Tomography
For CHUMCross Hole Ultrasonic Monitor
(CSL Tester) with tomography support
Tomography
[Overview] [Realtime] [FuzzyLogic] [Parametric] [Matrix inversion] [3D] [Horizontal slices] [Additional reading]
Overview:
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:

Single depth encoder (not used by CHUM): The crosssection is logged three times: Horizontally, +45° and 45°. The three cross sections are combined on a postprocessing phase. The distribution of information is uniform all over the crosssection, and does not concentrate on the suspected zones. (picture 11).

Two depth encoders: Horizontal and diagonal readings are logged in the same crosssection. The operator collects much more information around defects, at any angle, and normal amount of data on good pile sections, This results in a better resolution, and smaller logs (Better information distribution) (picture 12)

Multiple receivers: are chained at fixed distances to the same line, the data gathered is same as in (1), The section needs to be logged once. This method, popular in geophysics, is hardly used in piling.
picture 11
picture 12
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.
Fuzzy Logic tomography
(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:

Find the most common FAT/Attenuation value X from all horizontal pulses. Since reallife piles are mostly solid, this value represents good* concrete.

For each pulse (including diagonals), assign a value representing how good* it is. 0=bad concrete, 1=as solid as X. the value may be calculated by FAT, attenuation, or a combination of both (Operator control)

break the pile into pixels, for each pixel, find all pulses crossing it

A pixel is good* if at least one of the pulses crossing it is good (fuzzy "or")
CHUM is actually using a faster recursive method, using a variable pixel size:

Start with the whole cross section as a single "pixel"

if all pulses passing through the current pixel agree*, or if the pixel is small enough then

this pixel is done  and painted according to the pulses value

else

break the pixel into to two pixels (vertically or horizontally, according to proportions) and submit each pixel to step 2
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:

Quick and intuitive.

Excellent cost/benefit ratio.

Very easy to explain.

Easy to view the results in the field, and to get an immediate feedback.

No special cost incurred
Cons:

Always shows small triangular ghost shadow

Might be sensitive to noise (Adequate filtering reduces this significantly)
RealTime tomography:
(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:

See pros for Fuzzylogic

Makes sure that the correct amount of data is logged: Sparse on the good portion of the pile, dense around the defects. Quality data is the most important factor for the success of any postprocessing method.
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
Parametric tomography
(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:

The initial vertical position of a defect is calculated from the 1D horizontal pulses

only one defect exists at the same vertical level

Defects are boxshape (rectangles in the cross section)

Defects are uniform (fixed velocity)

Calculation can be done on one defect at a time (superposition)
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:

Based on horizontal pulses only, assume large (Full width, generous height) defects on all locations of 1D anomalies.

For each defect:

Calculate the forward model

Calculate the error E = f( Actual data, Calculated data )

change the vector <X,Y,Width,Height,Velocity> to the direction of the biggest effect (Gradient descent)

Keep on changing in small steps, until no change can reduce E

If the defect is smaller than a threshold value (5x5cm)  drop it
Parametric tomography can give surprisingly accurate results. The results can quantify the defects (for example: "30x30cm anomaly at 3.5m").
Pros:

Quick and intuitive

Not sensitive to noise

Quantifiable, clean results
Cons:

Simplistic (Real defects are never boxshaped voids  Do we really care?)

The more realistic the forward model is, the longer it takes to calculate.

Gradient descent solution is sensitive to local minima (Reduced by trying random leaps)
Matrixbased inversion
(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:

Quantifiable results (Sound velocity)

No ghost shadows
Cons:

Slow, requires computing power, and is therefore not commonly performed in the field, but as postprocession in office

Overinterpretation: Inversion problems have many possible solutions. Matrixinversion based tomography tends to ignore this fact, and presents the results with high resolution and high confidence, leading the viewer to ignore the fact that the solution is NOT unique.
3D tomography
(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:

Nice, impressive pictures (Usually colorful)
Cons:

Data not actionable: Hard to make sound engineering calls based on pictures...

Slow, requires a lot of computing

Sometimes requires additional costly software modules, or third party services

Low additional value for cost (most of the data can be learned from the 2D plots)
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
plus much more.
Horizontal slices tomography
(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:

Nice, impressive pictures (Usually colorful)

Actionable: can cautiously assess the reduction of crosssection and effect on capacity
Cons:

Gives the wrong impression that the whole cross section is covered. We have little understanding on the width of the ultrasonic wave front.
Animated 3d tomography
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
Additional reading

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.