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Understanding the relationship of degree-range and the depth of a gravity anomaly

David Smith
Delivered As: 
Abstract Text: 

The relationship between spherical harmonic degree and scale suggests that we might be able to use a range of degrees to represent a specific distance or scale, in particular the depth beneath the surface. For example, on the Moon, the degree 540 has a scale of 10 km and the degree 108 has a scale of 50 km so it might be possible to study the crust of the moon by investigating the gravity field in the degree range 108-540.
A density contrast at depth creates a gravity field that can be represented as a spherical harmonic series. The gravity anomaly at the surface and the spectrum of the gravity field contain information about the density contrast and its location, although not uniquely. We try to use the observed field at the surface and the power of the gravity field in discrete ranges to infer the location of the source creating the gravity anomaly.
We use a high resolution GRAIL gravity model of the Moon in the degree ranges 108-135, 135-180, 180-270, and 270-540 to represent the gravity field of the lunar crust in 10-km layers from 10 to 50 km depth. We investigate the concept of spherical harmonic degree range and depth by modeling density contrasts of different sizes in the 10-km thick layers in the lunar crust and investigating the relationship between the power spectrum of the degree ranges and the depth of the modeled density contrast. Preliminary results suggest that for small 10-km sized anomalies the largest gravity anomaly appears at the depth of the model anomaly.

"Irene Lia Schlacht
SSERVI Identifier: 

Recognizing that science and human exploration are mutually enabling, NASA created the Solar System Exploration Research Virtual Institute (SSERVI) to address basic and applied scientific questions fundamental to understanding the Moon, Near Earth Asteroids, the Martian moons Phobos and Deimos, and the near space environments of these target bodies. As a virtual institute, SSERVI funds investigators at a broad range of domestic institutions, bringing them together along with international partners via virtual technology to enable new scientific efforts."