CROSS-CORRELATION

Idea:

Exploit individual tracks as gravity acceleration profiles to detect lava tubes

using cross-correlation with a know reference signal

Method:

• Reference signal:

gravity anomaly (i.e acceleration) from analytic rille

Fig.4: Analytical vertical (left) and horizontal (right) gravity anomaly.

• Test signal:

track data i.e. relative acceleration GRAIL-A / GRAIL-B

–Reconstructed from a priori model (+ residuals)

–From KBRR data

• Cross-correlation between signals operates as “matching filter”

Fig.5: Cross-correlation profiles for proof of concept

Observations:

In figure 5, an artificial signal similar to the reference signal is embedded

into some of the track data to simulate the presence of a rille.

The cross-correlation coefficient profile of the reference and test signals

depicts the similarity between the two signals. (left plot in Figure 5)

More insightful representation: cross-correlation coefficient as color on

the track path in longitude-latitude space. (right plot)

Lava Tube Detection with GRAIL data L. Chappaz1, H. J. Melosh1,2, K. C. Howell1,and the GRAIL mission team. 1School of Aeronautics and Astronautics, Purdue University,

West Lafayette, Indiana 47907-2045, Earth, Atmospheric and Planetary Science, Purdue University, West Lafayette, Indiana 47907-2051.

INTRODUCTION

The success of the NASA’s GRAIL mission now provides the highest resolution and most accurate gravity data for the Moon. The low altitude at which some of this data was collected potentially allows the

detection of small-scale surface or subsurface features. We have focused on the specific task of detecting the presence and extent of empty lava tubes beneath the mare surface. In addition to their importance

for understanding the emplacement of the mare flood basalts, open lava tubes are of interest as possible habitation sites safe from cosmic radiation and micrometeorite impacts [1]. The existence of such

natural caverns is now supported by Kaguya’s discoveries of deep pits in the lunar mare [2]. In this investigation, a first stage of the analysis is to develop tools to best exploit the rich gravity data toward the

numerical detection of these small features. Two independent strategies are considered: one based on gradiometry techniques and a second one that relies on cross-correlation of individual tracks.

GRADIOMETRY

Idea:

Detect topographical or underground structures by inspecting the gravitational potential

Method:

• Gravitational potential computation

(Bouguer/Free air – from spherical harmonics – truncated and tapered)

• Gradient and Hessian of potential

(Central differences – Angular or spatial derivatives)

• Eigenvalue of the Hessian with largest magnitude

Observations:

A strong positive structure in the eigenvalue map coincides with Shroeder’s valley on the

Free-Air potential map (upper plot)

Structure is not observed on the Bouguer bottom map

Similar maps with different truncation and taper filters feature the rille signature

Smaller structures are not yet successfully detected, but the continuous improvement of

the gravity harmonic solutions is promising.

Fig.1: Known sinuous rilles and caves

CONCLUSION

GRAIL gravity data unprecedented resolution enables the

gradiometry approach to detect Shroeder’ Valley while the

gravity harmonic solutions are still improving.

The second method based on cross-correlation is promising

and the tools to exploit the KBRR data are still being

developed.

A combination of both strategies is the main avenue of

research for the further development of tools to detect and

identify small structures such as lava tubes beneath the lunar

mare.

References: [1] De Angelis et al. (2001) BAAS 33, 1037. [2]

Haruyama et al. (2009), GRL 36, L21206. [3] Hanna et al.

(2012) Science DOI:10.1126/science.1231753 .

Peak from

artificial rille

Fig.2: LOLA topography: Shroeder’s Valley (deepest and

widest known sinuous rille: ~ 170 km long, ~ 500 m deep, ~

4km wide)

ABTRACT No. 2019

Contact: lchappaz@purdue.edu

Fig.3: Local eigenvalues map in

the Shroeder Valley region

with topography overlaid.

Truncation:

D&O 75 – 620

Tapering:

Inf. 5 D&O - Sup. 15 D&O

Top map: Free-Air potential

Bottom map: Bouguer potential