Gravity Forward and Inverse Modeling on Unstructured Grids in gOcad.

Nacim Foudil Bey and Souvannavong Vimol and Guillaume Caumon. ( 2007 )
in: Proc. 27th Gocad Meeting, Nancy

Abstract

This work aims at calculating the gravity surface response of a 3D model using tetrahedral unstructured grid. The vertical gravity component is computed assuming that elementary cell masses are reduced to a point at their center. In theory, this formula is only valid for infinitesimal tetrahedra (point mass) and for tetrahedron distances between barycenter and point greater than the cell dimensions. This is approximately the case for deep geological structures. In other cases, especially near the surface, a mesh refinement based on 8 tetrahedra is performed to subdivide recursively coarse cells. This decomposition is performed in order to keep similar size proportions in each new tetrahedron. This recursive process is performed automatically for each new tetrahedron as long as the previous condition is not respected. The gravitational surface anomaly is then approximated by summing the effects of every tetrahedron at every location of a 2D gridded surface. An option to compute the 3D components of the gravity field is also provided. The gravity field anomaly is meanly induced by density variations in the ground, by topography and by geographic location. In the present work, the Bouguer gravity anomaly is estimated after filtering the topography, the free air and the terrain effects in a one way process. A Nettleton method is proposed to the user for selecting the density correction. Finally, the surface response is computed on a planar 2D surface accounting for complex topography effects or at the standard Geoids reference. The suggested inverse method uses a classical MVL modified Gauss-Newton method which was implemented on unstructured grid. It aims at estimating the model parameters (density) at the center of each elementary tetrahedron from the gravity surface anomaly. The procedure iteratively optimizes an objective function which measures the global difference between the observed and the computed gravity surface anomaly. The stopping condition is reached when this difference does not vary significantly between two successive iterations. These algorithms have been implemented as a gOcad plug-in. Several tests have been performed on analytical models including a homogeneous sphere, a rectangular prism, immersed into a homogeneous constant density medium in order to estimate the precision of the technique used. This module is demonstrated on a real dataset.

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    BibTeX Reference

    @inproceedings{P301_Foudil,
     abstract = { This work aims at calculating the gravity surface response of a 3D model using tetrahedral
    unstructured grid. The vertical gravity component is computed assuming that elementary cell masses are
    reduced to a point at their center. In theory, this formula is only valid for infinitesimal tetrahedra (point
    mass) and for tetrahedron distances between barycenter and point greater than the cell dimensions. This is
    approximately the case for deep geological structures. In other cases, especially near the surface, a mesh
    refinement based on 8 tetrahedra is performed to subdivide recursively coarse cells. This decomposition is
    performed in order to keep similar size proportions in each new tetrahedron. This recursive process is
    performed automatically for each new tetrahedron as long as the previous condition is not respected. The
    gravitational surface anomaly is then approximated by summing the effects of every tetrahedron at every
    location of a 2D gridded surface. An option to compute the 3D components of the gravity field is also
    provided.
    The gravity field anomaly is meanly induced by density variations in the ground, by topography and
    by geographic location. In the present work, the Bouguer gravity anomaly is estimated after filtering the
    topography, the free air and the terrain effects in a one way process. A Nettleton method is proposed to
    the user for selecting the density correction. Finally, the surface response is computed on a planar 2D
    surface accounting for complex topography effects or at the standard Geoids reference.
    The suggested inverse method uses a classical MVL modified Gauss-Newton method which was
    implemented on unstructured grid. It aims at estimating the model parameters (density) at the center of
    each elementary tetrahedron from the gravity surface anomaly. The procedure iteratively optimizes an
    objective function which measures the global difference between the observed and the computed gravity
    surface anomaly. The stopping condition is reached when this difference does not vary significantly
    between two successive iterations. These algorithms have been implemented as a gOcad plug-in. Several
    tests have been performed on analytical models including a homogeneous sphere, a rectangular prism,
    immersed into a homogeneous constant density medium in order to estimate the precision of the
    technique used. This module is demonstrated on a real dataset. },
     author = { Foudil Bey, Nacim AND Vimol, Souvannavong AND Caumon, Guillaume },
     booktitle = { Proc. 27th Gocad Meeting, Nancy },
     title = { Gravity Forward and Inverse Modeling on Unstructured Grids in gOcad. },
     year = { 2007 }
    }