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Inference from Inadequate and Inaccurate Data, II.

G Backus1

  • 1UNIVERSITY OF CALIFORNIA (LA JOLLA).

Proceedings of the National Academy of Sciences of the United States of America
|February 1, 1970
PubMed
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Inference from Inadequate and Inaccurate Data, III.

Proceedings of the National Academy of Sciences of the United States of America·1970

This study presents a new technique for estimating physical object properties using limited data. It simplifies complex problems involving discontinuous functions, making them easier to solve for applications like geophysical inverse problems.

Area of Science:

  • Applied Mathematics
  • Computational Physics
  • Geophysics

Background:

  • Estimating properties of complex physical objects from limited measurements is a significant challenge.
  • Previous methods required observed and sought-for properties to be Fréchet differentiable functionals on a Hilbert space.
  • Many real-world problems involve discontinuous functionals or arbitrary linear spaces, limiting prior approaches.

Purpose of the Study:

  • To develop a technique for estimating unknown properties of physical objects when direct modeling is intractable.
  • To extend previous work by handling discontinuous functionals and arbitrary real linear spaces.
  • To provide a unified approach applicable to various inverse problems and numerical analysis tasks.

Main Methods:

  • The study introduces a method to reduce problems with discontinuous functionals to a tractable case involving differentiable functionals.

Related Experiment Videos

  • This involves transforming the problem space to accommodate arbitrary real linear spaces.
  • The technique builds upon the framework of Hilbert spaces and Fréchet differentiable functionals.

    • Main Results:

    • A novel technique is presented for estimating P properties from D measurements when the object requires more than D parameters for full specification.
    • The method effectively handles cases where functionals are discontinuous and defined on restricted domains.
    • The approach is shown to be applicable to a range of geophysical inverse problems and numerical analysis tasks.

    Conclusions:

    • The developed technique offers a powerful way to address complex inverse problems previously considered intractable.
    • It broadens the applicability of functional analysis methods to a wider array of scientific and engineering challenges.
    • This work facilitates more accurate property estimation in fields like geophysics and numerical analysis.