### 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 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Mathematics and Computers in Simulation*,

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

**Inverse resistivity problem : Geoelectric uncertainty principle and numerical reconstruction method.** / Mukanova, Balgaisha; Orunkhanov, Murat.

Research output: Contribution to journal › Article

*Mathematics and Computers in Simulation*, vol. 80, no. 10, pp. 2091-2108. https://doi.org/10.1016/j.matcom.2010.04.002

}

TY - JOUR

T1 - Inverse resistivity problem

T2 - Geoelectric uncertainty principle and numerical reconstruction method

AU - Mukanova, Balgaisha

AU - Orunkhanov, Murat

PY - 2010/6

Y1 - 2010/6

N2 - 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 R2 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.

AB - 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 R2 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.

KW - Inverse problem

KW - Numerical solution

KW - Resistivity reconstruction

KW - Uncertainty principle

UR - http://www.scopus.com/inward/record.url?scp=77953130716&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953130716&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2010.04.002

DO - 10.1016/j.matcom.2010.04.002

M3 - Article

VL - 80

SP - 2091

EP - 2108

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

IS - 10

ER -