This is the file used to define a finite difference mesh for 2D
modelling and inversion. In the file, the x-z plane is divided into a
rectangular grid. By convention, the z-axis is positive down. fdmesh.dat
has the following structure:
The mesh can be designed by considering it as consisting of a core portion representing the region of interest and a padding zone which ensures that the boundary conditions in the finite difference modelling are handled correctly. In the core portion, the horizontal mesh is mainly controlled by the experiment grid on which to collect the data, so the mesh partition in this region is usually uniform given that the data are collected at constant intervals and the cell width is an integer fraction of the station spacing (or dipole length of the array). The finite difference algorithm used in the program can only place sources at nodal points and it produces solutions for the potential at the nodal points in the mesh. It is thus imperative that the mesh is designed such that each electrode is located on a node. This condition is ensured if all electrodes correspond to horizontal nodes, since the current version of the DCIP2D library works with surface data only. Generally, two cells are recommended between adjacent stations (i.e., per dipole length). In the presence of topography, one might use a finer partitioning in sections where the topographic relief changes rapidly. This helps to better approximate the topographic surface using the finite difference mesh.
In the presence of surface topography, the top of the finite difference mesh corresponds to the highest point on the surface (see also the description of topo.dat). Since the current sources are all on the surface of the earth, the vertical mesh has thicknesses which generally increase with depth. The cell thickness should be small near the surface and increase slowly in the upper region that is within the array's depth of investigation. Finer partitioning can be used at a depth where there is rapid change in the conductivity for forward modelling or where one might expect anomalous structures in the inversion. The maximum depth for the mesh should be considerably larger than the depth of investigation provided by the survey. The thickness of the cells, especially near the surface, should be determined in reference to the horizontal partitioning so that the cells do not have an extremely large aspect ratio (width divided by thickness). Cells with extreme aspect ratio tend to degrade the quality of the forward solution and they can also cause undesirable abrupt changes in the inversion results. It is good practise to keep the aspect ratio of cells less than 5.
Once the core mesh is designed, a set of padding cells is required to extend the mesh horizontally. Three to five cells whose width progressively increases by a factor of two to three provide sufficient extension so that the boundary conditions are adequately handled. The general rules for the mesh design and specific parameters used for an automatic mesh generator are described in the JACI Technical Note TN004.
It is good practice to generate the mesh and perform a forward modelling using a uniform conductivity model. If the mesh has been properly designed then the apparent conductivities obtained from the forward modelled responses should not deviate from the true conductivity by more than a few percent. If the deviation is larger, the mesh should be modified and the halfspace test performed again. This test is valid when there is no topography. However, a mesh designed properly for a model with topography should pass the halfspace test when the mesh is used alone without topography.
Example of fdmesh.dat file:
A 48×27 mesh with the region of interest being X=[-100,100]. There are
9 segments in the file defining the horizontal partitioning which goes
from X=-300. to X=300. The region [-100,100] has been divided into 40
equal length cells. Four padding cells of increasing width extend the
mesh out to [-300,300]. In the Z partitioning there are 14 segments over
the depth range [0,300]. Note that the bottom depth is considerably
larger than the depth of investigation of the survey.