Gravity Forward and Inverse Modeling on Unstructured Grids in gOcad.

@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 }
}