STRUCTURE OF THE
MOON BY SEISMIC DATA
V.Yu. Burmin
Schmidt Institute of Physics of the
Earth, Russian Academy of Sciences,
Moscow, Russia
Introduction
Between 1969 and 1972 by the American lunar program "Apollo" was
deployed a network of high-sensitivity seismometers in the central part of
the visible side of the Moon. Seismometers, "Apollo" continued to work for
eight years, during which they passed on information about the natural
seismic activity of the Moon, and the structure of the lunar crust and upper
mantle. However, the deep portion of the Moon has remained inaccessible
to the Apollo seismic network. As a result of observing not only the physical
state and composition, but even the very existence of the lunar core
remains in question.
Since the seismic data, "Apollo" was impossible to determine the size and
physical condition of the lunar core, this information was obtained from the
study of the moment of inertia of the Moon, physical libration, and measurement of electromagnetic induction. As a result, it is assumed that the
Moon has a small (R <400 kms), perhaps partially liquid core. Suggestive
of its structure - it is solid solutions or melts of iron-nickel to Fe-FeS.
The first results of the velocity of seismic wave propagation in the interior of
the Moon were published Nakamura et al. in 1973, 1974. On left fig. shows
the travel-times of the first arrival of the P- and S-waves. In right fig. shows
the distribution of P-and S-wave velocities for the crust, mantle and core of
the Moon, obtained Nakamura et al. in 1974.
Hear in left fig. shows the velocity distribution of P- and S-waves in the crust
and mantle of the Moon to a depth of 800 kms, obtained Nakamura et al. in
1976 for the same travel-time curves. In right fig. shows the velocity
distribution of P- and S-waves in the crust and mantle of the Moon, obtained
Goins et al. in 1981. A comparison of these velocity curves shows that the
variation of velocities with depth in both figures differ slightly, but in right fig.
values of P-wave velocity is slightly lower than in the left fig. but S-wave
velocity at depths greater than 500 kms in right fig. conversely, higher than in left fig.
Here present the velocity curves
for P-and S-waves, which are
piece-wise constant function up
to a depth of 1000 kms
(Nakamura, 1983). From a
physical point of view, the
constant velocity in the range of
depths from 500 to 1000 kms is
not entirely justified, since the
density and elastic modulid varies
with depth.
Besides these, there are a number of more recent work on the velocity
structure of the moon . However, from my point of view, the subsequent
results of the interpretation of seismic data did not improve the previous
results. Due to the imperfections of the techniques, the results were
internally inconsistent, and significantly different from previous results,
especially in the middle and lower mantle of the Moon.
In recent years there appeared articles devoted to the refinement the
radius of the Moon’s core by seismic data.
In the article
(Garcia et al.,
2011) on reflected
shear waves the
estimations of a
core of 38040
kms and average
density 5.21.0
g/cm3 are given.
In (Weber et al., 2011) for
the reflected and converted
waves from the lunar core of
the proposed three-layer
model of the core. The
internal core of radius 240
kms is supposed solid. A
solid core surrounded by a
liquid outer core, the
thickness of which 90 kms.
Further assumed a
transitional layer of partially
molten core-mantle
boundary of 150 kms.
If the works to determine the velocity distribution in the interior of the Moon published
a lot, then the density distribution is studied in a much lesser extent. The most fully
investigated this question in the works of O. Kuskova and V. Kronrod.
In left fig. presents the density distribution in the lunar mantle for the two composite
models of the Moon obtained by the method Monte-Carlo and satisfying values of
seismic velocities, and mass and moment of inertia of the Moon.
In right fig. the acceptable variation of the density of the lunar mantle eutectic Fe-FeS
core with a radius of 100-200 kms.
Input data
The initial data for determining the velocity in the interior of the Moon were
taken record-section seismograms shown in fig. Records of seismic events
obtained from the radial long-period seismic stations of Apollo from falling
meteorites and events as resulting of dumping space station modules.
The results of determining the velocity of seismic waves in the mantle
The results of determining the velocities
of P- and S-waves are shown in figure.
Thickness of the crust according to
various sources varies from 30-45 kms to
60 kms. We have taken the crust
thickness 54 kms. The figure shows that
in the mantle of the Moon in the depth
range 120 - 480 kms there is a decrease
in the velocity of both P- and S-waves. In
the depth range 480 - 1100 kms of
seismic wave velocities change little and
remain almost constant. At a depth of 480
km there is a jump of velocities of P-and
S-waves, which caused a sharp change
in the apparent velocity of travel-time in
the values of 7.2 km/s to 7.8 km/s for Pwaves and from 4.2 km/s to 4.5 km/s for Swaves.
In this figure points are the experimental and lines are theoretical travel-time
curves P-wave obtained for the velocity distributions. From this figure it can
be clearly seen that the theoretical travel-time curves well fit the experimental points.
In this figure points are the experimental and line is theoretical travel-time curves
S-wave obtained for the velocity distributions. From this figure it can be
clearly seen that the theoretical travel-time curves well fit the experimental
points.
The density and elastic modules of the mantle of the Moon are
determined from the equations Williamson - Adams for a given velocity
distribution of P- and S-waves. To determine the distribution of velocities
of seismic waves at depths greater than 1100 kms we have not observed
data. Therefore, in contrast to the determination of the density in the core
of the Earth, which is known the depth of the mantle-core boundary
according to the reflected waves and the distribution of the velocity of Pwaves in the core, the Moon does not know exactly of any position of the
boundary mantle-core and the velocity distribution in the core. The initial
data for determining the radius four models of the core of the Moon
considered in accordance with results of Kuskov and Kronrod. For
calculations were taken one of the last values of the dimensionless
moment of inertia of the Moon – 0.3931 ± 0.02% (Konopliv et al., 1998).
The mass of the Moon was taken to be 7.349  1022 kg ± 0,1%.
The results of determinations are shown in next figures.
In figure shows the values of seismic velocities, density and elastic module
correspond to the iron-nickel composition of the core and are VP = 6.15
km/s, VS = 3.20 km/s,  = 8.10 g/cm3, r = 308.0 km.
Here shows the curves and the corresponding values of the elastic
parameters of the iron with a 10% admixture of the sulfur core. For such
core: VP = 5.81 km/s, VS = 2.96 km/s,  = 5.66 g/sm3, r = 400.0 km.
This figure corresponds to the eutectic (Fe-FeS) composition of the core.
For it the VP = 5.52 km/s, VS = 2.01 km/s,  = 5.15 g/cm3, r = 438.5 km.
Finally, in figure shows the distribution of seismic velocities, density and
elastic modules for troilit (FeS) core. In this case, VP = 5.22 km/s, VS = 1.31
km/s,  = 4.70 g/cm3, r = 492.0 km.
Summary and Conclusions
In this report, based on data obtained in the 70's Apollo program and a
better method of interpreting seismic data held redefinition of the velocity
distribution in the mantle of the Moon. Advantages of the method of interpretation is, first, to use the formulas for the invertion of discontinuous
travel-time, and secondly, what could be more important in the approximation of the observed travel-time convex cubic splines, which, unlike the
others, previously used, methods of determining the apparent velocities
are the best device for this purpose. As a result, velocity curves obtained
by best satisfying the observed data, ie, the experimental travel-times.
Thank you for your attention!