IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v80y2010i10p2091-2108.html
   My bibliography  Save this article

Inverse resistivity problem: Geoelectric uncertainty principle and numerical reconstruction method

Author

Listed:
  • Mukanova, Balgaisha
  • Orunkhanov, Murat

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 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.

Suggested Citation

  • Mukanova, Balgaisha & Orunkhanov, Murat, 2010. "Inverse resistivity problem: Geoelectric uncertainty principle and numerical reconstruction method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2091-2108.
  • Handle: RePEc:eee:matcom:v:80:y:2010:i:10:p:2091-2108
    DOI: 10.1016/j.matcom.2010.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475410000911
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2010.04.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:80:y:2010:i:10:p:2091-2108. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.