RI 9361 - Direct Tomographic Reconstruction and Applications to Mining

In this U.S. Bureau of Mines report, the conditions required for the direct reconstruction of a tomogram from observed line integrals are examined. Because of the limited access to the working faces in coal mines, the special case of access to only two opposite faces is emphasized. Classical matrix methods were used for small dimensional (2 by 2, 3 by 3, and 4 by 4) applications to determine the limitations and the requirements for a solution. The results for large (n by n) grids were then inferred and generalized from those of the smaller grids and matrices. Limited access tomography is found to be appropriate for in-seam hazard detection from seismic and microwave data, but it is shown that additional data must be added to obtain a direct solution.