Physics of the Earth and Planetary Interiors 257 (2016) 187–192
Contents lists available at ScienceDirect
Physics of the Earth and Planetary Interiors
journal homepage: www.elsevier.com/locate/pepi
Letter
Insights into mare basalt thicknesses on the Moon from intrusive
magmatism
Chloé Michaut ⇑, Mélanie Thiriet, Clément Thorey
Institut de Physique du Globe de Paris, Université Paris Diderot, Sorbonne Paris Cité, F-75013 Paris, France
a r t i c l e
i n f o
Article history:
Received 25 February 2016
Received in revised form 24 May 2016
Accepted 27 May 2016
Available online 9 June 2016
Keywords:
Moon
Mare basalt thickness
Intrusive magmatism
Domes
a b s t r a c t
Magmatic intrusions preferentially spread along interfaces marked by rigidity and density contrasts. Thus
the contact between a lunar mare and its substratum provides a preferential location for subsequent
magmatic intrusions. Shallow intrusions that bend the overlying layer develop characteristic shapes that
depend on their radius and on the overlying layer flexural wavelength and hence on their emplacement
depth. We characterize the topography of seven, previously identified, candidate intrusive domes located
within different lunar maria, using data from the Lunar Orbiter Laser Altimeter. Their topographic profiles
compare very well with theoretical shapes from a model of magma flow below an elastic layer, supporting their interpretation as intrusive features. This comparison allows us to constrain their intrusion
depths and hence the minimum mare thickness at these sites. These new estimates are in the range
400–1900 m and are generally comparable to or thicker than previous estimates, when available. The largest thickness (P1700 m) is obtained next to the Hortensius and Kepler areas that are proposed to be the
relicts of ancient volcanic shields.
! 2016 Elsevier B.V. All rights reserved.
1. Introduction
Determining the thicknesses of the lunar maria is crucial to constrain the amount of melt produced in the lunar interior and the
thermal evolution of the Moon. Unfortunately, they are still poorly
constrained. Direct methods use radar sounding to detect interfaces within the subsurface. The lunar-orbiting Apollo 17 radar
sounding experiment first detected two interfaces at apparent
depths of 0.9 and 1.6 km in Mare Serenitatis and one at !1.4 km
in Mare Crisium (Peeples et al., 1978). More recently, the Lunar
Radar Sounder (LRS) of the SELENE mission has detected horizontal
subsurface interfaces at only a few hundred meters depth within
all major lunar maria (Ono et al., 2009; Pommerol et al., 2010).
The radar onboard of Chang’E 1 also detected several subsurface
interfaces in the northern Mare Imbrium, the deepest one at
!360 m (Xiao et al., 2015). However, this method is not able to discriminate between the base of the mare and interfaces in between
different flow units (Peeples et al., 1978; Ono et al., 2009; Xiao
et al., 2015).
Regional constraints on mare basalt thicknesses have been
placed by evaluating the difference between the observed topography of flooded basins and craters and their initial one, estimated by
⇑ Corresponding author.
E-mail address: [email protected] (C. Michaut).
http://dx.doi.org/10.1016/j.pepi.2016.05.019
0031-9201/! 2016 Elsevier B.V. All rights reserved.
comparison with basins and craters the same size (Head, 1982; De
Hon, 1979). However, the crater depth to radius relationship is
associated to relatively large uncertainties, especially for large
basins whose morphologies largely depend on the impactor and
target properties (Milković et al., 2013). Regional constraints on
mare thicknesses can also be given by studying the gravitational
signal recorded above the maria. Lunar maria are, however, often
coincident with lunar mascons, and a major difficulty is to extract
the signal due to the mare basaltic flows themselves from the signal coming from the processes of impact basin excavation, relaxation and cooling (Melosh et al., 2013; Gong et al., 2016).
Local constraints on mare thicknesses can be given by studying
the geological processes that deform them. For instance, impacts
lead to craters that open – or not – a window through the mare
on its substratum, providing in any case a constraint on mare
thickness at the impact site (Budney and Lucey, 1998; Thomson
et al., 2009). Alternatively, magmatic intrusions, intruding below
a lunar mare, can create characteristic surface deformations that
depend on the local mare thickness.
A dozen of low-slope lunar domes have been proposed as candidate intrusive domes, i.e. as being formed by magma spreading
below an elastic layer as laccolith intrusions (Wöhler et al., 2009;
Michaut, 2011). Most of them are situated within, though on the
side of, different maria. The absence of spectral contrast between
these domes and their surroundings and their elongated outlines
188
C. Michaut et al. / Physics of the Earth and Planetary Interiors 257 (2016) 187–192
compared to typical lunar extrusive domes were the first arguments in favor of their intrusive origin (Wöhler et al., 2009). Their
morphologies (shape, slope, radius) have previously been determined by morphometric measurements using telescopic images
acquired at oblique illumination (Wöhler et al., 2009). These measurements reveal low flank slopes between 0.2 and 0.6" and large
diameters between 10 and 30 km compared to terrestrial laccoliths
that are typically twice as small (Wöhler et al., 2009; Michaut,
2011). Using a model of magma spreading below an elastic layer,
Michaut (2011) has characterized the surface deformations
induced by shallow magmatic intrusions and has shown that the
size discrepancy between terrestrial laccoliths and candidate intrusive domes on the Moon could be well explained by differences in
gravity and magma viscosity in between lunar and terrestrial settings, supporting the intrusive interpretation.
This episode of magmatism occurred after extrusion of the
maria which have been raised by the intruding magma. The
magma could have been emplaced at the contact between the
mare and it substratum or in between different mare units, but
we suggest that the former is the most plausible scenario. By
studying the deformation affecting the mare basalt layer overlying
the intrusion, we place constraints on the local mare thickness. In
particular, the theory of magma flow below an elastic plate predicts that the intrusion shape depends on its radius and on the
overlying layer flexural wavelength, that itself mainly depends
on its elastic thickness (Michaut, 2011; Michaut et al., 2013;
Lister et al., 2013; Thorey and Michaut, 2014; Hewitt et al.,
2015). Here, we study the topography of these low-slope lunar
domes, located in different maria, using the high-resolution Lunar
Orbiter Laser Altimeter data from the Lunar Reconnaissance Orbiter. The observed shapes well correspond to the theoretical shapes
predicted by the model and we use these shapes to constrain the
local mare thickness.
2. Materials and methods
2.1. Model summary
We consider the axisymmetric spreading of magma below an
overlying layer of constant elastic thickness d and above a rigid
layer. We summarize below the model, which is described in detail
in several papers (Michaut, 2011; Michaut et al., 2013; Lister et al.,
2013; Thorey and Michaut, 2014). The flow driving pressure P is
the sum of the bending pressure due to the elastic deformation
of the overlying layer and the pressure due to magma weight:
3
Pðr; z; tÞ ¼
Ed
r4 hðr; tÞ þ qm gðhðr; tÞ % zÞ
12ð1 % m2 Þ r
ð1Þ
where r and z are radial and vertical coordinates, t is time, qm
magma density, hðr; tÞ intrusion thickness, g gravity, E Young’s mod! !
! """
ulus, m Poisson’s ratio, and r4r h ¼ 1r @r@ r @r@ 1r @r@ r @h
. By applying
@r
flow momentum and mass conservation, the following equation
for the evolution of the flow thickness with time and radial coordinate has been obtained (Michaut, 2011; Michaut et al., 2013; Lister
et al., 2013; Thorey and Michaut, 2014):
#
$
3
@h
Ed
@
3 @
¼
rh
ðr4r hðr; tÞÞ
2
@t 12ð1 % m Þ12gr @r
@r
#
$
qm g @
3 @h
þ wðrÞ
rh
þ
12gr @r
@r
ð2Þ
where g is magma viscosity and wðrÞ injection velocity, i.e. the
velocity given by a constant flux Poiseuille flow through a cylindrical central feeder conduit of diameter a.
Eq. (2), made dimensionless using a characteristic horizontal
scale K, vertical scale H and time scale s, becomes
#
$
#
$
@h 1 @
1 @
3 @
3 @h
¼
rh
ðr4r hðr; tÞÞ þ
rh
@t
r @r
@r
r @r
@r
%c
& 32 #1 r2 $
þH %r 2
%
2
c 4 c2
ð3Þ
where H is the Heaviside function, c ¼ a=K and
K¼
!1=4
#
$1=4
3
Ed
12gQ 0
pK2 H
H
¼
s¼
2
Q0
12qm gð1 % m Þ
pqm g
ð4Þ
where Q 0 is the constant volume flux through the feeder conduit
and K the flexural wavelength of the overlying elastic layer.
This equation was resolved using a pre-wetting film of negligible thickness hf compared to flow thickness to avoid divergent viscous stresses at the contact line between the rigid support and the
elastic overlying layer (Lister et al., 2013; Hewitt et al., 2015).
Numerical results show that the flow evolves following different
regimes (Fig. 1) (Michaut, 2011). In the first regime, the flow is controlled by the elastic deformation of the overlying layer and develops a bell shape described by the following function:
hðr; tÞ ¼ h0 ðtÞ 1 %
r2
RðtÞ2
!2
ð5Þ
where h0 ðtÞ is the flow height at the center r ¼ 0 and RðtÞ is the flow
radius. In this bending regime, gravity is negligible, the pressure is
constant over the flow interior and pressure gradients are localized
at the front. The maximum height h0 evolves with the radius R following a power-law relationship with an exponent equal to 8=7
(Lister et al., 2013), i.e. very close to 1 (Fig. 1). When the flow
reaches a critical size of !4K, the current enters an intermediate
regime where bending and gravity contributes almost equally to
the flow. In this regime, the height decreases with time, the current
flattens and the dimensional flow shape is described by (Lister et al.,
2013):
(
#
$#
#
$
#
$$)
R%r
R%r
R%r
hðr; tÞ ¼ h0 ðtÞ 1 % exp % pffiffiffiffiffiffiffi cos pffiffiffiffiffiffiffi þ sin pffiffiffiffiffiffiffi
2K
2K
2K
ð6Þ
Finally, when magma weight becomes dominant, the flow
evolves as a gravity current; the height evolves toward a constant
while the radius evolves with time following RðtÞ / t1=2 (Huppert,
1982; Michaut, 2011; Lister et al., 2013).
2.2. Dome topography
We draw the topographic profiles of candidate intrusive domes
proposed by Wöhler et al. (2009) using the 128 ppd (!236 m/pixel)
LOLA gridded topography, obtained from the Planetary Data System Geosciences Node and verified our results using the 256 ppd
data set. We compare their shapes to theoretical shapes derived
from the model, assuming the dome shape reflects the intrusion
shape. A bell-shape dome would characterize a dome that has
solidified in the bending regime and its radius R would be such that
R ' 4K. On the contrary, a flat-top dome would have a final radius
R ( 4K. Finally, the shape of an intrusion in the intermediate
regime would depend on K and hence on d following (6).
Over a total of 12 domes that have been observed by Wöhler
et al. (2009, 2010) using morphometric data, we have been able
to isolate and characterize the topography of 7 (Fig. 2). The other
domes were mixed with other types of relief and particularly difficult to isolate. Cross-sections going through the highest point of
each dome were realized in all directions. Topographic profiles
C. Michaut et al. / Physics of the Earth and Planetary Interiors 257 (2016) 187–192
189
Fig. 1. Left: intrusion central thickness normalized by H versus intrusion radius normalized by K, where H and K are given by (4). The intrusion successively evolves through
different regimes of propagation characterized by different shapes. The flow is first in an elastic bending regime with a bell shape (top right). At a radius close to 4K, it
transitions to an intermediate regime with a shape described by (6) (middle-right). Finally, as gravity becomes dominant, the flow becomes a gravity current with a flat-top
(bottom right) (Michaut, 2011; Lister et al., 2013).
Fig. 2. Topography of the different candidate intrusive domes (the color scale is in m). We use the 128 ppd (!236 m/pixel) LOLA gridded data set. In each pair of images, the
topographic profile in black (Left) represents the cross section along the black line on the map (Right). The red curve on the left images is the theoretical shape given by (5) in
the bending regime or by (6) in the intermediate regime. All profiles go through the dome maximum height. (For interpretation of the references to colour in this figure
caption, the reader is referred to the web version of this article.)
going through reliefs having no obvious links with the domes (i.e.
faults, local peaks, etc. . .) were discarded. For each retained crosssection we estimated a radius and a maximum height. The final
mean radius and maximum height of the dome were determined
from the average of these measurements while the associated error
bars were given by their dispersion. Using these morphological
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C. Michaut et al. / Physics of the Earth and Planetary Interiors 257 (2016) 187–192
dP
3qm gð1 % m2 ÞR4
43 E
!1=3
ð7Þ
which corresponds to a lower bound for the intrusion depth. For
typical values for the different parameters, E ¼ 5 ) 109 Pa, m ¼
0:25; g ¼ 1:62 m s%2 and qm ¼ 3000 kg m%3 (Wieczorek et al.,
2001; Thorey et al., 2015), these lower bounds range from 400 to
1900 m (Table 1).
Intrusions solidified in a bending regime and characterized by
a constant set of physical parameters (depth, viscosity and intrusion rate in particular) should plot on the same curve where
Fig. 3. Maximum thickness of the lunar intrusive domes obtained using the
topographic profiles as a function of radius (blue symbols) compared with values
obtained by morphometric measurements (red symbols) (Wöhler et al., 2009,
2010), in loglog scale. New values from topographic measurements are in general
larger than estimates from morphometric technics. Squares: domes with a bell
shape, Circle: dome with a flatter top. The trend h0 / R8=7 (Lister et al., 2013)
provides a relatively good fit to the data, suggesting similar conditions of intrusion.
The domes V1 and V2 are located next to each other in Mare Serenitatis. Error bars
were estimated from the dispersion of the radius and maximum height measurements made on different topographic profiles in different directions. (For interpretation of the references to colour in this figure caption, the reader is referred to the
web version of this article.)
parameters, we then compared the topographic profiles with the
theoretical shapes given by (5) and (6). The best correspondence
was defined from the one that minimized the differential between
the model and the altimetric profile.
3. Results
Dome heights are in the range 84–261 m and radius between
6.3 and 18.3 km. Though these values are coherent with estimates
from morphometric studies, the domes generally appear higher
than what was previously found by Wöhler et al. (2009). In particular, the domes M13 and L6 are significantly larger in height and
radius; only the dome Gr1 appears a bit shorter, for a comparable
radius (Figs. 2 and 3). In general, the topographic profiles compare
well with the theoretical shape of a subsurface intrusion solidified
in the bending regime: over the 7 domes whose topography has
been isolated, 6 show a good fit between their topography and
Eq. (5) (Fig. 2). This not only supports their intrusive nature but
suggests that they solidified in the bending regime implying that
their radius is such that R 6 4K. Given that K depends mostly on
the overlying layer elastic thickness, we obtain a minimum value
for d:
h0 / R8=7 in a thickness versus radius diagram. Intrusions defining
parallel trends with variable offsets on this diagram indicate the
variation of one of these parameters. In general, the domes are
very dispersed geographically and occur in different maria, their
morphologies should thus reflect different conditions of intrusion.
However, their thickness to radius relationship, as re-estimated
from our new topographic measurements, are relatively well fitted by a single line characteristic of a bending regime (Fig. 3).
The variability in intrusion depth (between >400 and 1900 m)
in between different mare implies a factor of maximum 3 variations in K that must be compensated by a factor of !3 variations
in H, where H and K are given by (4), for the data to plot on the
same curve. Such a variation can be accommodated by a variation
of maximum 100 of the value of lQ (4). Given the very large
range of possible values for this product (over at least 10 orders
of magnitude), this shows that the nature of the magma and conditions of intrusion were comparable, suggesting similar origins
(Michaut, 2011).
Domes V1 and V2 in Mare Serenitatis are the only domes
located next to each other (Table 1). The principle of parsimony
would guide us to interpret them as resulting from magmatic
intrusions characterized by similar parameters. Their thickness to
radius trend is not perfectly fitted by the scaling law for the bending regime (Fig. 3), but given the error bars, we can still interpret
them as resulting from two magma pulses of the same nature
intruding the same interface. We deduce that, for both domes, their
intrusion depth, and hence the thickness of Mare Serenitatis at this
site, is P1300 m.
The last dome whose topography has been isolated, Ar1e,
located in Mare Frigoris, shows a topography with a flatter top, that
is characteristic of an intrusion in a regime where both elastic
bending and magma weight are important. Although several
impacts have degraded the top of this dome, Eq. (6) fits very well
its overall shape (Fig. 2), for a flexural wavelength value of
K ¼ 2750 * 150 m, corresponding to an overlying layer thickness
value between 780 and 920 m.
4. Discussion and conclusion
The topography of the domes suggest that they formed by
intrusion of magma solidified in a bending regime or close to the
transition to the gravity current regime such as laccoliths on Earth
Table 1
Domes information. The radius and height of these domes were obtained using the 128 ppd LOLA topographic data set.
Dome
Long.
Lat.
Mare
Height (m)
Radius (km)
Shape
Depth (m)
Ar1e
V1
V2
C11
M13
L6
Gr1
1.05
10.20
10.26
36.75
%31.53
%29.16
%68.62
55.71
30.70
31.89
11.06
11.68
47.08
%4.45
Frigoris
Serenitatis
Serenitatis
Tranquilitatis
Insularum
Sinus Iridum
Grimaldi basin
125 * 15
162 * 11
102 * 10
84 * 9
261 * 11
103 * 12
165 * 9
12 * 1:9
15 * 1:5
6:3 * 0:7
10:2 * 1:4
18:3 * 1:8
12:5 * 0:7
12 * 1:1
Intermediate
Bell
Bell
Bell
Bell
bell
bell
850 * 70
P 1300 * 150
P 400 * 50
P 770 * 130
P 1680 * 220
P 1000 * 50
P 960 * 120
C. Michaut et al. / Physics of the Earth and Planetary Interiors 257 (2016) 187–192
(Michaut, 2011; Bunger and Cruden, 2011). On Earth, laccoliths
generally form in between sedimentary strata, along bedding
planes or interfaces in between different rocks characterized by
rigidity or density contrasts (Kavanagh et al., 2006; Walker,
1989; Pollard and Johnson, 1973). Similarly, these lunar laccoliths
probably formed along interfaces in between different mare flow
units or more likely at the base of the mare which should be
marked by a stronger rigidity and density contrast.
Our results also suggest that the magma forming these domes
was of similar nature and intruded at comparable rates. Thus, they
probably all result from the same magmatic episode, subsequently
to mare basalt extrusion. If, following mare basalt extrusion, the
magma became drier or richer in crystals, because formed at a
lower temperature, (or both), its buoyancy would be reduced,
favoring an intrusion of magma below the previously erupted
magma, while its viscosity would increase, favoring thick,
laccolith-type intrusions such as those observed here. Thus, an
evolution of the melt composition toward a more crystal-rich
and volatile-poor magma in the mare source region could well
explain these features.
Using our theoretical model, we obtain lower bound for the
elastic thicknesses of layers overlying the intrusions between 400
and 1900 m. As argued above, these estimates probably reflect
the local thicknesses of the maria if the pile of basaltic flow layers
forming the mare behaved as a coherent elastic unit. In particular,
our results suggest that the border of Mare Serenitatis, at the site of
domes V1 and V2, is thicker than !1300 m. This values fits well
with the deepest reflector detected at an apparent depth of
1.6 km in Mare Serenitatis by the Lunar Sounder Experiment
(Peeples et al., 1978). In the same area, De Hon (1979) proposed
a thinner value of 1000 m. Within Mare Serenitatis but further
East, Weider et al. (2010) estimated the thickness of 6 different layers, for a total of about 1500 m, a value that also compares well
with our estimate. For the mare in Sinus Iridum, we obtain a thickness larger than 1000 m at the site of dome L6, in agreement with
the study of De Hon (1979). Within the Grimaldi Basin we obtain a
comparable thickness of order a kilometer (i.e. P960 m), which
provides the first thickness estimate at this site. The border of Mare
Tranquilitatis at the site of dome C11 appears thicker than !770 m
also in good agreement with the isopach map of De Hon and
Waskom (1976) which shows a value in between 500 and
1000 m at this site. Our method also allows to well constrain the
thickness of Mare Frigoris, one of the least studied mare, in the
range !800–900 m below Ar1e. Finally, our largest value is found
in Mare Insularum, at the site of dome M13, which shows a minimum thickness of 1680 m, a much thicker value than what was
proposed by De Hon (1979). This dome borders the Hortensius
and Kepler areas, two areas that were proposed by Spudis et al.
(2013) as being ancient lunar volcanic shield complexes. The
recent study of Gong et al. (2016) that uses GRAIL’s gravity data
to constrain mare thicknesses also situates the thickest pile of
mare basalt next to the Marius Hill area.
These intrusive domes are only detected within relatively small
maria (Grimaldi Basin, Mare Frigoris) or on the border of the largest basaltic maria (Mare Serenitatis, Cauchy region of Mare Tranquilitatis and Hortensius to Kepler areas). The center of the largest
maria may have been too thick to allow for their bending and dome
formation at the surface. However, late-stage eruptive units in
basin-filling mare also preferentially occurred on the basin margins (Solomon and Head, 1979; McGovern and Litherland, 2011).
Together, these observations more likely suggest that the compressional stress state in the upper elastic lithosphere due to the
weight of the basins shut off magma ascent in the basins center
and favored its lateral transport to more distal locations
(Solomon and Head, 1979, 1980; McGovern and Litherland, 2011;
McGovern et al., 2013).
191
Acknowledgments
The authors thank Patrick J. McGovern and an anonymous
reviewer for their thoughtful comments on the manuscript. The
authors acknowledge the financial support of the UnivEarthS Labex
program at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11IDEX-0005-02) as well as the PNP/INSU/CNES. The python library
used to extract lunar surface images and topographic profiles is
freely available on Github: https://github.com/cthorey/pdsimage.
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