article Open Access

The Retrieval of Harmonics from a Covariance Function

Geophysical Journal International · 1973 · Vol. 33(3) · pp. 347–366

В. Ф. Писаренко✉(Schmidt Institute of Physics of the Earth)

Abstract

A new method for retrieving harmonics from a covariance function is introduced. The method is based on a theorem of Caratheodory about the trigonometrical moment problem. The relation between this method and the ‘maximum entropy’ spectral estimator is discussed, and the effect of a small addition of a noise component is investigated. A numerical example is discussed.

Underwater Acoustics Research Statistical Mechanics and Entropy Scientific Research and DiscoveriesHarmonicsCovarianceCovariance functionMathematicsEstimatorApplied mathematicsMaximum entropy spectral estimationSpherical harmonicsMathematical analysisPrinciple of maximum entropy

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