Geodesic
2D and 3D algorithms of introcontinuation
Numerical methods and programming, Tome 17 (2016) no. 3, pp. 291-298

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The introcontinuation of a potential field for the localization of sources in the field's anomalies is discussed. A mathematical model of the field is proposed on the basis of the Dirichlet problem with a condition on the day surface. New 2D and 3D algorithms are developed to determine the critical points for the field continued into the lower half-plane. These algorithms are based on a finite-difference approximation of Berezkin's complete normalized gradient and on the determination of its critical points. Two versions of the finite-difference introcontinuation reduce a priori information requiring for the algorithms. A model experiment for the areal version (3D) procedure is considered to illustrate the determination of objects by the observed gravity field.
Mots-clés : introcontinuation, Laplace equation, Poisson equation
Keywords: Berezkin's complete normalized gradient, finite-difference complete normalized gradient, Dirichlet problem, mathematical model, inverse problem. 
@article{VMP_2016_17_3_a9,
     author = {Yu. V. Glasko},
     title = {2D and {3D} algorithms of introcontinuation},
     journal = {Numerical methods and programming},
     pages = {291--298},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_3_a9/}
}
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Yu. V. Glasko. 2D and 3D algorithms of introcontinuation. Numerical methods and programming, Tome 17 (2016) no. 3, pp. 291-298. http://geodesic.mathdoc.fr/item/VMP_2016_17_3_a9/