Mathematics – Probability
Scientific paper
Mar 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002stin...0242919k&link_type=abstract
Geophysical Bulletin of Hokkaido University, p. 325
Mathematics
Probability
Moonquakes, Anomalies, Libration, Modulation, Periodic Variations, Hilbert Transformation, Occurrences, Perigees, Perturbation, Predictions, Probability Theory, Regularity, Standard Deviation, Temporal Distribution
Scientific paper
The periodicity of about 27.3 days has been known for deep moonquakes observed by Apollo Seismic Network on the moon. There still remain the fluctuation of the periodicity about 2 days and the modulation due to Earth-Moon orbital configuration. In order to identify the category of deep moonquakes, detailed analysis of the periodicity of deep moonquakes is made by the Hilbert transform. Thirty groups of identified deep moonquakes with large event numbers are parameterized by their phases of occurrence timing in the Earth libration looking from the moon. Clearly shown is the periodicity of about 206 days resulting from the perturbation of perigee by the sun and 6 years from the beating of anomalistic and nodical periodicities. The former has been suggested fro m the amplitude variation of deep moonquake signals and is shown quantitatively here. There are many groups of deep moonquakes of which temporal variation of occurrence phases is so regular that the empirical formulae could be determined to predict the time of phases of deep moonquake occurrences. Standard deviation of observed and predicted phases of event occurrences at best is about 0.03 radian, which is about 3 hours. Most of standard deviations are twice or thrice larger than this. Some groups do not show clear regularity in occurrence phases. The present empirical analysis would not help for the identification of those groups of events. Generally speaking the average time interval of Apollo deep moonquakes is about 23 hours. The empirical formulae give the prediction of deep moonquake occurrences much precise than this, so that the present analysis would help the identification of category of deep moonquakes observing arrival times of signals measured in the future mission.
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