Detection and characterization of buried lunar craters with GRAIL data

Accepted Manuscript

Detection and Characterization of Buried Lunar Craters with GRAIL Data Rohan Sood, Loic Chappaz, Henry J. Melosh, Kathleen C. Howell, Colleen Milbury, David M. Blair, Maria T. Zuber PII: DOI: Reference:

S0019-1035(17)30158-6 10.1016/j.icarus.2017.02.013 YICAR 12374

To appear in:

Icarus

Received date: Revised date: Accepted date:

29 February 2016 7 February 2017 9 February 2017

Please cite this article as: Rohan Sood, Loic Chappaz, Henry J. Melosh, Kathleen C. Howell, Colleen Milbury, David M. Blair, Maria T. Zuber, Detection and Characterization of Buried Lunar Craters with GRAIL Data, Icarus (2017), doi: 10.1016/j.icarus.2017.02.013

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ACCEPTED MANUSCRIPT

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Highlights

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• Gravity mapping observations from NASA’s GRAIL mission are employed

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to detect, characterize and validate the presence of large impact craters

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buried beneath the lunar maria. • Gravity gradiometry detection strategy is applied to both free-air and Bouguer

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gravity field to identify gravitational signatures that are similar to those ob-

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served over buried craters.

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• The presence of buried craters is further supported by individual analysis

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of regional free-air gravity anomalies, Bouguer gravity anomaly maps, and

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• Other large, still unrecognized, craters undoubtedly underlie other portions of the Moon’s vast mare lavas.

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forward modeling.

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Detection and Characterization

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of Buried Lunar Craters with GRAIL Data

Rohan Sood a,b , Loic Chappaz a , Henry J. Melosh c ,

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Kathleen C. Howell a , Colleen Milbury c , David M. Blair d , and

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Maria T. Zuber e

Purdue University, West Lafayette, IN 47907 (U.S.A.)

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of Aeronautics and Astronautics,

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a School

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b Current

affiliation: Department of Aerospace Engineering and Mechanics,

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The University of Alabama, Tuscaloosa, AL 35487 (U.S.A.)

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c Department

d Haystack

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e Department

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of Earth, Atmospheric and Planetary Sciences,

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Massachusetts Institute of Technology, Cambridge, MA 02139-4307 (U.S.A.) c 2015 Rohan Sood, Loic Chappaz, Henry J. Melosh, Copyright

Kathleen C. Howell, Colleen Milbury, David M. Blair, and Maria T. Zuber

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Observatory, Massachusetts Institute of Technology, Westford, MA 01886-1299 (U.S.A.)

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Purdue University, West Lafayette, IN 47907 (U.S.A.)

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of Earth, Atmospheric, and Planetary Sciences,

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Number of pages: 46

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Number of tables: 4

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Number of figures: 31

Preprint submitted to Icarus

23 February 2017

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Proposed Running Head:

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Buried Lunar Craters.

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Please send Editorial Correspondence to:

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Rohan Sood

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Department of Aerospace Engineering and Mechanics

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The University of Alabama

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238 Hardaway Hall

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401 7th Ave., Box 870280

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Tuscaloosa, AL 35487, USA

Email: [email protected]

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Phone: (765) 409-2871

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ACCEPTED MANUSCRIPT ABSTRACT

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We used gravity mapping observations from NASA’s Gravity Recovery and

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Interior Laboratory (GRAIL) to detect, characterize and validate the pres-

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ence of large impact craters buried beneath the lunar maria. In this paper

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we focus on two prominent anomalies detected in the GRAIL data using the

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gravity gradiometry technique. Our detection strategy is applied to both free-

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air and Bouguer gravity field observations to identify gravitational signatures

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that are similar to those observed over buried craters. The presence of buried

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craters is further supported by individual analysis of regional free-air gravity

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anomalies, Bouguer gravity anomaly maps, and forward modeling. Our best

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candidate, for which we propose the informal name of Earhart Crater, is ap-

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proximately 200 km in diameter and forms part of the northwestern rim of

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Lacus Somniorum, The other candidate, for which we propose the informal

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name of Ashoka Anomaly, is approximately 160 km in diameter and lies com-

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pletely buried beneath Mare Tranquillitatis. Other large, still unrecognized,

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craters undoubtedly underlie other portions of the Moon’s vast mare lavas.

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Keywords: MOON; MOON, INTERIOR; MOON, SURFACE; CRATERING

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Introduction

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NASA’s Discovery Program has supported a series of low-cost scientific and

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exploration missions. Among these, the Gravity Recovery and Interior Lab-

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oratory (GRAIL) mission focused on high quality mapping of the Moon’s

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gravitational field. Launched in 2011, the sister spacecraft, Ebb and Flow,

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entered lunar orbit on December 31, 2011 and January 1, 2012, respectively,

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after a 3.5 month low-energy cruise phase. GRAIL’s Primary Mission lasted

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for a period of 88 days during which the two spacecraft mapped the lunar

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gravity (Zuber et al., 2012) from an average altitude of 55 km. The technique,

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satellite-to-satellite tracking, employed for mapping the Moon is similar to

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that used by Gravity Recovery and Climate Experiment (GRACE) to map

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the Earth’s gravitational field. GRAIL’s Extended Mission began on August

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8, 2011 during which the altitude of the dual spacecraft was lowered to ap-

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proximately 23 km and additional gravitational data was collected. A final

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phase at still lower altitude mapped the Orientale basin at particularly high

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resolution before the two spacecraft exhausted their remaining propellant and

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on December 17, 2012, were steered to an impact on the lunar surface.

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One of the overarching objectives of the investigation reported in this paper is

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the detection, characterization and validation of the existence of buried craters

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within lunar maria. These craters form a subset from among numerous other

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types of subsurface features on the Moon. Although the surface topography is

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easily destroyed by later impact events, the configuration of the crust-mantle

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interface is much less easily altered and thus will survive even if the surface

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has been modified beyond easy recognition. The quasi-circular anomalies de-

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tected are consistent with the work carried out by Neumann et al. (2015) 5

ACCEPTED MANUSCRIPT and Evans et al. (2016) that have identified buried craters due to the density

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contrast between the surrounding crust and mantle material uplifted by the

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excavation of large impact craters. The origin of the impact plays a critical role

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in determining the shape of the density contrast along with any subsequent

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events that may alter the gravitational footprint of the anomaly. In particular,

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the proposed Earhart crater predated Serenitatis and was almost completely

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overprinted by the impact that resulted in the formation of Serenitatis that

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was subsequently followed by volcanism, thus flooding the basin with lava

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basalts.Previous work by Chappaz et al. (2014) employed a detection strategy

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based on gravity gradiometry to detect subsurface features such as buried lava

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tubes.

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The gradiometry method has long been used for prospecting for oil, gas and

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minerals on the Earth (Mueller, 1964). It focuses on determining the second

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horizontal derivatives of the gravitational potential, which can then be inter-

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preted to delineate subsurface density variations. Our implementation begins

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with the spherical harmonic gravity field of the Moon derived from GRAIL

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data (Zuber et al., 2013). The spherical harmonic data are truncated and ta-

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pered to a predetermined degree and order to enhance the short wavelength

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Technique

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structures of interest. For any scalar field, a widely employed method to detect

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or highlight ridges or valleys within the field of interest involves the computa-

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tion of the Hessian matrix, and consequently, the eigenvalues and eigenvectors

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that are associated with the Hessian of the scalar field. The Hessian of the

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gravitation potential is defined as the matrix of second partial derivatives of 6

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the potential function with respect to the spherical coordinates of the position

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vector, i.e.,

Hij =

∂ 2U ∂xi ∂xj

(1)

where xi , xj = (λ, φ, r), and, λ is longitude, φ is latitude and r denotes the

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radial distance. In essence, the eigenvalue of largest magnitude and the corre-

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sponding eigenvector are associated with the direction of maximum gradient in

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the field. In this investigation, similar to the development in Andrews-Hanna

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et al. (2013), eigenvalue maps that depict the magnitude of the largest mag-

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nitude eigenvalue for each point on a grid of the lunar surface are produced.

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Either the free-air potential or the Bouguer potential (which corrects the free-

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air potential for topography and terrain by assigning a nominal density of 2560

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kg/m3 , the Moons average crustal density) can be employed in the analysis, de-

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pending on the objective. For the purpose of this investigation, localized maps

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that focus on specific regions are most relevant. A negative density anomaly

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(that creates a trough in the potential) corresponds to a positive eigenvalue on

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the gradiometry map, or eigenvalue map, because of the additional derivative

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of the potential function in the computation of the Hessian.

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This detection strategy, based on maximum eigenvalue, is used in conjunction

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with traditional free-air and Bouguer gravity maps. Related technique relying

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on anti eigenvalue has also been proposed to detect buried craters (Evans

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et al., 2016). To further support our interpretation we use forward modeling to

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validate the existence of a buried crater, as well as comparison with the gravity

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signatures of known unburied craters of similar size. Our analysis focuses on

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two features within Mare Tranquillitatis and Mare Serenitatis. The first feature 7

ACCEPTED MANUSCRIPT is completely buried by subsequent volcanic flows, whereas the second feature

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is only partially buried, although it was never previously recognized as a crater

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until gravity data became available. The density contrast between the buried

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feature and the overlying mare basalt, in addition to a central anomaly created

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by the mantle uplift beneath these large craters, produce gravity signatures

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that permit the identification of these distinct quasi-circular anomalies.

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Because the Moon lacks an atmosphere, as well as fluvial and sedimentologi-

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cal processes and plate subduction, impact craters are typically well preserved

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by terrestrial standards. Nevertheless, later impacts may alter a preexisting

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crater or even completely remove any visible topographic evidence of its former

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presence or may be covered under the ejecta blanket of the nearby impacts.

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Additionally, volcanic activity and subsequent emplacement of thick piles of

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mare basalt flows can be especially effective in burying existing craters ei-

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ther partially or completely. A widely cited lunar ‘ghost’ crater is the 112-km

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diameter Flamsteed P ring located in southern Oceanus Procellarum as il-

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lustrated in Figure 1. The interior of Flamsteed P is completely filled with

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mare basalt. The discontinuous ring of hills are believed to be remnants of

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Buried Craters

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the crater rim, making the Flamsteed P ring a prime example of a crater that

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was nearly, but not quite completely, buried by basalt flows. Smaller craters,

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craters with lower rims, or those buried by thicker basalt piles, however, may

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be completely obscured. Thus, visual detection based on regional imagery may

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not be effective in identifying completely buried craters. 8

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Fig. 1. Flamsteed P ring forming a discontinuous ring of hills. Courtesy: NASA/Lunar and Planetary Institute, Lunar Orbiter 4, image 143, h3.

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Detection of Buried Craters

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The non-circularity of the gravitational footprint of the features can be further

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analyzed within the context of the interpreted impact origin. The anomalies

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under investigation in this paper closely resemble approximately 100 large

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quasi-circular positive Bouguer anomalies revelaed by GRAIL data. Neumann

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et al. (2015) interpreted these non-circular and circular anomalies as due to the

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density contrast between the surrounding crust and mantle material uplifted

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by the excavation of large impact craters. A large number of these anomalies

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are unambiguously associated with known impact basins or peak-ring craters,

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although 16 (Neumann et al., 2015, table S6) of these anomalies are described

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as the traces of otherwise obliterated ancient impact craters. Evans et al.

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(2016) further identified 104 circular (positive and negative) Bouguer anoma-

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lies in the Moons mare regions which they interpreted as complex impact 9

ACCEPTED MANUSCRIPT craters flooded by basalt, an interpretation based on the circularity and size

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of the anomalies, although not supported by the type of detailed modeling

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reported in this paper. Both of these papers assumed that the anomalies were

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associated with impact craters rather than volcanic intrusions because of the

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near-circular pattern of the anomalies, which ranged in diameter from 30 to

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150 km (Evans et al., 2016) and 100 km or more (Neumann et al., 2015),

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and in magnitude up to several hundred mgal. An alternative interpretation

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is that these anomalies are caused by subsurface igneous intrusions. However,

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volcanic intrusions only rarely approximate a circular disk of the observed di-

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ameter (most such intrusions are linear) and the magnitude of the anomalies,

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typically more than 100 mgal, would require thickness of intrusive magma of

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more than 5 km, assuming a density contrast between intrusive rock and the

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surrounding crust of 500 kg/m3 . This thickness greatly exceeds that of most

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terrestrial intrusions and, moreover, would be expected to uplift the overlying

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crust into a positive relief feature resembling a broad laccolith, which is at

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odds with the lack of observed topographic expression for our two features.

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The gravity signatures of volcanic intrusions most similar to those we report

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are found in floor-fractured craters, which are believed to form when igneous

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intrusions uplift the floors of craters ranging between 10 and 200 km in di-

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ameter. A recent study of such craters by Jozwiak et al. (2016) shows that

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the Bouguer anomalies of the intrusions are seldom circular, are associated

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with non-axisymmetric domed uplifts and volcanic features, are usually offset

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from the crater center, and are typically only a few tens of mGal, approaching

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100 mGal only in the case of Humboldt crater. Even in this case, Jozwiak

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et al. (2016) attribute most of the anomaly to mantle uplift beneath this large

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(207 km diameter) crater. The best-known volcanic intrusion on the Moon 10

ACCEPTED MANUSCRIPT is probably the highly volcanic Marius Hills region, which is marked by a

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broad topographic swell that rises about 500 m above the surrounding plains

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and possesses a quasi-circular positive Bouguer anomaly that ranges up to

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about 100 mGal. This positive anomaly is surrounded by an annular negative

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anomaly of about -50 mGal that resembles a flexural moat. As we show in

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the Supporting Material, a gravity gradient analysis of the Marius Hills re-

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gion does not exhibit the same degree of circularity of either of our Earhart

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or Ashoka anomalies.

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In the current investigation, two features are presented as a part of detec-

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tion and validation efforts. The apparent features investigated include a com-

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pletely buried anomaly within northern Mare Tranquillitatis and the partially

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buried rim of what is almost certainly an impact crater lying in the north-

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western region of Lacus Somniorum (northeast of Mare Serenitatis). In this

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paper, the provisional name “Ashoka” is adopted for the Mare Tranquillitatis

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anomaly and “Earhart” for the barely-visible crater in Lacus Somniorum. Ap-

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parently,“Earhart” has never been previously recognized as a crater but, based

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on the knowledge of the quasi-circular gravity anomaly location, it is possible

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to visualize an incomplete quasi-circular structure in the surface topography

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(Figure 7). These provisional names were selected to honor Ashoka Maurya,

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in whose kingdom was situated Lonar, India’s first known impact crater (and

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one of a very few terrestrial craters in basaltic rock), and Amelia Earhart, a

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female explorer and early aviatrix, respectively. 11

ACCEPTED MANUSCRIPT 4.1 Speculated Buried Crater 1 (Ashoka)

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The first subsurface anomaly under investigation lies at the northern edge of

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Mare Tranquillitatis. The vicinity around the Ashoka anomaly is filled with

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mare basalt and has been subjected to subsequent impacts as apparent in

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Figure 2 using topography data collected by LOLA. The figure is centered

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around the speculated buried crater. Recent work by Robinson et al. (2012)

Fig. 2. Local topography in the vicinity of the Ashoka anomaly. The color bar

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represents the elevation in meters with respect to a lunar reference sphere of radius

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1738 km.

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confirmed the presence of a sublunarean void at coordinates 8.335o N and

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33.222o E marked by a red dot and commonly known as the Mare Tranquil-

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litatis skylight. For this investigation, the authors will limit the discussion to

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buried craters, however, additional work investigating skylights and lava tubes

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is also being carried out. Based on solely visual analysis of the topography for

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the region of interest, there appears to be no evidence of any buried structure.

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Thus, to detect the presence of a subsurface feature, free-air and Bouguer

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gravitational data is exploited. 12

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Gradiometry, Free-air and Bouguer Gravity Anomalies

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For this application, two gravity models up to degree and order 900 are con-

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sidered (Lemoine et al., 2014). Each model is truncated on both ends of the

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SH expansion and tapered to attenuate the resulting ringing. The gradiometry

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technique is then applied to the localized region for the two gravity models.

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Figure 3 illustrates the corresponding local averaged maximum eigenvalues

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for the free-air gravity, Bouguer gravity, and the correlation between the two

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gravitational fields. The figure suggests some form of quasi-circular anomaly

Fig. 3. Local gradiometry maps of the free-air gravity field (left), the Bouguer gravity

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anomaly field (center), and the correlation between the free-air and Bouguer gravity fields (right) for the Ashoka anomaly. The maps overlay local topography and the

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color scale represents the signed magnitude corresponding to the largest eigenvalue

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of the Hessian derived from the gravitational potential.

about 120 km in diameter with its approximate central coordinates at 8.9o N and 31.0o E.

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The Ashoka anomaly is further explored by generating regional free-air and

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Bouguer gravity maps for the area under investigation. Figure 4 illustrates lo-

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cal maps for the two gravity models. The figure on the left reflects the free-air

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gravity anomaly field and the figure on the right represents Bouguer gravity

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Fig. 4. Regional free-air and Bouguer gravity anomaly maps for Ashoka.

anomaly field over Ashoka. A subsurface quasi-circular anomaly is clearly ap-

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parent in both anomaly fields, further supporting the existence of a buried

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crater at this location. The non-circularity of the gravitational footprint may

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be attributed to later impacts, thus altering altering the preexisting crater or

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even completely remove any visible topographic evidence of its former presence

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by being covered under the ejecta blanket of the nearby impacts. Additionally,

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volcanic activity and subsequent emplacement of thick piles of mare basalt can

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be especially effective in burying and altering the circularity of the craters.

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4.1.2 Buried Peak-ring Basin: Ashoka

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To better visualize the gravity signature and any form of existing topographic

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evidence that may still exist after being partially buried under lava deposition

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or under ejecta from later impacts, a larger area surrounding the anomaly is

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investigated. The free-air and Bouguer gravity anomaly fields appear in Figure

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5 for 540 km by 510 km wide region in the vicinity of Ashoka overlying regional

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topography. The two gravitational maps clearly illustrate a central anomaly

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with a slight gravitational ‘high’ relative to its surrounding. To investigate the 14

ACCEPTED MANUSCRIPT possibility of the central anomaly being associated with potentially a larger

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buried structure, we employed the power-law fit to ring diameters (Dring ) and

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rim-crest diameters (Dr ) of peak ring basins provided by Baker et al. (2011).

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The power law trend follows the equation Dring = [0.14 ± 0.10](Dr )1.21±0.13 .

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With the knowledge of the inner anomaly being approximately 120 km in di-

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ameter as evident from Figure 3, the rim-crest of the basin can be calculated to

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be approximately 265 km in diameter. The black circle on the Bouguer gravity

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map outlines the inner anomaly ring, approximately 120 km in diameter, and

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Fig. 5. Free-air gravity map (left) and Bouguer gravity map (right) for Ashoka. The color represents free-air and Bouguer gravitational acceleration in the respective

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maps. The positive anomaly at 4.8o N and 23.4o E is part of (Neumann et al., 2015, table 1), and the two positive anomalies are #43 and #48 of Evans et al. (2016).

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The reason for picking the Ashoka anomaly, and not the two small but stronger positive anomalies, is because of the gravity gradient data in Figure 3, suggesting

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that Ashoka is larger and deeper than these two other anomalies. 272

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the dotted magenta circle marks the supposed crater rim-crest, approximately

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265 km in diameter. Comparing the two maps, the dotted magenta boundary

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coincides, over a small fraction, with topographic feature in the lower half of

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the circle. Although, the gradiometry technique along with regional free-air 15

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and Bouguer gravity maps aid in recognizing subtle features associated with

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the buried anomaly, additional analysis using forward modeling technique is

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employed to further verify the existence of a buried basin.

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4.2

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Similar to the detection and validation efforts outlined for Ashoka, the sec-

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ond anomaly, Earhart, lying in the northwestern region of Lacus Somniorum

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(northeast of Mare Serenitatis) is also investigated. To detect and confirm the

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presence of the subsurface anomaly, gradiometry based analysis is carried out

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for which free-air and Bouguer gravitational data is once again exploited. The

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proposed Earhart crater predated Serenitatis and was almost completely over-

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printed by the impact that resulted in the formation of Serenitatis that was

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subsequently followed by volcanism, thus flooding the basin with lava basalts,

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as well as the ejecta blanket of the Serenitatis impact.

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4.2.1 Gradiometry, Free-air and Bouguer Gravity Anomalies

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The gradiometry detection technique is applied to the localized region. Gravity

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models up to degree and order 900 with predetermined truncation and tapers

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are utilized (Lemoine et al., 2014). Figure 6 illustrates the corresponding local

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averaged maximum eigenvalues for the free-air gravity, Bouguer gravity, and

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Speculated Buried Crater 2 (Earhart)

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the correlation between the two gravitational fields, respectively. The maps

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depicts a subsurface quasi-circular anomaly of about 80 km in diameter with

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its center at 41.2o N and 21.8o E. Even though Earhart is a partially buried

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crater, so that its topography does not reflect its circularity, both free-air and

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Bouguer eigenvalue maps illustrate a circular-shaped gravity anomaly. 16

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Fig. 6. Local gradiometry maps for the free-air gravity anomaly field (left), Bouguer gravity anomaly field (center), and the correlation between the free-air and Bouguer gravity anomalies (right) for the Earhart anomaly. The maps overlay local topog-

raphy and the color scale represents the signed magnitude corresponding to the

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largest eigenvalue of the Hessian derived from the gravitational potential. 300

Continuing the validation to support the existence of Earhart, regional free-

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air and Bouguer gravity anomaly maps are generated. Figure 7 illustrates

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local maps for the free-air gravity anomaly field on the left and Bouguer grav-

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ity anomaly field on the right. Evidence for the presence of a quasi-circular

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Fig. 7. Regional free-air and Bouguer gravity maps for Earhart.

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anomaly is apparent in the two gravity maps, a small fraction of which coin-

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cides with the partial rim structure in the topography. In total, the detection

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process and analysis supports the existence of the Earhart buried crater but 17

ACCEPTED MANUSCRIPT additional evidence is warranted that is later accomplished by forward mod-

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eling.

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4.2.2 Earhart Crater’s Regional Topography

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The region is presently flooded with mare basalt that has been subjected to

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a number of small impacts; the region appears in Figure 8a using topography

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(b) Earhart depicted by black circle.

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(a) Topography near Earhart.

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data collected by LOLA. Based on visual analysis of Figure 8a, it appears

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Fig. 8. Speculated Buried Crater 2.

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that there is a partially buried, discontinuous ring structure interior to the

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black circle as illustrated in Figure 8b. The heavy modification of Earhart also

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suggests that it predated the Serenitatis impact and is overlain by Serenitatis

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ejecta.

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4.2.3

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A similar analysis for buried peak-ring basin is also completed for a wider

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area surrounding Earhart. Figure 9 reflects free-air and Bouguer gravity for

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Buried Peak-ring Basin: Earhart

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a 900 km by 900 km wide region in the vicinity of Earhart. Once again,

Fig. 9. Free-air gravity map (left) and Bouguer gravity map (right) for Earhart. The

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color represents free-air and Bouguer gravitational acceleration in the respective maps. 320

gravity maps are overlaid on regional topography for better visualization. The

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gravitational maps clearly illustrate a bulls-eye shaped anomaly with a gravity

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‘high’ relative to its surrounding. As evident from the Bouguer gravity map,

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no other gravitational footprint is as distinguishable as the Earhart anomaly.

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Neumann et al. (2015) clearly identified and used the edge of the Bouguer

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high to locate the inner ring of a crater. Applying the similar strategy to

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Earhart anomaly, the black circle on the Bouguer map outlines the inner

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ring, approximately 80 km in diameter. The dotted magenta circle outlines

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the boundary of the crater rim-crest, approximately 190-200 km in diameter

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calculated using power-law fit as given by Baker et al. (2011). Other than

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the few weak signatures scattered along the map, additional anomalies to the

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south are simply gravitational highs at the boundary between mare Serenitatis

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and topographic structures. In the case of Earhart, some topographic features

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along the southwestern edge of the dotted magenta circle are apparent. There 19

ACCEPTED MANUSCRIPT is also the possibility of the crater being buried under the ejecta of mare

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Imbrium and Serenitatis as evident from additional topographic structures in

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the region. Once again, the topography alone does not aid in the detection

338

process for the circular anomaly, i.e., the bulls-eye pattern marked by black

339

and magenta circles. The gradiometry based technique assists in the detection

340

process. The free-air and Bouguer gravity maps also support the verification

341

process for the anomalies but additional forward modeling carried out in the

342

subsequent sections will assist in strengthening the case for the buried crates.

343

5

344

The gradiometry strategy relies on the gravity models derived from the GRAIL

345

data to detect features of interest. It is essential to assess the validity of such

346

detections. To adequately apply the concept that serves as a basis for the

347

characterization of a feature is based on a model that describes the gravita-

348

tional signature of an anomaly and estimates the required parameters from

349

the gradiometry maps. Following the initial setup, the gravitational potential,

350

gravity anomaly, and Hessian matrix are computed for the forward model

351

and compared with the initial simulation for each candidate structure. The

352

performance of the forward model is assessed by its ability to match the ob-

353

served signatures that correspond to the feature of interest on the gradiometry

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Forward Model Development

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335

354

maps. The objective is the development of a simple and computationally in-

355

expensive strategy to describe the gravitational anomaly that is associated

356

with a buried crater. It is assumed that the crater is buried beneath mare

357

flood basalts, ejecta blanket of subsequent impacts, and has no topographic

358

expression. Then, the gravity anomaly for a given buried crater arises from 20

ACCEPTED MANUSCRIPT the density contrast between crustal material, mare material, and mantle ma-

360

terial. A simple diagram that represents the assumed layering outside of the

361

crater is depicted in Figure 10. The formation of a crater disturbs this initial

362

layering, creating density contrasts that result in gravitational anomalies. It is

363

important to note that the objective of the forward model is not to provide a

364

perfectly matching model but a rapid and simple modeling approach to serve

365

as a basis for the validation of potential buried features. Additionally, the tool

366

that is used for such detections is primarily the gradiometry. The gradiom-

367

etry technique is most sensitive to density gradients directly, not simply the

368

magnitude of a given contrast. In this analysis, the gradient of interest is the

369

radial density contrast across the crater. Thus, some simplifying assumptions

370

are adopted, and in particular, the details of the composition of the floor of the

371

crater are not included. The model is formulated in terms of simple density

372

contrast between two types of material: crust and mantle/mare.

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Fig. 10. Layering scheme outside the crater employed in the forward models, as

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assumed to characterize an uncratered portion of the mare.

373

5.1 Construction of a Shape Model for Buried Craters

374

The morphology and characteristics of lunar craters as a function of their size

375

is fairly well-known. As crater size increases, different crater morphologies 21

ACCEPTED MANUSCRIPT appear, running upward in size from simple craters, to complex craters, and

377

finally peak ring basins (Baker et al., 2011; Pike, 1980; Allen, 1975; Melosh,

378

2011). In this analysis, the focus is on complex crater and peak ring basin mor-

379

phologies, as these types are most similar in size to the candidate detections.

380

The objective is to construct a relatively simple geometrical shape model for

381

such structures in terms of simple elementary blocks to allow rapid evaluation

382

of the corresponding gravity anomaly. In this analysis, any crater feature in

383

the forward model is a series of discrete annular rings or a stack of disks.

384

5.1.1 Buried complex crater model

385

On the moon, complex craters are features of diameter, Df , larger than 20 km

386

and smaller than about 200 km. Such craters are characterized by a relatively

387

flat floor, terraced walls and small central peak or peak cluster (Baker et al.,

388

2011; Pike, 1980; Allen, 1975; Melosh, 2011). Our focus is on buried features,

389

hence it is assumed that the crater is filled with lava material and the entire

390

structure is buried under a layer of mare, as illustrated in Figure 11. Note that

391

to construct a model that describes the gravity anomaly due to the presence

392

of a buried crater, the relevant information is not the physical structure of

393

the crater directly but the density contrast that is associated with the buried

394

structure. Within this context, the lava flooding in the crater cavity, up to the

395

initial mare/crust interface, is a mass surplus and corresponds to a positive

396

gravity anomaly. Similarly, the rim of the crater, because it is surrounded by

397

mare material, corresponds to a mass deficit and a negative gravity anomaly.

398

The forward model for a complex crater is then comprised of two building

399

blocks: the rim and lava fill. The lava fill is modeled as a disk with positive

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22

ACCEPTED MANUSCRIPT

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Fig. 11. Complex crater geometry.

density contrast ∆ρ = ρmare − ρcrust ≈ 640kg/km3 (Kiefer et al., 2012; Wiec-

401

zorek et al., 2013; Gong et al., 2015), a diameter equal to the assumed crater

402

diameter and a constant thickness. The rim is constructed as a series of rings

403

with an inner diameter equal to the assumed crater diameter. The width of

404

each ring in the rim model is fixed and the thickness of a given ring is com-

405

puted such that the height of the rim is proportional to 1/r3 ,(Melosh, 2011)

406

where r is the radius of a given ring. The density contrast of the rim is opposite

407

to that of the lava fill value. For simplicity, the rim structure is constructed

408

such that the volume of the fill and the rim are equal.(Melosh, 2011) A sample

409

forward model for a 100 km diameter crater is illustrated in Figure 12 where

410

the density contrast that is associated with the presence of a buried lava fill

411

and rim is represented in red and blue, respectively. It is also assumed that

412

the model is axisymmetric with respect to the center of the crater, i.e., the

413

left edge of the lava fill.

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400

0

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depth, km

5

−5

−10

0

20

40

60 80 Radial distance, km

100

120

Fig. 12. Axisymmetric forward model for complex crater including lava fill (red) and rim (blue)

23

ACCEPTED MANUSCRIPT 5.1.2

Buried complex crater model with mantle uplift and central peak

415

Based on the initial simple forward model for a complex crater, additional

416

crater features can also be included. A central peak may form, and similar

417

to the rim, such a peak corresponds to a mass deficit or a negative gravity

418

anomaly (Allen, 1975). Also, depending on the crustal thickness, the size of

419

the crater, and other parameters, a mantle uplift in the center region of the

420

crater may appear. Similar to the lava fill, the mantle uplift is a mass surplus

421

because denser mantle material replaces crustal rocks. The same density con-

422

trast between mare fill and crust is assumed for the crust/mantle interface,

423

that is, ∆ρ = ρmantle − ρcrust ≈ 640kg/km3 . A downward crustal bulge of-

424

ten forms outboard of the mantle uplift, constituting a mass deficit (Milbury

425

et al., 2015), as illustrated in Figure 13. Note that while we model this mass

426

deficit as crustal thickening, higher porosity may also be a contributor.

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Fig. 13. Assumed geometry for a buried complex crater with mantle uplift, crustal

Our forward model for a complex crater, composed of a lava fill and a rim

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bulge and central peak in addition to a lava fill and crater rim.

428

structure, is further augmented with a central peak, mantle uplift, and crustal

429

bulge, as shown in Figure 13. The central peak is constructed as a conical

430

stack of disks with fixed thickness that originates on the crater floor with a

431

given basal diameter. The subsequent disks are added in the model such that

432

the final structure satisfies the prescribed final central peak diameter at the 24

ACCEPTED MANUSCRIPT chosen height. The mantle uplift model is constructed similarly. The series

434

of disks originates at the interface between the crust and the mantle with

435

a diameter equal to Df /2. The thickness of individual disks, the height and

436

apex diameter of the mantle uplift are prescribed to construct the mantle up-

437

lift model. In the complex crater model, the mantle uplift apex diameter is

438

assumed to be equal to zero (that is, the mantle uplift is a cone terminating

439

in a point). Finally, a model for the crustal bulge is also incorporated. The

440

crustal bulge is constructed similarly to the rim, that is, a series of rings with

441

fixed radii that originate at Df /2 and terminate at Df . The height of indi-

442

vidual rings is governed by either a short or long wavelength sine function

443

to produce a lobe-shaped structure. The density contrast for each of these

444

structures is assigned consistent with the gravity anomaly type, that is, pos-

445

itive or negative. A sample forward model of a complex crater with mantle

446

uplift, crustal bulge and central peak is illustrated in Figure 14. While these

447

features are detectable in the gravity signature, the mantle uplift dominates.

448

The other smaller features are more apparent in the gradiometry profiles as

449

the eigenvalue is most sensitive to gradients in the field, even of smaller mag-

450

nitude. While these higher-order features may contribute to a better fit, they

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433

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0 −10

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depth wrt R0, km

do not dominate the traits of the gravity and gradiometry curves. Finally, the

−20

AC

−30

0

20

40

60

80 100 120 Radial distance, km

140

160

180

200

Fig. 14. Forward model for complex crater.

451

452

gradiometry technique is very sensitive to sharp changes in the gravitational

453

potential function. In the initial forward model for a complex crater, note the 25

ACCEPTED MANUSCRIPT sharp transition between the lava fill and the rim. In reality, a transition region

455

between the cavity and the rim exists. The forward model is thus augmented

456

with such a transition region to alleviate the artificial sharpness of the shape

457

model. This transition region, similar to the rim, is constructed as a series

458

of rings located between the lava fill disk and the first ring of the rim. The

459

height of each ring is determined such that a smooth transition between the

460

depth of the fill and the height of the rim is achieved. Note that, while sharp

461

discontinuities do not necessarily reflect in the gravity anomaly depending on

462

the magnitude, they are more significant in the gradiometry technique. Thus,

463

this transition region is primarily included for numerical purpose rather than

464

in a pursuit of physical fidelity.

465

5.1.3 Buried peak ring crater model

466

Larger crater structures on the Moon are called peak ring basins. The overall

467

morphology of peak ring basins is similar to complex craters but a peak ring

468

may form inside the crater rim with a diameter roughly equal to Df /2. Also,

469

such craters may exhibit a broader plateau-shaped mantle uplift, as illustrated

470

in Figure 15. Then, the forward model for a peak ring basin is constructed

471

similarly to the complex crater scenario and the model is augmented with a

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454

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peak ring. Similar to the crustal bulge, the peak ring is constructed as a stack

Fig. 15. Peak ring crater geometry. 472

26

ACCEPTED MANUSCRIPT

473

of annular rings that lies on the crater floor. The width of each ring is fixed

474

and the height is determined with a sine function to produce a bell-shaped

475

structure. The overall width and height of the peak are prescribed to complete

0 −10 −20 −30 0

50

100

150 200 Radial distance, km

250

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depth wrt R0, km

the model, as illustrated for a sample peak ring basin in Figure 16.

300

350

Fig. 16. Peak ring crater geometry. The center of the axisymmetric structure is on the left and the outer part of the crater is on the right of this profile.

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476

Note that the different elements of the forward model may imply specific as-

478

pects of the rheology of mantle. However, while the rheology of the mantle is

479

important, to first order, the density contrast dominates the driving factors

480

that affect the gravity signature of an anomaly. Additional details leading to

481

forward model development and steps towards computation of the gravita-

482

tional potential, acceleration, and the Hessian matrix from a shape model for

483

buried craters is provided in Supplementary material.

484

5.2

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Forward Model Validation

485

The forward modeling approach is validated by applying the strategy to two

486

known exposed impact structures, Compton crater and Schroedinger basin.

487

The capability of the models to represent the gravity anomalies that are as-

488

sociated with these features serves as a basis to evaluate the performance of

489

the forward model. 27

ACCEPTED MANUSCRIPT 5.2.1

Compton Crater

491

Compton is a complex crater located on the far side of the Moon, at 55.3◦ N,

492

103.8◦ E, with a diameter Df approximately equal to 162 km. The free-air

493

and Bouguer anomalies that are associated with the crater are illustrated on

494

the left and right images, respectively, in Figure 17. The free-air anomaly

495

is characterized by a large positive gravity anomaly that corresponds to the

496

crater rim, while the Bouguer anomaly is poorly correlated with the crater,

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490

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although it is, in general, smaller inside the crater than exterior to it. The

PT

Fig. 17. Free-air (left) and Bouguer (right) gravity anomaly for Compton crater. 497

absence of a positive Bouguer anomaly in the center of the crater suggests

499

an absence of mantle uplift. To compare the gravity data and the forward

500

model, an azimuthal average profile of the gravity anomalies is computed, as

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498

501

illustrated on the left plot in Figure 18. A series of concentric great circles

502

for a predetermined diameter range are constructed at a pole and rotated

503

to the center of the crater or anomaly of interest. For each rotated circle,

504

the gravity, or eigenvalue, anomaly is sampled along the circle and averaged.

505

This series of points constitute the azimuthally averaged profile as a function 28

ACCEPTED MANUSCRIPT

506

of radial distance from the anomaly center. All subsequent gravity profiles

507

discussed in this analysis are azimuthally averaged. The gradiometry technique

508

is also applied to this region and a similar profile for the maximum magnitude eigenvalue of the Hessian is displayed in the left plot in the figure. Recall Gravity Anomaly

Eigenvalue

100

Free−air Bouguer

eigenvalue, eotvos

20

0

0

−20

−40

−50

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gravity anomaly, mgal

50

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40

−60

−100

−80

100 150 radial distance, km

200

50

100 150 radial distance, km

200

M

50

Fig. 18. Azimuthal average for the free-air and Bouguer gravity anomaly (left) and

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eigenvalue (right) profile for Compton crater. 509

that a mass deficit corresponds to a negative gravity anomaly and a positive

511

eigenvalue, while a mass surplus is associated with a positive gravity anomaly

512

and a negative eigenvalue. Note that Compton is an exposed crater, thus, the

513

objective with the forward model is to represent the free-air gravity anomaly

514

and the eigenvalue.

515

A forward model for Compton is constructed assuming that the crater can

516

be reasonably represented as a large complex crater with a central peak. In

517

fact, Compton is understood to be transitional to a peak-ring basin. Some-

518

times denoted a “protobasin” (Baker et al., 2011), the central peak cluster is

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510

29

ACCEPTED MANUSCRIPT surrounded by a very subdued ring of hills with a diameter equal to about

520

half the rim diameter. However, these hills are too small to contribute sub-

521

stantially to the gravity anomaly and our model neglects them. Compton is

522

not flooded with lava, so the density contrast is accordingly adjusted. In this

523

case the rim and the central peak reflect a mass surplus and the crater cavity,

524

lacking any lava fill, corresponds to a mass deficit. The parameters for each

525

structure in the forward model are summarized in Table 1, where the symbols

526

hRim , hF ill , hCP , wCP , and hCrust denote the height of the rim, lava fill, central

527

peak, and crust, respectively; the resulting shape model is displayed in Figure

528

19. Note that the parameter hF ill in this context corresponds to the crater

529

cavity height, as the crater is assumed to be exposed rather than buried and filled with lava material. Table 1

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519

Compton forward model characteristics hF ill

0.75 km

1.2 km

hCP

M

hRim

hCrust

13 km

30 km

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1.7 km

wCP

530 1

PT

0.5

−0.5

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depth with respect to reference sphere, km

0

−1

−1.5

−2

−2.5

−3

−3.5

−4

0

50

100 Radial distance, km

150

200

Fig. 19. Forward model for Compton crater.

30

ACCEPTED MANUSCRIPT The gravity anomaly and the eigenvalues that are associated with the for-

532

ward model are computed and compared with the free-air profiles from the

533

GRAIL data. These profiles are represented in Figure 20 in red and black

534

for the data and the forward model, respectively. Also, to better assess the

535

fit of the forward model, a red envelope that depicts the 1-σ azimuthal dis-

536

persion of the gradiometry and gravity data is overlaid on the figure. Note

537

that the parameters in the forward model could be further tuned to achieve

538

an even better agreement, but, overall the forward model is successful in re-

539

producing the gravity signature that corresponds to Compton crater. Recall

540

that the objective is not to provide a perfectly matching model but, rather, a

541

rapid and simple modeling approach to serve as a basis for the validation of

542

potential buried feature detection. Interestingly, the gradiometry fit requires

543

a small mantle uplift beneath the crater center, which is not apparent from

544

the Bouguer or Free Air data contours alone. It is simply that the mantle

545

uplift that is incorporated in the forward model is not significant enough to

546

have an expression in the gravity anomaly but does reflect in the eigenvalue

547

technique, as the gradiometry technique is most sensitive to variations in the

548

gravity field.

549

5.2.2 Schroedinger Basin

550

A second simulation is completed for a larger structure, that is, Schroedinger

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531

551

basin. This feature is a peak ring basin located on the far side of the Moon, at

552

75◦ S, 132.4◦ E, with a diameter Df approximately equal to 312 km. The free-

553

air and Bouguer anomalies associated with the basin are illustrated on the

554

left and right images, respectively, in Figure 21. The free-air anomaly is again

555

characterized by a large positive gravity anomaly that corresponds to the rim 31

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ACCEPTED MANUSCRIPT

Fig. 20. Free-air gravity anomaly (left) and eigenvalue (right) azimuthal profiles for Compton crater computed with GRAIL data (red) and forward model (black).

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of the basin, but also features a prominent central positive anomaly. Unlike

Fig. 21. Free-air (left) and Bouguer (right) gravity anomaly for Schroedinger basin. 556

557

Compton, the Bouguer gravity signature is characterized by a pronounced 32

ACCEPTED MANUSCRIPT positive anomaly in the center of the basin, indicative of a substantial mass

559

surplus, that may correspond to features such as a mantle uplift or thick

560

section of volcanics. The azimuthal average profile for the gravity anomalies

561

and the eigenvalues are computed and illustrated on the left and right images,

562

respectively, in Figure 22. Note the steep gradient in the eigenvalue profile

563

toward the center of the crater. Such a negative eigenvalue is indicative of a

564

mass surplus consistent with mantle uplift or lava fill. However, the slope of

565

the profile dictates a sharp feature toward the center of the anomaly, only

566

consistent with mantle uplift. The objective is then to represent the free-air

CR IP T

558

gravity anomaly and eigenvalue with the forward model strategy. Eigenvalue

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Gravity Anomaly 250

60

200

Free−air Bouguer

40

150

0

ED

−50

−100

PT

−150

eigenvalue, eotvos

50

M

gravity anomaly, mgal

20

100

0

−20

−40

−60

−80

−200

100 150 200 250 radial distance, km

300

50

100 150 200 250 radial distance, km

300

CE

50

Fig. 22. Azimuthal average for the free-air and Bouguer gravity anomaly (left) and

AC

eigenvalue (right) profiles for Schroedinger basin.

567

568

A forward model for Schroedinger is constructed assuming the feature is rea-

569

sonably represented as a peak ring basin. In addition to the central peak, the

570

forward model includes a mantle uplift, crustal bulge, and peak ring. Similarly 33

ACCEPTED MANUSCRIPT

571

to Compton, the crater is exposed, for which we adjust the density contrast.

572

The peak ring, similar to the rim and central peak, is a mass surplus and

573

the crater cavity is a mass deficit. The parameters for each structure in the

574

forward model are summarized in Table 2, where the additional symbols hM U ,

575

hCB , and hP R denote the height of the mantle uplift, crustal bulge, and peak

Table 2 Schroendiger forward model characteristics.

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ring, respectively; the resulting shape model is displayed in Figure 23.

hRim

hF ill

hCP

wCP

hCrust

hM U

1.25 km

1.85 km

0.4 km

30 km

30 km

15 km

0

4.3 km

0.4 km

−10

M

−15

−20

−25

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depth with respect to reference sphere, km

−5

PT

−30

−35

hP R

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576

hCB

0

50

100

150 200 Radial distance, km

250

300

Then, the gravity anomaly and the eigenvalue that are associated with the

AC

577

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Fig. 23. Forward model for Schroedinger basin.

578

forward model are computed and compared with the free-air profiles from the

579

GRAIL data. These profiles are illustrated in Figure 24 in red and black for the

580

data and the forward model, respectively. Similar to Compton, in fact slightly

581

better, the forward model provides a good overall agreement with GRAIL data

582

and is successful in reproducing Schroedinger’s gravity signature, although it 34

ACCEPTED MANUSCRIPT

583

requires a much larger mantle uplift, consistent with the basin’s much larger

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size.

M

Fig. 24. Azimuthal average for the free-air gravity anomaly (left) and eigenvalue (right) profiles for Schroedinger basin computed with GRAIL data (red) and forward

ED

model (black).

6

Forward Model Application to Buried Features

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585

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584

586

After initially validating our forward modeling strategy with two known lunar

587

craters, the next step in the analysis is an application of the forward mod-

588

eling approach to the speculated buried craters that we detected with our

589

gradiometry technique. The objective of subsequent investigation is to con-

590

struct a forward model that captures the overall gravitational signature of the 35

ACCEPTED MANUSCRIPT potential features, both in terms of the gravity anomaly and the eigenvalue.

592

Compared to the validation scenarios, where the size and overall features of

593

the craters were known, an additional challenge in characterizing the Ashoka

594

and Earhart anomalies is the absence of any a priori information other than

595

the gravity filed itself.

596

6.1

597

The first speculated buried crater, informally named Ashoka, is centered at

598

8.7◦ N, 31.2◦ E, and the diameter of the positive Bouguer anomaly is approxi-

599

mately equal to 100-120 km. The size of the anomaly is not, however, necessar-

600

ily the size of the structure. Similar to Compton and Schroedinger, azimuthal

601

average profiles for the gravity anomalies and eigenvalues are produced to

602

compare with the forward model, as illustrated on the left and right images,

603

respectively, in Figure 25. In contrast to the previous two craters, however,

604

Taking into consideration that Ashoka is a buried feature and, thus, the ob-

605

jective is to represent the Bouguer gravity anomaly and eigenvalue with the

606

forward model strategy.

607

As the exact size of the potential crater is unknown several forward models for

608

the Ashoka anomaly are constructed. The model that seems to best capture

609

the overall anomaly is a complex crater morphology with a pronounced mantle

610

uplift. The parameters for the forward model are summarized in Table 3, where

611

hM are denotes the thickness of the lava layer; the corresponding shape model

612

is then illustrated in Figure 26.

613

The gravity anomaly and eigenvalue for the forward model are computed and

CR IP T

591

AC

CE

PT

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M

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Ashoka anomaly

36

ACCEPTED MANUSCRIPT

Gravity Anomaly

Eigenvalue Free−air Bouguer

120 10 100 0

60

40

−10

−20

20 −30 0 −40 −20

−50 100 150 radial distance, km

200

50

100 150 radial distance, km

200

AN US

50

CR IP T

eigenvalue, eotvos

gravity anomaly, mgal

80

Fig. 25. Azimuthal average for the free-air and Bouguer gravity anomaly (left) and eigenvalue (right) profile for Ashoka crater. Table 3

Ashoka crater forward model characteristics. hRim

hF ill

hCP

wCP

hCrust

hM U

hCB

hM are

160 km

1 km

2 km

0 km

0 km

20 km

12 km

4 km

3.5 km

ED

M

Df

displayed in black on the left and right plots, respectively, in Figure 27. For

615

comparison, profiles from GRAIL data are also overlaid in blue, and although

616

the agreement between the data and the forward model is not as complete

617

as in the validation scenarios, the overall fit is satisfying. Recall that the ob-

618

jective is not to provide a perfectly matching model but, rather, a rapid and

AC

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PT

614

619

simple modeling approach to serve as a basis for the validation of potential

620

buried feature detection. The construction of the shape model in this scenario

621

is driven by several factors. First, note the steep gradient in the eigenvalue

622

profile toward the center of the crater. Such a negative eigenvalue is indicative

623

of a mass surplus consistent with mantle uplift or lava fill. However, the slope 37

ACCEPTED MANUSCRIPT

0

−10

−15

−20

−25

−30

0

20

40

60

80 100 Radial distance, km

120

140

CR IP T

depth with respect to reference sphere, km

−5

160

180

CE

PT

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M

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Fig. 26. Forward model for Ashoka crater.

Fig. 27. Azimuthal average for the Bouguer gravity anomaly (left) and eigenvalue

AC

(right) for Ashoka crater computed with GRAIL data (blue) and forward model (black).

624

of the profile dictates a sharp feature toward the center of the anomaly, only

625

consistent with mantle uplift. The distinction between the two mantle uplift

626

models, without or with a plateau, is reflected in the slope of the eigenvalue

627

curve. The plateau-shaped model is associated with a flatter eigenvalue curve 38

ACCEPTED MANUSCRIPT in the innermost region of the crater as the mass surplus no longer varies radi-

629

ally. In this scenario, the slope of the eigenvalue curve remains steep up to the

630

cater center. Also, the location of the positive peak in the eigenvalue profile,

631

corresponding to a mass deficit, hence, consistent with the rim of the crater,

632

constrains the diameter of the feature to some range. There is, however, no

633

signature consistent with a central peak or a peak ring; such features would

634

be expressed as a central positive eigenvalue peak and another positive peak

635

halfway between the center and the rim. The accumulation of this informa-

636

tion further constrains the possible morphology of the buried structure. The

637

anomaly appears to be consistent with a crater that is sufficiently large to

638

possess a pronounced mantle uplift, yet not so large that the mantle uplift

639

exhibits a plateau shape or a peak ring.

640

6.2

641

The second speculated buried crater, informally named Earhart, is centered

642

at 41.5◦ N, 21.7◦ E, and the diameter of the Bouguer anomaly is similar to

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that of Ashoka. The azimuthal average profiles for the gravity anomalies and

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eigenvalues that are associated with Earhart crater are illustrated on the left

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and right images, respectively, in Figure 28. The profiles appear very similar to

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the Ashoka anomaly scenario, but with a stronger positive Bouguer anomaly

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at the center of the crater. A similar morphology to Ashoka is adopted to

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construct the forward shape model, with parameters summarized in Table 4.

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The Curve Fitting strategy detailed in the supplementary material is applied

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following which optimization is performed on the initial solution as initial guess

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and the corresponding optimized shape model is illustrated in Figure 29. The

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Earhart anomaly

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Gravity Anomaly

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100 150 200 radial distance, km

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eigenvalue, eotvos

gravity anomaly, mgal

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Fig. 28. Azimuthal average for the free-air and Bouguer gravity anomaly (left) and eigenvalue (right) profile for Earhart crater. Table 4

180 km

1 km

hF ill

hCP

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wCP

hCrust

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hCB

hM are

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Earhart crater forward model characteristics.

profiles for the forward model and those from the GRAIL data, represented

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in black and blue, respectively, are overlaid in Figure 30 on the left and right

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plots, respectively.

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Overall, the size of the crater is similar to the initial simulation, Df ≈ 200

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km and, notably, the mare fill is thinner such that the crater rim lies just

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underneath the surface. Also, the agreement between the eigenvalue profiles

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is improved, although some discrepancy in the inner part of the crater still

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remains. 40

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80 100 Radial distance, km

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depth with respect to reference sphere, km

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Fig. 29. Forward model for Earhart crater after curve fitting.

Fig. 30. Azimuthal average for the Bouguer gravity anomaly (left) and eigenvalue

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(right) for Earhart computed with GRAIL data (blue) and forward model (black). 660

7

Summary

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Gravitational analysis using gradiometry technique lead to the detection of

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buried craters that is consistent with the observations and buried craters iden-

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tified by other authors (Neumann et al., 2015; Evans et al., 2016), however, 41

ACCEPTED MANUSCRIPT the interpretation is non-unique due to the nature of gravity data. As a part

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of the validation process, a partially and a completely buried structure are

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investigated. Gravitational signatures that correspond to two putative buried

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craters, here identified as Ashoka and Earhart craters, are corroborated by

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evidence from free-air and Bouguer gravity anomaly maps, further sharpened

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by our gradiometry technique. Forward modeling further supports the pres-

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ence of a completely buried Ashoka crater and a partially buried Earhart

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(b) Earhart crater.

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(a) Ashoka crater.

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crater, shown in Figure 31. Preliminary analysis based on gradiometry tech-

Fig. 31. Regional Bouguer maps: Black circle outlines the mantle uplift and the

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dotted magenta circle marks the crater rim derived from the forward model for the two craters. The forward modeling technique revealed the true size of the two

nique suggested that the two buried craters were 120 km and 80 km in diam-

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craters under investigation. 671

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eter. However, further analysis to complete the study, encompassing forward

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modeling, revealed that the true size of the two buried craters is indeed ap-

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proximately 160 km (Ashoka crater) and 200 km (Earhart crater) in diameter.

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The forward modeling approach is validated by applying the strategy to two

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known exposed impact structures, Compton crater and Schroedinger basin; 42

ACCEPTED MANUSCRIPT the strategy is successful in reproducing the gravity signatures that corre-

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spond to both features. The strategy offers an initial assessment of the gravity

680

anomalies that are detected, and generally matches the observed values for

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Earhart and Ashoka. Further refinement of the forward model, in particular,

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the mantle uplift model, may be required in future work. Current ongoing

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efforts include the implementation of automatic curve fitting techniques to

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improve the agreement between the forward model and the GRAIL data.

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Acknowledgements

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The research work described in this paper made use of GRAIL data and was

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carried out at Purdue University. The GRAIL mission is supported by the

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NASA Discovery Program under contract to the Massachusetts Institute of

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Technology and the Jet Propulsion Laboratory, California Institute of Tech-

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nology.

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