R3 is a forward/inverse solution for 3d current flow in a rectangular prism mesh. r3 can also provide an inverse solution for a 3-D resistivity distribution based on computation of 3-D current flow using a finite element mesh based on brick type (hexadedral) elements. The inverse solution is based on a regularised objective function combined with weighted least squares (an ‘Occams’ type solution) as defined in Binley and Kemna (2006).The code supplied has been compiled for Pentium processors, users working on different platforms should contact the author.

R3 requires input for generation of the finite element mesh. The user must define the mesh as a series of columns (x), rows (y) and layers (z). The user must also specify the position of the electrodes within the mesh. The electrodes can be located anywhere in the mesh, provided they fall on node points. The mesh that is created by the user consists of a foreground region and a background region. The foreground region is the area of interest. The background region is employed to account for the infinite boundary conditions. The user should gradually increase the spacing of the mesh away from the foreground region to avoid excessive computational effort. R3 will output calculated parameters (resistivity) for the entire mesh and the user must extract results for the region they wish to study. The region is parameterised in terms of resistivity blocks by grouping patches of elements.

Measurements are defined in a separate file as a set of four electrode indices. Each electrode is defined as a "borehole" number and an "electrode" number (note that the "borehole" index is used simply to help group electrode strings and does not have to refer to a "borehole"; note also that the "borehole" index can be the same for all electrodes if the user wishes not to use this labelling).

The current version will work with 200 unique electrode positions and 3000 measurements. The finite element mesh should not be larger than 75 nodes in the x direction, 75 nodes in the y direction and 51 nodes in the z direction. The maximum number of parameters is 40,000. If larger problems need to be solved please contact the author.

References

Binley, A. and A. Kemna, 2005, Electrical Methods, In: Hydrogeophysics by Rubin and Hubbard (Eds.), 129-156, Springer.