Stability for the one dimensional inverse problem via the gel’fand-levitan equation

DOI10.1080/00036818208839398zbMath0499.73019OpenAlexW2004643479MaRDI QIDQ3965646

Robert W. Carroll, Fadil Santosa

Publication date: 1982

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036818208839398

zbMATH Keywords

stability theoremimpulse responsesone dimensional inverse problemimpedance relative to measurement of responsereformulate Gel'fand-Levitan equationsensitivity of calculation

Mathematics Subject Classification ID

Bulk waves in solid mechanics (74J10) Inverse problems for waves in solid mechanics (74J25) Inverse problems involving ordinary differential equations (34A55) Ordinary differential operators (34L99)

Related Items (6)

Patterns and structure in systems governed by linear second-order differential equations ⋮ Reconstruction of blocky impedance profiles from normal-incidence reflection seismograms which are band-limited and miscalibrated ⋮ Series representation for the Jost solution of the Sturm‐Liouville equation in impedance form ⋮ Partial differential equation techniques in transmutation ⋮ Transmutation for systems by spectral methods ⋮ Transmutation via the momentum plane

Cites Work

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• Impedance profile inversion via the first transport equation
• Inverse boundary value problems and a theorem of Gel'fand and Levitan
• The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems
• The inversion of acoustical impedance profile by methods of characteristics
• About the stability of the inverse problem in 1-D wave equations application to the interpretation of seismic profiles
• Scattering techniques for a one dimensional inverse problem in geophysics
• Inverse scattering techniques in geophysics
• Numerical Stability in an Inverse Scattering Problem
• Stable Solution of the Inverse Reflection Problem for a Smoothly Stratified Elastic Medium
• On complete recovery of geophysical data
• Continuous and Discrete Inverse-Scattering Problems in a Stratified Elastic Medium. I. Plane Waves at Normal Incidence

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