA, Ryosuke1∗ ; OTSUBO, Toshimichi2 ; SEKIDO, Mamoru3 ; HANADA, Hideo41

Dept. of Astronomical Science, SOKENDAI, 2 Hitotsubashi University, 3 National Institute of Information and Communications
Technology, 4 RISE Project Office, National Astronomical Observatory
In order to estimate lunar interior structure from lunar libration and tidal displacement, we are developing new analysis software for precise determination of lunar orbital/rotational motion using lunar laser ranging (LLR) observation data.
As the first step of the software development, we construct an LLR observation model. The model consists of the newest
physical models compatible with IERS Conventions (2010) such as Earth orientation, solid tides of the Earth and the Moon,
atmospheric delay correction, and some relativistic factors affecting laser propagation delay. For the purpose of calculating thesecomponents precisely, we use modules of the geodetic data analysis software ”c5++” [Otsubo et al., JpGU, 2011]. Comparison
between observed and calculated ranges is done by combining our own-developed observation model and the lunar orbit/libration
obtained from the numerical ephemeris DE430 (provided by NASA JPL). In this calculation, there are 3577 LLR normal points
distributed from June 1996 to July 2013, observed at Apache Point, Grasse, Matera and McDonald. The mean value of theresiduals of one-way ranges is about 5.7 cm, and the standard deviation is about 4.8 cm.
The following steps are numerical integration of lunar orbit and libration, and the least-squares fitting of integrated ephemeris
to observed values. As the date of the submission, only the orbital motion can be determined, and some relating parameters suchas positions of retroreflector arrays, lunar mass and the lunar displacement Love numbers are to be estimated. For the models
of lunar orbital motion, we implement post-Newtonian EIH equation of motion and perturbations from spherical harmonics ofgeopotential and J2 term of solar gravity field.
The presentation contains the current status of software development. We will report the results of above-mentioned observation modeling, numerical integration of lunar motion, and estimation of lunar physical parameters.
Keywords: Moon, lunar laser ranging; LLR, ephemerides, libration

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PPS03-07

Room:A03

Time:May 28 15:45-16:00

Summary of the development of a small telescope for lunar rotation and the experimentson the ground.
HANADA, Hideo1∗ ; TSURUTA, Seiitsu1 ; ASARI, Kazuyoshi1 ; ARAKI, Hiroshi1 ; NODA, Hirotomo1 ;KASHIMA, Shingo1 ; FUNAZAKI, Ken’ichi2 ; SATOH, Atsushi2 ; TANIGUCHI, Hideo2 ; KATO, Hiromasa2 ;KIKUCHI, Mamoru2 ; YOKOKAWA, Ringo2 ; SHINKE, Syota2
1

RISE Project, National Astronomical Observatory, 2 Faculty of Engineering, Iwate University

We have been developing a small telescope like Photographic Zenith Tube (PZT) for observations of lunar rotation since the1990s. We know the lunar rotation by positioning of stars from the lunar surface, and the accuracy of 1 milli-arc-second (1mas)
can detect components of physical librations related to dissipation in the Moon. Observation of lunar rotation is one of theessential and basic observations for investigating the interior of the Moon.
We have already developed a bread board model (BBM) of a PZT type telescope for basic experiments. Technical development
for improvement of the accuracy, environmental test of key elements were made by using the BBM. A new tripod makes it
possible to set the telescope on the slope of less than 30 degrees, and it keeps the tube vertical within the error of 20 arc-seconds.
PZT has a potential to observe deflection of the vertical (DOV) with an accuracy better than 0.1 arc-seconds on the ground. It will
be possible to reduce the effect of atmospheric turbulence to be smaller than 0.1 arc-seconds by statistical procedure of observed
data. It is also possible to reduce the effect of the ground vibrations to be less than 0.1 arc-seconds judging from the laboratory
experiments.
We performed observations on the ground in September of 2014, in order to check the total system of the telescope and thesoftware. It is also important to evaluate the effect of the ground vibrations and temperature change upon the stellar position
on CCD. The goal of the observations on the ground is to attain the accuracy of better than 0.1 arc-seconds. The results ofthe preliminary observations showed that the scatter of stellar positions was about 0.4 arc-seconds, which is a little larger than
expected. It is partly due to insufficient signal to noise ratio of star images. Verification of 1 mas on the Moon will be possible ina laboratory equipped with a special space chamber providing the environment on the Moon in the future.

Keywords: libration, PZT, telescope, mercury pool, lunar interior

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