Random Orthogonal Set Functions and Stochastic Models for the Gravity Potential of the Earth

Abstract

The covariance function of the Newtonian potential of a random orthogonal set function of the unit sphere in three dimensions is derived, and it is shown that the coefficients to the series expansion of this are simply related to the moments of the covariance measure of the random set function. Furthermore, as an applicaton, it is shown that available gravity data indicates a mass distribution inside the Earth which becomes more and more irregular as one approaches the center of the Earth.

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Document Details

Document Type
Technical Report
Publication Date
Dec 27, 1973
Accession Number
AD0783077

Entities

People

  • Steffen L. Lauritzen

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Coefficients
  • Confidence Limits
  • Covariance
  • Data Science
  • Gravity
  • Gravity Anomalies
  • Information Science
  • Legendre Functions
  • Maximum Likelihood Estimation
  • Military Research
  • Probability
  • Random Variables
  • Statistical Analysis
  • Statistics
  • Stochastic Processes
  • United States

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Space Exploration and Orbital Mechanics.