Gravity Gradiometry for Lunar Surface Exploration Kieran A. Carroll, Ph.D. Chief Technology Officer, Gedex Inc., 407 Matheson Blvd. East, Mississauga, Ontario, Canada L4Z 2H2,
[email protected]
Lunar Rock Detectability
Introduction
(The only off-Earth planetary surface gravity measurements made to date!)
Past Lunar surface exploration missions have employed various techniques to determine the nature of the Lunar surface and near-sub-surface, e.g.: •Geological techniques cameras, return of physical samples •Geochemical techniques neutron probes, gamma-ray spectrometers •Geophysical techniques active and passive seismic experiments, heat-flow probes, magnetometers, gravimeters (Fig. 1), a bi-static RF electrical-properties experiment, and active and passive Lunar radar sounders from orbit These and various other types of instruments have been considered for future Lunar surface exploration missions, including a rock abrasion tool such as that used on Mars rovers, scanning LIDAR for 3D mapping, alpha proton X-ray spectrometer, IR and UV multi-spectral cameras, ground-penetrating radar. Another type of geophysical instrument in common use for terrestrial exploration is the gravity gradiometer. Here we consider the question: Would a gravity gradiometer be a suitable instrument for Lunar surface exploration? (A full-length paper on this topic was published in [5].)
Terrestrial Gravity Gradiometry Surface-based: Torsion-balance gravity gradiometers based on the design of Eötvös were used for oil & gas exploration in the early 1900s (Fig. 2). These had an accuracy of ~ 1E, each measurement taking hours.
We carried out a forward modeling study to estimate gravity and gravity gradient signal strengths for rocks in the Lunar near sub-surface versus depth (Fig. 8, 9). To estimate density contrasts, a background regolith density of 1.6 g/cm3 was assumed (Fig. 6). Rock densities of (2.0, 2.5, 3.1, 8.0) g/cm3 were modeled, representative of highland rocks (e.g., Ferroan anorthosites, KREEP rocks, Mg-rich rocks), Mare basalts and meteoric nickel-iron respectively.
∂ϕ Γij = − ∂xi ∂x j 2
The gravity gradient is a 3x3 tensor of the second derivatives of the gravitational potential. It is measured in S.I. units of m/s2/m = s-2. Geophysicists use the eotvos unit, 1E = 10-9 s-2. Figure 6: Lunar regolith bulk density versus depth model derived from Apollo core samples [6].
The gravity gradient measured in a non-rotating reference frame is a second-order tensor, which when projected onto a reference frame is a 3x3 symmetric matrix.
Figure 7: Various conjectured Lunar sub-surface geological features of interest [6].
Undersea: The US Navy deployed gravity gradiometers on nuclear submarines in the 1970s, for mapping missile launch-site gravity fields.
Figure 4: The operating mechanism of an OQR type gravity gradiometer.
Gedex HD-AGG (1 sec)
Lunar Rover Gradiometer (10 sec) (60 sec)
m Lines represent spherical rocks of radii from 5cm to 2m with densities of 2.0, 2.5, 3.1 and 8.0 g/cm3
m
m
GOCE Gradiometer (10 sec)
Source Depth (m)
m
Gedex HD-AGGTM: Forward modeling and inversion studies indicate that many more economic deposits will be detectable if accuracy of 1E and spatial resolution of 50-100m (i.e., sampling at 1 Hz) can be achieved [2]. Gedex is developing a High-Definition Airborne Gravity GradiometerTM system to meet that performance spec., using an Orthogonal Quadrupole Responder (OQR) type instrument (Fig. 4, 5).
Figure 2: (left) Eötvös torsion-balance gravity gradiometer, (right) first field measurement station, ca. 1891 [3].
Gravity Gradient (E)
Instrument located 1m above the surface
Airborne: These naval gravity gradiometers were adapted for airborne use in the 1990s, and several are now flying mineral and oil & gas exploration surveys (Fig. 3), achieving ~ 5E accuracy with a spatial resolution of ~ 300m (sampling at 1/6 Hz) from fixedwing aircraft.
Figure 8: Peak gravity gradient signal (GZZ) from rocks buried in Lunar regolith (RMS, for several instruments and sampling times).
Gravity gradient makes beams “scissor” – this is what we measure
Instrument located 1m above the surface
Gravity (milliGal)
Space: The first use of a gravity gradiometer in space is the instrument on the GOCE Earth-orbiting satellite, which has achieved ~ 0.003E resolution at a 0.1 Hz sampling rate. However, this instrument is unsuitable for use on a planetary surface.
Fig. 7 illustrates some of these: • Resolve stratigraphy at a local and regional scale • Locate buried rocks and map ejecta deposits • Search for gravitational signature of the megaregolith boundary • Locate geological boundaries, faults, and buried craters • Map volcanic landforms and intrusive bodies • Search for lava tubes • Prospect for in-situ resources
Rover Mounted Gravity Gradiometer Instrument
Figure 1: The Apollo 17 Lunar Traverse Gravimeter was used to infer the presence of a 1 km thick basalt block beneath the Taurus-Littrow valley floor [1].
Γ xx Γ xy Γ xz Γ Γ Γ yx yy yz Γ Γ Γ zy zz zx
Some Lunar Surface Gravity Gradient Surveying Applications
Apollo 17 Traverse Gravimeter Experiment (60 sec) Scintrex CG-5 Relative Gravimeter (60 sec) Apollo 17 Lunar Surface Gravimeter (60 sec?) (did not work)
A Gedex instrument design study resulted in the following specifications: • Operating Mode: Take measurements while stationary, to minimize instrument noise • Measurements made: DC gravity gradient components and vertical gravity component • Gravity gradient components measured: GXX-GYY, GXX-GZZ, GYY-GZZ, GXY, GXZ, GYZ • Derived gravity gradient components: GXX, GYY, GZZ • DC Gravity gradient error: < 1 E (RMS) • DC Gravimeter (GZ ) error: < 1 milliGal (RMS) • Total measurement time per station: 10 minutes (longer measurements reduce RMS errors) • Horizontal resolution achievable: approx. equal to the depth of each density anomaly (Fig. 10). • Mass: < 15 kg • Size: < 35 x 35 x 30 cm • Challenges: • Bias and bias drift, achieving absolute gradient measurements • Correcting for instrument/rover self-gravity • Multi-station LIDAR mapping needed to allow topography corrections, and to determine measurement station locations accurately
Conclusions • Gravity gradient signals from near-surface rocks embedded in Lunar regolith are large enough to be detected easily using existing-technology gravity gradiometers. • The gravity signals from those rocks are barely detectable using the best existing gravimeters. • Requirements for a useful rover-mounted gravity gradiometer have been inferred from these results. • These are compatible with the expected performance of next-generation gravity gradiometer technology that Gedex is developing. • As with terrestrial exploration, we expect that geophysical data from multiple sources will be synergistic for Lunar sub-surface exploration. z
GYY
GXX
x
GZZ
y 5m
m
Source Depth (m)
Figure 3: Gzz from a 7x20 km airborne gravity gradiometry survey, Botswana, 2006 [4].
Figure 5: (left) Gedex’s HD-AGG instrument, (right top) installed in aircraft, (right bottom) HD-AGGTM airborne.
Figure 9: Peak gravity signal (GZ) from rocks buried in Lunar regolith (RMS, for several instruments and sampling times).
Figure 10: Gravity gradient components from a traverse over a 50-tonne spherical source, 5m sub-surface
References: [1] Talwani, M., “The Apollo 17 gravity measurements on the moon,” The Leading Edge, Society of Exploration Geophysicists, Vol.22, No.8, Aug. 2003, pp.786-789; [2] Carroll, K.A. & Annecchione, M., “Detectability of Natural Resource Structures by a Low-Noise Airborne Gravity Gradiometer System,” AGU, Fall Meeting 2009, San Francisco, abstract #NS33A-08; [3] Ádám J., “Geodesy in Hungary and the Relation to IAG around the turn of 19th/20th Century - A Historical Review,” The Geodesist's Handbook 2000, Journal of Geodesy, 74(2000), 1(7-14); [4] Hatch, D. et al., “Performance of the Air-FTG® System Aboard an Airship Platform,” Proc. Australian Earth Sciences Convention, July 2nd-6th, 2006, Melbourne Australia; [5] Carroll, K.A., “Gravity Gradiometry for Lunar Surface Exploration,” ASTRO 2010 – 15th CASI Canadian Astronautics Conference, Toronto, 4-6 May 2010; [6] Heiken, G.H., Vaniman, D.T., & French, B.M. eds, Lunar Sourcebook, Lunar and Planetary Institute, Houston, 1991.
