Dictionary:Tomography

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1. (t∂ mog’ r∂ fē) A method for finding the velocity and reflectivity distribution from a multitude of observations using combinations of source and receiver locations, or of determining the resistivity distribution from conductivity measurements using a transmitter in one well and a receiver in another well (see Figure T-10). Tomography is derived from the Greek for ‘‘section drawing.’’ Generally space is divided into cells and the data are expressed as line integrals along raypaths through the cells.


Figure. T-10. Conductivity crosshole tomography uses measurements from a transmitter in one borehole to a receiver at many locations in another borehole, and then repeats for a number of transmitter locations to determine the conductivity in a grid of cells in the intervening space. (Courtesy Kurt Strack.)


2. Transmission tomography involves borehole-to-borehole, surface-to-borehole, or surface-to-surface observations.

3. Reflection tomography (q.v.) involves surface-to-surface observations (as in conventional reflection or refraction work). In seismic tomography, slowness (or velocity), and sometimes an attenuation factor, is assigned to each cell and traveltimes (and amplitudes) are calculated by tracing rays through the model. The results are compared with observed times (and amplitudes); the model is then perturbed and the process repeated iteratively to minimize errors. Raypaths have to be recalculated after each change of assumed velocity.

4. Diffraction tomography involves calculations assuming least-time travelpaths according to Fermat’s principle rather than Snell’s law bending at cell boundaries.

5. Layer-based tomography divides the earth into layers, allowing for lateral variation of velocity within the layers, instead of subdivision into cells. Tomographic methods include the algebraic reconstruction technique (ART), the simultaneous reconstruction technique (SIRT), and Gauss Seidel methods (q.v.). See Ivansson (1986)[1] and Lo and Inderwiesen (1994)[2].


References

  1. Ivansson, S., 1986, Seismic borehole tomography—theory and computational methods: Proc. IEEE, 74, 328–338.
  2. Lo, T. W. and Inderwiesen, P., 1994, Fundamentals of seismic tomography: Soc. Expl. Geophys.


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