Probability distributions for magnetotellurics

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Estimates of the magnetotelluric transfer functions can be viewed as ratios of two complex random variables. It is assumed that the numerator and denominator are governed approximately by a joint complex normal distribution. Under this assumption, probability distributions are obtained for the magnitude, squared magnitude, logarithm of the squared magnitude, and the phase of the estimates. Normal approximations to the distributions are obtained by calculating mean values and variances from error propagation, and the distributions are plotted with their normal approximations for different percentage errors in the numerator and denominator of the estimates, ranging from 10% to 75%. The distribution ... continued below

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Stodt, John A. November 1, 1982.

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Description

Estimates of the magnetotelluric transfer functions can be viewed as ratios of two complex random variables. It is assumed that the numerator and denominator are governed approximately by a joint complex normal distribution. Under this assumption, probability distributions are obtained for the magnitude, squared magnitude, logarithm of the squared magnitude, and the phase of the estimates. Normal approximations to the distributions are obtained by calculating mean values and variances from error propagation, and the distributions are plotted with their normal approximations for different percentage errors in the numerator and denominator of the estimates, ranging from 10% to 75%. The distribution of the phase is approximated well by a normal distribution for the range of errors considered, while the distribution of the logarithm of the squared magnitude is approximated by a normal distribution for a much larger range of errors than is the distribution of the squared magnitude. The distribution of the squared magnitude is most sensitive to the presence of noise in the denominator of the estimate, in which case the true distribution deviates significantly from normal behavior as the percentage errors exceed 10%. In contrast, the normal approximation to the distribution of the logarithm of the magnitude is useful for errors as large as 75%.

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  • Report No.: DOE/ID/12079-84
  • Grant Number: AC07-80ID12079
  • DOI: 10.2172/891515 | External Link
  • Office of Scientific & Technical Information Report Number: 891515
  • Archival Resource Key: ark:/67531/metadc883922

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Creation Date

  • November 1, 1982

Added to The UNT Digital Library

  • Sept. 21, 2016, 2:29 a.m.

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  • Nov. 30, 2016, 6:16 p.m.

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Stodt, John A. Probability distributions for magnetotellurics, report, November 1, 1982; United States. (digital.library.unt.edu/ark:/67531/metadc883922/: accessed October 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.