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    Stability and the inverse gravimetry problem with minimal data

    Date
    2020-10-11
    Author
    Isakov, Victor, 1947-
    Titi, Aseel
    Metadata
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    Citation
    Isakov, V., & Titi, A. (2020). Stability and the inverse gravimetry problem with minimal data, Journal of Inverse and Ill-posed Problems (published online ahead of print 2020), 000010151520200115
    Abstract
    The inverse problem in gravimetry is to find a domain ð • inside the reference domain ω from boundary measurements of gravitational force outside ω. We found that about five parameters of the unknown ð • can be stably determined given data noise in practical situations. An ellipse is uniquely determined by five parameters. We prove uniqueness and stability of recovering an ellipse for the inverse problem from minimal amount of data which are the gravitational force at three boundary points. In the proofs, we derive and use simple systems of linear and nonlinear algebraic equations for natural parameters of an ellipse. To illustrate the technique, we use these equations in numerical examples with various location of measurements points on\partialΩ. Similarly, a rectangular D is considered. We consider the problem in the plane as a model for the three-dimensional problem due to simplicity.
    Description
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    URI
    https://doi.org/10.1515/jiip-2020-0115
    https://soar.wichita.edu/handle/10057/19650
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