Minneapolis, MN: U.S. Department of the Interior, Bureau of Mines, TN 432, 1994 Apr; :1-2
Objective: Improve the reliability and accuracy of subsurface images using constrained tomography with enhanced ray-tracing capabilities. Background: Geophysical tomography is a technique for imaging the structure of a rock mass using seismic or radio waves, in the same way that medical CAT scans image human tissue using X-rays. Tomography has found numerous practical applications related to mining, including lithologic and structural characterization, fracture detection and fluid monitoring, void detection, and evaluation of stress state and integrity of mine structures. Problems: Two fundamental problems have largely prevented geophysical tomography from enjoying the tremendous success achieved by medical tomography. The first is a consequence of practical limitations on the placement of sources and receivers of wave energy: ideal resolution can be attained only when the region being imaged is entirely surrounded by sources and receivers, so that it is crossed by rays traveling in all possible directions. When such coverage is impossible or impractical, the inversion becomes underdetermined: there is not enough information in the measured data to provide a mathematically unique solution. The second major problem in geophysical tomography is the necessity for detailed ray tracing. Commercial software, as well as previous U.S. Bureau of Mines (USBM) software, employs a ray-shooting algorithm that may be unable to model some ray paths when velocity contrasts are larger than about 100%. These "shadow zones' result in loss of data and degradation of reconstructed images. Approach: The USBM has developed new software for PC-based tomographic processing that implements two important advances for dealing with ray tracing and the non-uniqueness problem. The new program, MIGRATOM (migrating wavefront tomography), models the propagation of a continuous wavefront (according to Huygens' Principle from optics), rather than tracing individual ray paths, and thus avoids the shadow-zone problem that affects programs based on ray shooting. In addition, MIGRATOM incorporates concepts of fuzzy logic into the application of constraints to help reduce the non-uniqueness problem. How It Works: MIGRATOM uses the simultaneous iterative construction technique (SIRT), which involves repetitive updating of an arbitrary starting model until it satisfies the measured data values. The use of different starting models allows the user to assess the robustness or uniqueness of the image obtained. MIGRATOM can be set up to run under the straight-ray approximation (which executes rapidly) or to account for refraction of ray paths (which is more computationally intensive but more physically realistic). Straight-ray reconstructions are always a useful first step, and they provide an indication of when curved-ray processing is needed. In an underdetermined inversion, the problem of non-uniqueness can be reduced by incorporating constraints based on any additional information available about the site. Such information may range across a spectrum from objective, quantitative data (such as measured borehole velocities) to more subjective, qualitative limitations (such as the constraint that the structure should be generally layered, with possible localized anomalies). To accommodate the varying degrees of uncertainty in these constraints, MIGRATOM borrows the fuzzy logic concept of the continuous Boolean function: a constraint can be designated as having a "truth" value anywhere from 0 (certainly false) to 1 (certainly true). This allows MIGRATOM to give greater weight to the better determined constraints. Applications: USBM researchers have used MIGRATOM for a variety of mining-related applications, including detection of abandoned underground workings, evaluation of the stress distribution in mine pillars, and characterization of fractures prior to in situ leach mining.
Minneapolis, MN: U.S. Department of the Interior, Bureau of Mines, TN 432