UBC-GIF technical note TN-004: mesh design for DCIP2D

As in any iterative inversion algorithm, the quality of the inversion results using the DCIP2D package depends to a large extent upon the accuracy of the forward modelling. The prime factor affecting the forward modelling is the discretization of the model given by the finite difference mesh. The DCIP2D Manual discusses aspects of mesh design, however, we have seen several poorly designed meshes resulting in poor conductivity / chargeability inversion results. In this technical note, we reiterate those rules.

General Rules of Mesh Design

  1. Every electrode in the data set must be placed on a nodal point in the mesh. This is true for UBC-GIF code DCIP2D only.

    2.  
  2. There should be two or three cells between adjacent electrode locations, i.e., per dipole length. Thus the width of cells is usually an integer fraction of the dipole length, a.

    3.  
  3. The cell thickness of the first layer should be a fraction of the dipole length, a, with a lower limit of about 1/5 to 1/10. At the same time the aspect ratio (width divided by thickness) of the cells in this region should not exceed 5. The finite difference solution deteriorates as this aspect ratio increases.

    4.  
  4. The core portion of the mesh is defined horizontally by the position of the first and last electrodes. The depth extent should be greater than the array's depth of penetration and the thickness should generally increase with depth. The cell thickness can increase smoothly and progressively with depth or there can be several depth zones in which the cell thickness is constant. The thickness of the cells in each zone will increase with the depth of the zone.

    5.  
  5. In the horizontal direction there should be one or two cells outside the primary model domain which have the same width as those inside. This is essential for the finite difference approximation when the electrode is at the end of the line. Beyond that, cells of logarithmically increasing width are used to pad the mesh. The padding cells should extend to a distance that is greater than the maximum length of the array, L.

    6.  
  6. Similar padding cells for the vertical direction are placed below the core mesh. The thickness of these cells increases logarithmically until the thickness of the padding zone is greater than L.

    7.  
  7. Once a mesh is formed, it should be tested by performing a forward modelling on a uniform halfspace conductivity model. If the mesh is designed properly, the forward modelled halfspace responses should not deviate from the theoretical value by more than a few percent.

The automatic mesh generator built into the code follows these rules. If you have irregular mesh the software will try to create a sensible mesh based upon the data, but the automated process is not perfect and may generate meshes that are unreasonably large. For additional information see the UBC-GIF tutorial on 2D inversion of resistivity and chargeability. The general web site for this tutorial is http://www.eos.ubc.ca/research/ubcgif/tutorials/invtutorial/index.html, while the specific page discussing meshes is at http://www.eos.ubc.ca/research/ubcgif/tutorials/invtutorial/dcres.html.