Alexander E. Stott | Searcharxiv

arXiv2020

On-deck seismology: Lessons from InSight for future planetary seismology

Before deploying to the surface of Mars, the short-period (SP) seismometer of the InSight mission operated on deck for a total of 48 hours. This dataset can be used to understand how deck-mounted seismometers can be used in future landed missions to Mars, Europa, and other planetary bodies. While operating on deck, the SP seismometer showed signals comparable to the Viking-2 seismometer near 3 Hz where the sensitivity of the Viking instrument peaked. Wind sensitivity showed similar patterns to the Viking instrument, although amplitudes on InSight were ~80% larger for a given wind velocity. However, during the low wind evening hours the instrument noise levels at frequencies between 0.1 and 1 Hz were comparable to quiet stations on Earth, although deployment to the surface below the Wind and Thermal Shield lowered installation noise by roughly 40 dB in acceleration power. With the observed noise levels and estimated seismicity rates for Mars, detection probability for quakes for a deck-mounted instrument are low enough that up to years of on-deck recordings may be necessary to observe an event. Because the noise is dominated by wind acting on the lander, though, deck-mounted seismometers may be more practical for deployment on airless bodies, and it is important to evaluate the seismicity of the target body and the specific design of the lander. Detection probabilities for operation on Europa reach over 99% for some proposed seismicity models for a similar duration of operation if noise levels are comparable to low-wind time periods on Mars.

physics.geo-ph↗

arXiv2017

Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.

math.NA↗