### Abstract

Mathematical model of vertical electrical sounding by using resistivity method is studied. The model leads to an inverse problem of determination of the unknown leading coefficient (conductivity) of the elliptic equation in R^{2} in a slab. The direct problem is obtained in the form of mixed BVP in axisymmetric cylindrical coordinates. The additional (available measured) data is given on the upper boundary of the slab, in the form of tangential derivative. Due to ill-conditionedness of the considered inverse problem the logarithmic transformation is applied to the unknown coefficient and the inverse problem is studied as a minimization problem for the cost functional, with respect to the reflection coefficient. The Conjugate Gradient method (CGM) is applied for the numerical solution of this problem. Computational experiments were performed with noise free and random noisy data.

Original language | English |
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Pages (from-to) | 2091-2108 |

Number of pages | 18 |

Journal | Mathematics and Computers in Simulation |

Volume | 80 |

Issue number | 10 |

DOIs | |

Publication status | Published - Jun 1 2010 |

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### Keywords

- Inverse problem
- Numerical solution
- Resistivity reconstruction
- Uncertainty principle

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics

### Cite this

*Mathematics and Computers in Simulation*,

*80*(10), 2091-2108. https://doi.org/10.1016/j.matcom.2010.04.002