[Overview] [Realtime] [FuzzyLogic] [Parametric] [Matrix inversion] [3D] [Horizontal slices] [Additional reading]
While normal (1D) CSL can only show the depth of an anomaly, tomography can help in the visualization of the shape, size and location of anomalies. It is an analysis and presentation method of captured CSL data, that projects the logged results into two dimensional (2D) plane or three dimensional (3D) body.
What is calculated?
Some of the tomography techniques described herein are linear  assuming that
waves travel in straight lines. Tomography usually uses the velocity or energy
data. To convert those into linear quantities, propagation time is used for velocity,
and attenuation is used for energy.
More advanced tomography techniques use bentray and wave front analysis in an iterative approach.
In CHUM (Cross Hole Ultrasonic Monitor), the operator may choose FAT based tomography, attenuation based tomography, or a combination.
Logging of the data:
Several methods for data logging exist:
1  2 



CHUM is using the following tomography algorithms: RealTime, Fuzzy logic, Parametric and Matrixbased inversion. CHUM also supports 3D and horizontal slices tomography.
See here (downloads/TomographyDemo.exe) a demonstration animation (No setup required!) of the tomography datacollection process.
(Unique to CHUM)
The
basic idea: A pixel is as Solid*/Good* as the best* pulse that passes through it.
All terms marked with * are fuzzy values: 0.0 means false, 1.0 means absolutely
true. 0.5 may be interpreted as "maybe", and 0.9 as "most probably" the following
table summarizes the logic operators used:
p and q  p or q  not(p) 
min(p,q)  max(p,q)  1p 
The (simplified) algorithm:
CHUM is actually using a faster recursive method, using a variable pixel size:
The image on the right shows the pixels that have been used to produce a tomography. Most of the pile is solid, and broken into big pixels. Areas with mixed good* and bad* data are broken into smaller pixels until the pixels are small enough, or all pulses through it agree*.
Compared to fixedsize pixels, the total number of pixels is very small, and the smallest pixels are much smaller. The variable pixel size method has a considerable advantage in both calculation time and resolution.
CHUM also filters the pulses before looking at a pixel, to reduce sensitivity to noise. The details of the filter are not presented here for brevity.
Pros:
Cons:
(Unique to CHUM)
Realtime tomography allows viewing the defect shape while the logging is being
performed. The operator starts with both probes at the bottom of the pile, and start
pulling. When encountering a defect, it will appear as a fullwidth void. At this
point, the operator starts lowering and raising one or both of the cables to log
diagonally. While doing this, the defect shape is formed onscreen. When done, postprocessing,
using any tomography method, can be applied to the logged data.
CHUM's realtime tomography is a simplified version of the fuzzylogic tomography, which does not require a highend computer to enable the complex calculations in realtime.
Pros:
Cons:
See cons for FuzzyLogic
Sensitive to noise: After logging lots of diagonal readings through a defect, it appears smaller or even disappears. This is later corrected in postprocessing
Nonquantifiable results
(Unique to CHUM)
The basic idea: Guess the location of a defect; apply a forward model to calculate what would the FAT/Attenuation be. Move/Resize the defect around until the forward model best matches the actual data.
Some simplifying assumptions in CHUM:
Under those assumptions  there are only 5 parameters for each defect (location
& velocity). The depth and height will not change much from the 1D data, and it
is simple to reach convergence.
The algorithm:
Pros:
Cons:
(Fully supported by CHUM)
Commonlyused tomography methods based on matrix pseudoinversion. Both are traditionally
used only on FAT/Velocity, never on attenuation (for no reason other than tradition)
Pros:
Cons:
(Fully supported by CHUM)
After taking several (3 or more) cross sections from different testtube pairs,
the data may be combined to plot a threedimensional picture of the pile, assessing
defects volume, and 3D shape.
3D tomography can be based on any of the tomography methods described above (Not including realtime)
Pros:
Cons:
CHUM3DT is our 3D engine and viewer 3D View: Rotate, Tilt, Pane, Zoom, etc slice: vertically & horizontal Peel: hide high velocities by clicking on the palette 
(Fully supported by CHUM)
A
method in which the 1D and 2D cross sections from the whole pile are combined to
plot a horizontal cross section of the pile at a specified depth.
Pros:
Cons:
Using existing "gaming" 3D techniques to interactively pane, rotate and zoom into a pile. The user can "fly" into defects, and assess their size and shape
click here to see the movie in your media player.
Aki, K., et al. (1974): Threedimensional seismicvelocity anomalies in the crust and uppermantle under the U.S.G.S. California seismic array (abstract), Eos Trans. AGU, 56, 1145.
Amir, E.I & Amir J.M. (1998): Recent Advances In Ultrasonic Pile Testing, Proc. 3rd Intl Geotechnical Seminar On Deep Foundation On Bored And Auger Piles, Ghent 1998
Khamis Y. Haramy and Natasa MekicStall (2000): Crosshole sonic logging and tomographic imaging survey to evaluate the integrity of deep foundationscase studies. Federal Highway Administration, Central Federal Lands Highway Division, Lakewood, CO.
Robert E. Sheriff and Lloyd P. Geldart (1995): Exploration Seismology, second edition. Cambridge University Press 1982, 1995.
Santamarina, J.C. and Fratta, D. (1998): Introduction to Discrete Signals and Inverse Problems in Civil Engineering, ASCE Press, Reston, VA., 327 pages.
Stain, R. T., 1982, "Integrity testing", Civil Engineering, pp. 5372.