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Research Note: Analysis of the Born Approximation.

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Title: Research Note: Analysis of the Born Approximation.
Authors: Foster, Douglas1 (AUTHOR) djfoster235@gmail.com
Source: Geophysical Prospecting. Feb2026, Vol. 74 Issue 2, p1-7. 7p.
Subject Terms: *Born approximation, *Elastic waves, *Sound waves, *Waves (Physics), *Theory of wave motion, *Scattering (Physics), *Reflectance
Abstract: The Born approximation has been extensively used to approximate scattered waves in a variety of areas in physics. The Born approximation utilizes specific terms of a series expansion and the general issues of convergence of the series and accuracy of the approximations are difficult to ascertain. I use a simple one‐interface model to examine these issues for both acoustic and elastic wavefields. The series converges in the normal incidence case, although to a value that is less accurate than that of the first‐order approximation. Also, for normal incidence and two‐dimensional acoustic waves, the series contains only odd terms. At non‐normal incidence angles the inclusion of higher order terms does increase accuracy over a reasonable range of incidence angles, but ultimately diverges from the exact reflection coefficient at large reflection angles. The series for elastic waves contains both odd and even terms, and the effects of mode conversions begin with the even second‐order term. Adding the second‐order term for the elastic case provides a more accurate prediction than the first‐order term alone, yet it is unclear if additional terms will continue to improve the accuracy of the approximation for non‐normal incidence. [ABSTRACT FROM AUTHOR]
Database: Energy & Power Source
FullText Text:
  Availability: 0
Header DbId: enr
DbLabel: Energy & Power Source
An: 192087363
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Research Note: Analysis of the Born Approximation.
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  Data: <searchLink fieldCode="AR" term="%22Foster%2C+Douglas%22">Foster, Douglas</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> djfoster235@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Geophysical+Prospecting%22">Geophysical Prospecting</searchLink>. Feb2026, Vol. 74 Issue 2, p1-7. 7p.
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  Data: *<searchLink fieldCode="DE" term="%22Born+approximation%22">Born approximation</searchLink><br />*<searchLink fieldCode="DE" term="%22Elastic+waves%22">Elastic waves</searchLink><br />*<searchLink fieldCode="DE" term="%22Sound+waves%22">Sound waves</searchLink><br />*<searchLink fieldCode="DE" term="%22Waves+%28Physics%29%22">Waves (Physics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink><br />*<searchLink fieldCode="DE" term="%22Scattering+%28Physics%29%22">Scattering (Physics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Reflectance%22">Reflectance</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: The Born approximation has been extensively used to approximate scattered waves in a variety of areas in physics. The Born approximation utilizes specific terms of a series expansion and the general issues of convergence of the series and accuracy of the approximations are difficult to ascertain. I use a simple one‐interface model to examine these issues for both acoustic and elastic wavefields. The series converges in the normal incidence case, although to a value that is less accurate than that of the first‐order approximation. Also, for normal incidence and two‐dimensional acoustic waves, the series contains only odd terms. At non‐normal incidence angles the inclusion of higher order terms does increase accuracy over a reasonable range of incidence angles, but ultimately diverges from the exact reflection coefficient at large reflection angles. The series for elastic waves contains both odd and even terms, and the effects of mode conversions begin with the even second‐order term. Adding the second‐order term for the elastic case provides a more accurate prediction than the first‐order term alone, yet it is unclear if additional terms will continue to improve the accuracy of the approximation for non‐normal incidence. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=enr&AN=192087363
RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1111/1365-2478.70140
    Languages:
      – Code: eng
        Text: English
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        PageCount: 7
        StartPage: 1
    Subjects:
      – SubjectFull: Born approximation
        Type: general
      – SubjectFull: Elastic waves
        Type: general
      – SubjectFull: Sound waves
        Type: general
      – SubjectFull: Waves (Physics)
        Type: general
      – SubjectFull: Theory of wave motion
        Type: general
      – SubjectFull: Scattering (Physics)
        Type: general
      – SubjectFull: Reflectance
        Type: general
    Titles:
      – TitleFull: Research Note: Analysis of the Born Approximation.
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              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
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            – TitleFull: Geophysical Prospecting
              Type: main
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