The lunar mascon basins have strongly free air gravity anomalies, generally exceeding 100 milligals at an elevation of 100 km. The source of the anomalies is a combination of mantle uplift beneath the impact basins and subsequent infilling by high-density mare basalts. The relative contribution of these two components is still somewhat uncertain, although it is generally accepted that the amount of mantle uplift greatly exceeds the thickness of the basalts. Extensive studies have been carried out of the crustal structure of mare basins, based on gravity data, and their tectonic evolution, based on compressive and extensional tectonic features. The present study endeavored to develop a unified, self-consistent model of the lunar crust and lithosphere incorporating both gravity and tectonic constraints

Thurber, Clifford H.

English

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FINAL TECHNICAL REPORT 
Investigation of Lunar Crustal Structure and Isostasy 
Grant No. NAGW-760 
Principal Investigator: Clifford H. Thurber 
Dept. of Earth & Space Sciences 
SUNY at Stony Brook 
Stony Brook, NY 11794 
Project Period: 8/ 1 / 85  to 713 1 /87 
Report date: July 1987 
(6ASA-CR-181071) INVESTIGA2ICN CrF LUBAB ~ a 7 - 2 5 2 5 a  C f i E S l l A L  S I R U C I O K E  AID ISCSSAEY i i n a l  
Technical Regort 
12 p A v a i l :  1111s HC A 0 2 / B 2  A01 CSCL 03B Unclas 
( S t a t e  Univ. of Neu York) 
G3/Y1 6080151 
https://ntrs.nasa.gov/search.jsp?R=19870015825 2020-03-20T10:45:30+00:00Z
Investigation of Lunar Crustal Structure and Isostasy 
This project was originally conceived as a two-prong attack on the 
problem of the structure and isostatic state of the lunar crust, at a total 
projected cost of about $73,000. The project was started up with a funding 
level of $18,500, but notification of funding was quickly followed by a letter 
(included as Appendix A )  indicating the extreme unlikelihood of further 
funding. Thus one project task (crustal structure) was abandoned in favor of 
accomplishing at least part of the other task (isostatic state). 
Background 
The lunar mascon basins [Muller and Sjogren, 19683 have strongly 
positive free air gravity anomalies, generally exceeding 100 milligals at an 
elevation of 100 km. The source of the anomalies is a combination of mantle 
uplift beneath the impact basins and susequent infilling by high-density 
mare basalts. The relative contribution of these two components is still 
somewhat uncertain, although it is generally accepted that the amount of 
mantle uplift greatly exceeds the thickness of the basalts IBratt et al., 19851. 
Extensive studies have been carried out of the crustal structure of 
mare basins, based on gravity data [Bowin et al., 1975; Sjogren and Smith, 
1976; Thurber and Solomon, 1980; Phillips and Dvorak, 198 1; Janle, 198 1 a,b; 
Bratt et ai., 19851, and their tectonic evolution, based on compressive and 
extensional tectonic features [Solomon and Head, 1979; Comer et al., 1979; 
Solomon and Head, 19801. The present study endeavored to develop a 
unified, self-consistent model of the lunar crust and lithosphere 
incorporating both gravity and tectonic constraints. 
Method 
My approach to investigating the isostatic state of the lunar crust was 
to evaluate the capability of separating the contributions to the lunar gravity 
field due to crustal thickness variations, such as those determined by 
Thurber and Solomon (19781 and Bratt et al. [1984), from those due to 
flexural support of the mascon basin loads by the lunar elastic lithosphere. 
To this end, a computer program was developed to forward-model the 
gravitational signature of elasically-supported mare basin fill. The principal 
variables are the elastic lithosphere thickness and the excess mass of the 
mare basalt fill. 
The computer algorithm brings together the method for computing 
flexural deformation of an elastic lithosphere due to a cylindrical load 
[Brotchie and Silvester, 19691 with a novel expansion method for evaluating 
the gravity anomaly of a cylindrical anomalous mass, developed previously 
by the Principal Investigator (see Appendix B). Figure 1 illustrates the 
components of the procedure. The estimated excess mass load of the basalt 
fill of each mascon, approximated by a cylinder, deforms the Moon's elastic 
lithosphere. The lithosphere thickness for the basins have been estimated 
independently from flexurally-induced tectonic features: rilles and ridges 
(Solomon and Head, 19801. Deformation of the lithosphere gives rise to 
additional contributions to the gravity field, due to depression of the 
relatively low density crust, and uplift of the flexural bulge. Cylindrical 
approximations to these anomalous masses are deter mined, and the total 
resultant gravity anomaly field (mare fill, crustal depression, bulge uplift) is 
evaluated using the disk expansion. 
Parame ters and results 
Figure 2, from Solomon and Head [ 19801, shows the mare basins 
considered, along with lithosphere thickness estimates based on rilles (early 
stage loading) and ridges (late stage loading). The near-side Bouguer gravity 
anomaly map for the Moon, which primarily represents the signature of the 
mascons, is given in Figure 3. The gravity field is evaluated at a uniform 
elevation of 100 km above the means lunar surface. 
I have applied this program to evaluate the ability to use the near- 
side gravity data to resolve the flexural component of the gravity field. In 
this way, an independent estimate of the Moon's elastic lithosphere thickness 
could be derived. One could then investigate whether the tectonically- 
derived value of lithosphere thickness was "frozen into" the flexural 
signature of the gravity field at the time of loading, in a manner similar to 
that proposed for the Earth's ocean basins [Watts, 19781. Unfortunately, the 
results are negative. Figure 4 indicates the tiny difference the effect of 
flexural support contributes to the gravity field around Mare Crisium even 
when the lithosphere thickness there is varied from 80 km (the rille 
estimate) to 125 km (the ridge estimate). Thus the existing global gravity 
data cannot be used to derive independent constraints on the lunar 
lithosphere thickness. 
References 
Bowin, C., B. Simon, and W. R. Wollenhaupt, Mascons: A two body solution, 
j- Geophys. Res. 80,4947-4935, 1975. 
Bratt, S. R., S. C. Solomon, J. W. Head, and C. H. Thurber, The deep structure of 
Lunar Basins: Implications for basin for mation and modification, 
J. Geophys. Res. 90,3049-3064, 1985. 
Brotchie, J. P., and R. Silvester, On crustal flexure, J- Geophys. Res. 74, 
5240-5252, 1969. 
Janle, P., A crustal gravity model of the Mare Serenitatis - Mare Crisium area 
of the Moon, J. Geophys. 49, 57-65, 1981a. 
Janle, P., A lunar crustal gravity model across the Triesnecker - hyginus area, 
Mare Tranquilitatis and Mare Fecunditatis, Moons m d  Planets 24, 
441-451,1981b. 
Muller, P. M., and W. L. Sjogren, Mascons: Lunar mass concentrations, 
Science 16 1 , 680-684, 1968. 
Phillips, R. J., and J. Dvorak, The origin of lunar mascons: Analysis of the 
Bouguer gravity associated with Grimaldi, Multi-ring Basins, hoc. 
Lunar Planet. Sci. Conf. 12th, 91-104, 1981. 
Sjogren, W. L., and J. C. Smith, Quantitative mass distribution models for 
Mare Orientale, Proc. Lunar Planet. Sci. Cod. 7th, 2639-2648, 
1976. 
Solomon, S. C., and J. W. Head, Vertical movement in mare basins: Relation to 
mare emplacement, basin tectonics, and lunar thermal history, J. 
Geophys. Res. 84,1667-1682,1979. 
Solomon, S. C., and J. W. Head, Lunar mascon basins: Lava filling, tectonics, 
and evolution of the lithosphere, Rev. Geophys. Space Phys. 18, 
107-141, 1980. 
Thurber, C. H., and S. C. Solomon, An assessment of crustal thickness 
variations on the lunar near side: Models, uncertainties, and 
implications for crustal differentiation, hoc. Lunar Planet. Sci. 
Cod. 9th, 348 1-3497, 1978. 
Watts, A. B., An analysis of isostasy in the world's Oceans 1. Hawaiian- 
Emperor seamount chain, J. Geophys. Res. 83,5989-6004, 1978. 
Figure 1. Schematic diagram of the approach for calculating the flexure 
and resultant gravity field due to a mascon load. The top 
cylinder represents the excess density of the mascon, while 
the bottom two represent density deficiencies due to flexure 
of the lunar crust. A positive annulus of density is used to 
represent the flexural bulge. 
ORIaNAL PAGE IS 
OF POOR QUALITY 
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Figure 4. Comparison of computed gravity anomalies around 
Mare Crisium for thin (top) versus thick (bottom) 
lithosphere thickness estimates. Differences are 
in the milligal and below range. 
National Aeronautics and 
Space Administration 
Washington, D C 
20546 
A p p e n d i x  A 
Dear Colleague: 
The FY 86 budget as submitted by the President to Congress will affect the 
planetary geology and geophysics program as part of the larger solar system 
exploration program. 
a reduction of about 300K. 
increased 600K above the FY 85 level, the overall reduction reflects a cut of 
about 900K from data analysis (outer planets and Venus) projects. 
projects now classified as data analysis either belong in the core program or 
will provide iaportant contributions to the interpretation of new data from 
Galileo and VR!!, :he next two NASA planetary missions, as well as the Voyager 
Uranus encounter. For this reason, most of the data analysis programs will 
necessarily coa9ete with eldments in the SRdT core program, and some are 
already being rezusigczd to the core program. 
The present outlook for geology and geophysics indicates 
Although core SRCT funds for our programwere 
Many of the 
The inpact of t52 funding reduction will be felt in several ways: 1) most 
principal inves52ztors will have to lower sights and trim their funding 
requests, 2) soae P.I.'s nay suffer substantial cuts in their proposed 
budgets. This -ill 5e particularly true for projects where overlap or 
duplication of effort occurs and where little progress is shown in the work, 
3) aspiring new P.I.'s, research assistants, graduate students, and other 
skilled personnel kill probably be most affected. 
unfortunately (and inopportunely) our annual brochure proclaiming 
opportunities in geology and geophysics will soon be distributed to 
universities and colleges. 
This at a time when 
There nay be other adverse effects not yet realized, and I solicit your help 
in bringing these to light -- but thoughtfully and without over dramatizing 
their consequence. More importantly, it is very necessary to increase our 
visibility on the positive side. To this end, it would be very helpful to 
receive a brief description or outline of significant discoveries or new 
concepts developed from your work. 
on your T43's, but sometimes their importance is obscure or not fully 
recognized in this reporc form. 
need further amplification please follow through on this and send them to me; 
your comments will be appreciated. 
Ordinarily these accomplishments are shown 
If YOU believe that results from your work 
Sincerely, 
/&<&A?/J& 
David H. Scott 
Discipline Scientist 
Planetary Geology and Geophysics Program 
Solar System Exploration Division 
Office of Space Science and Applications 
Amendfx B 
Binomial expansion method for calculating the 
gravity anomaly due to a thin disk. 
The integral representation for the potential at point r of an infinitely 
thin disk of radius a, surface density d, centered at the coordinate origin, is 
given by: 
where G is the gravitational constant (see Figure B 1 1. The distance between 
points and rl can be expressed as 
where X is the angle between r and L. We can factor out the quantity 
(r* + r'2) from the right hand side of B2 and define q as 
and then rewrite B1 as 
U(r) - Gd 4' J2' r'/(r* + r.2) (1 - 2q cos X)-'12 r' d e  dr' (B4) 
We can substitute the binomial expansion of the last term in B4, given in 
closed form by 
If we now replace cos X with (sin l3 cos e) and integrate over de, the odd 
powers of n drop out, so replacing n with Zk, we are left with 
e 
U(t) - 2gGd Eo (4k)1/[Z4' (k02 (Zk)!] (sin 8)*' ofa q2' r' dr' (B6) 
The remaining integration can be solved easily by parts for any power k. 
Figure B 1 .  Geometry and notation fo r  the disk mass potentlal expansion. 


Investigation of lunar crustal structure and isostasy

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