The maximum entropy approach to inverse problems - spectral analysis of short data records and density structure of the Earth

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E. Rietsch


The maximum entropy principle as described in the first, introductory part of the paper is applied to 2 problems: the estimation of the power spectrum from a finite number of values of the autocovariance function, and the determination of the density within the Earth from its mass, radius, and moment of inertia. In both cases the available information is given in terms of known values of linear functionals and the maximum entropy principle is used to derive a probability distribution for the values of the unknown function. The expectation value of the probability distribution for the spectral power is shown to be equal to the well-known maximum entropy power spectrum. The expectation value for the density within the Earth is in ― with respect to the few data used ― good agreement with that of accepted Earth models.

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Rietsch, E. (1976). The maximum entropy approach to inverse problems - spectral analysis of short data records and density structure of the Earth. Journal of Geophysics, 42(1), 489-506. Retrieved from
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