text:
The Ezekiel WATCHMAN
God's Warning Message
. . . The end has come it has DAWNED for you; Behold it has come! . . . a day of trouble is near . . . Now upon you, I will soon pour out My fury . . . So you, son of man: I have made you A WATCHMAN for the house of Israel; therefore you shall hear a word from My mouth and WARN them for Me (Ezekiel 7:6-8; 33:7).
Behold, I will send you Elijah the prophet before the coming of the great and dreadful Day of the LORD (Malachi 4:5; Matthew 17:10-11).
t is so utterly tragic that the
Warning Scriptures
are ignored as meaningless to most of the membership. This is due primarily to their leaders who are
from the true teachings and their rejection of the endtime Elijah and the
Warning Messages
given through him by Jesus Christ of what is now being seen as the
impending destruction
of the House of Joseph.
History Repeating Itself
When looking closely at what took place in Jerusalem in 66-70 A.D., one can clearly see a direct parallel with what is being witnessed in
phenomenon UNPARALLELED
in our time in heavenly signs; such as: lightning striking twice the dome of St. Peters, a meteor striking Russiaboth taking place five days apart in February 2013! Also record-breaking acts in nature: devastating tornadoes, record-breaking floods, drought, snowfall, etc.
A Four-Year Warning
The duality of the warnings that began being given by God in 66 A.D. was four years before the destruction of Jerusalem in 70 A.D. Based on the many major unsolvable and accelerating problems facing the House of Joseph, it would appear there will be little more than four years, if any, before
also befalls the House of Joseph.
The Day of Pentecost
This Holy Day, observed in Jerusalem in 69 A.D., played a very significant role for it was on this Day the final warning came from God to the Jewish people of the impending destruction of their city.
Ancient History in Bible Light
, Page 261, Miller: Again on the night of the last Pentecost ever celebrated in the Sanctuary as the priests were going by night, as their custom was, to perform their sacred ministrations, they said that, in the first place, they felt a quaking, and heard a sound as of a great multitude, saying, Let us remove hence.
Josephus adds: But these men interpreted some of these signals [
the beginning of the heavenly signs occurred in 66 A.D.
] to their own pleasure, and some of them they utterly despised, until their madness was demonstrated, both by the taking of their city and their own destruction.
Historical writings reveal the destruction began taking place on the night of the Passover in 70 A.D.134 days later Jerusalem was conquered by the Romans and the Temple of God was burned to the ground.
Is History Repeating Itself?
Page 262:
The Escape of the Christians
. . . Some time before the siege, following the warning in Luke 21:20-22, they withdrew to Pella, beyond the Jordan, led by Symeon . . .
As it was with the Jews in Jerusalem who dismissed these heavenly warning SIGNS, so it is with present-day society who have moved on, leaving behind them what they have already witnessed with no serious contemplation.
Thus it will come to pass just as Jesus Christ said:
. . . It will come as a snare on all those who dwell on the face of the whole earth
(Luke 21:35)
Church Members Sleeping
The Church Era of the Laodiceans, due to their self-righteousness, is slumbering in sleep believing they are self-sufficient and in need of nothing! Matthew 25:1-13; Revelation 3:17.
The Philadelphian Era MUST learn from the past along with the present, otherwise there could be a most horrible and terrible price to pay with the cost of the crown of life and kingship (
Revelation 3:10-13
). The Apostle Paul wrote a warning for each of Gods people:
And do this, knowing the time, that now it is high time TO AWAKE OUT OF SLEEP; for now our salvation is nearer than when we first believed. The night is far spent, the day is at hand. Therefore cast off the works of darkness, and let us put on the armor of light
(Romans 13:11-12; Ephesians 6:10-18)
The Day of the Lord
Based on the miraculous heavenly signs in Jerusalem in 70 A.D., and with prophetic Scriptures in mind, undoubtedly there will be other heavenly visible SIGNS, as a type and forerunner of the very endtime pointing to the rapidly approaching closeness of the
Great Tribulation;
and the return of Jesus Christ.
Whether, or notthere are all of the other SIGNS connecting with prophecy that reveal how close we are to the end by the increasing gripping
leading us into the
famine, disease epidemics, nuclear warfare, and the Great Tribulation!
A time so terribly bad as never before witnessed or ever will be again
(Matthew 24:21; Daniel 12:1).
Are There Few to Be Saved?
Thinking about their own salvation and others, the disciples asked if only a very few would end up being saved. The answer Jesus Christ gave to His disciples should be of great concern met with soberness and soul searching:
Then one said to Him, Lord, are there FEW who are (
to be
) SAVED? And He said to them, Strive (
Grk: struggle, literally agonize as in agony
) to ENTER through the narrow gate, for MANY, I say to you, will SEEK TO ENTER and will NOT be able . . .
(Luke 13:23-28).
Grave Warnings
There are many grave warnings in Scripture of Gods people possibly being deceived and led astray by false teachers with their erroneous teachings. Members should always be vigilant and on guard knowing to follow them will lead into the
Great Tribulation
with possible loss of eternal life as warned by Jesus Christ:
Beware of false prophets (
), who come to you in sheeps clothing, but INWARDLY they are ravenous wolves . . . [
] Not everyone who says to me, Lord, Lord, shall ENTER the kingdom of heaven, BUT he who does the will of My Father in heaven . . .
(Matthew 7:15, 21-29)
To be under the protective caring love of Jesus Christ from all that we will soon be experiencing, we MUST be watching vigilantly, praying always seeking a closeness with our wonderful Father and Jesus Christ so as to be graced with His loving protective care and ultimately be able to stand before His glorious presence when He returns
(Luke 21:36)
. Nothing else really matters.
Heavenly Signs
Realizing the heavenly signs are already being seen as forerunners of the fullness of the Day of the Lord, no one will be able to say they were not
over many years by Gods late apostle when the fullness of these things come to pass:
Now WHEN these things
LOOK UP and Lift Up Your Heads, BECAUSE your redemption draws near
(Luke 21:25-28)
Surely everyone who watches the news media cannot help but realize how bad off this nation really is, including England and the other nations of Israel; so utterly bad off, there is no solution other than repentance and turning to God.
The House of Joseph is now on the very precipice of terrible problems soon to surface as never before witnessed by this generationthat will spell their end as nationsalong with the deaths of many of the members of Gods Church!
The Gospel/The Ezekiel Warning
In the little time left there is yet Gods Work to be completeda real loving and caring responsibility of taking His true gospel to the world as a witness and food for Gods scattered people along with the Ezekiel Warning Message
(Matthew 24:14; Ezekiel 33:1-11)
Should YOU not be in the faithful Church Jesus Christ is using in this end-time to support His Work
of the
Recorded Works
of His late apostle on our websites?
(Revelation 3:7-13; Matthew 24:45-47)
Please know by making the needed move could save oneself from experiencing the
Great Tribulation
and the possible loss of life! A coming time so utterly sad there will only be a few who will have heeded the
, the majority wont, as Gods prophet makes known:
The Duality of Scripture
Also I set WATCHMEN over you, saying, Listen to the sound of the Trumpet! But they said, We will NOT listen
(Jeremiah 6:17)
As to Why
. . . You have forsaken the LORD your God and the FEAR of Me is NOT in you, says the LORD God of hosts
(Jeremiah 2:19)
Faithful Flock
This small Church is being used by Jesus Christ as
to make all of those
of Gods late apostle available, which are even more timely and revealing
than they were then.
Most sincerely and lovingly I ask: Where will you and I be when
springs upon the Church and Israel as a snare
? Unless we are
watching, praying and enduring faithfully, while
to the
to the saints and
by Gods promised Elijah, we could be caught up in it and our cry to God would then be too late
(Malachi 4:4-6; Jude 3-4; Luke 21:34-36; Revelation 3:8, 10).
be preparing ourselves
while there is yet remaining
The MYSTERY OF THE AGES
Jesus Christ led His apostle and the promised Elijah
His teacher
to write the last book of his life,
to be A REMINDER of all of the doctrinal teachings Christ RESTORED
within His Church through him. By the use of this original
book (ISBN 0-396-08773-6) with the Holy Bible, His people should be enabled to recognize the strong deception that is now on His Church by Satan the devil and keep themselves away from it.
The Philadelphia Remnant
To be kept informed from a Biblical perspective the meaning of the continued
record breaking disasters
in the nations of Israel and other major problems that are now coming closer together we offer freely a subscription to our magazine. It can also be read on our website (
The Ten Commandments Book
This fairly new book continues to support what Jesus Christ used His Promised Elijah of the End-time to restore: the Ten Commandments, Statutes and Judgments, along with the original Doctrinal Teachings
(Malachi 4:4-6; Matthew 17:10-11; Jude 3)
The Three Elijahs
The book of
The Three Elijahs
can be read on our website (
) or downloaded from it. This book makes known how these
Three Men
were used by God to perform basically the same responsibilities and for the same reasons.
God had ample reason for these three men to have the same name as Elijah. And though John and Mr. Armstrong had their own names, they were
. . . to go forth before Him (Jesus Christ) in the spirit and power of Elijah
(Luke 1:16-17)
. The identity of the end-time Elijah is established with Biblical proof and by his fruits.


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subset: commoncrawl


text:
- Society of Exploration Geophysicists
We introduce two new traveltime picking schemes developed specifically for crosshole ground-penetrating radar (GPR) applications. The main objective is to automate, at least partially, the traveltime picking procedure and to provide first-arrival times that are closer in quality to those of manual picking approaches. The first scheme is an adaptation of a method based on cross-correlation of radar traces collated in gathers according to their associated transmitter-receiver angle. A detector is added to isolate the first cycle of the radar wave and to suppress secon-dary arrivals that might be mistaken for first arrivals. To improve the accuracy of the arrival times obtained from the crosscorrelation lags, a time-rescaling scheme is implemented to resize the radar wavelets to a common time-window length. The second method is based on the Akaike information criterion(AIC) and continuous wavelet transform (CWT). It is not tied to the restrictive criterion of waveform similarity that underlies crosscorrelation approaches, which is not guaranteed for traces sorted in common ray-angle gathers. It has the advantage of being automated fully. Performances of the new algorithms are tested with synthetic and real data. In all tests, the approach that adds first-cycle isolation to the original crosscorrelation scheme improves the results. In contrast, the time-rescaling approach brings limited benefits, except when strong dispersion is present in the data. In addition, the performance of crosscorrelation picking schemes degrades for data sets with disparate waveforms despite the high signal-to-noise ratio of the data. In general, the AIC-CWT approach is more versatile and performs well on all data sets. Only with data showing low signal-to-noise ratios is the AIC-CWT superseded by the modified crosscorrelation picker.
Radar traveltime tomography has become increasingly popular for hydrogeologic, environmental, and geotechnical applications (Tronicke et al., 2004; Gloaguen et al., 2007; Johnson et al., 2007). Such studies are possible because in the radar regime, the wave velocity is a function mainly of the dielectric permittivity distribution in the ground (Davis and Annan, 1989) and because the permittivity of free water is well contrasted relative to that in most geologic materials (Olhoeft, 1981). Experimental and theoretical models transform the dielectric permittivity into volumetric water content or porosity, depending on saturation conditions (Topp et al., 1980; Endres and Knight, 1992; Sihvola, 2000). Hence, mapping the radar-wave velocity field within the ground can lead to a permittivity distribution map of the imaged region and consequently characterize the region's porosity or water-content distribution.
Three general approaches exist to reconstruct the velocity field from borehole radar measurements. The most common approach regroups ray-based methods, which assume that radar-wave propagation can be described by the laws of geometric optics (Olsson et al., 1992; Zhou and Fullagar, 2001; Gloaguen et al., 2005). In this approach, the velocity field is constructed by the inversion of the first-arrival traveltime data. Another approach, also based on the inversion of first-arrival traveltime data, relies on Fresnel volume sensitivities that account for the finite frequency of the crosshole radar signal to improve the resolution (Day-Lewis et al., 2005; Buursink et al., 2008). The last approach, based on inverting the full radar waveform (Ernst et al., 2007; Kuroda et al., 2007), has yet to gain widespread use, mostly because of huge computing requirements. Obviously, the velocity model obtained from ray- and Fresnel-volume-based tomographic reconstruction depends on the quality of the first-arrival times, which is largely dependent on the fidelity of observation of the radar phase and the consistency of timing measurements. Therefore, the collection of high-quality first-arrival times is a prerequisite for determining accurate dielectric-permittivity, porosity, or water-content results.
To obtain insight into the repercussion of timing errors on velocity estimates, consider a wave traveling at constant velocity V over a distance l from a transmitter to a receiver. The traveltime of the wave over this distance is . The variations of velocity with respect to traveltime and distance are (1) Errors in traveltime and positioning lead to an error in velocity: (2)
Assuming exact positioning of the transmitter and receiver and defining as the relative error of the velocity estimate, we can see the latter is equal to the negative of the relative error of the traveltime. Hence, overestimating the traveltime by a given proportion will lead to underestimating velocity in the same proportion. It is interesting that, given a constant absolute timing error, the relative error decreases with increasing travel distance. It is therefore likely that the relative timing errors vary among crosshole measurement data sets. This results from the particular geometry of data acquisition that involves typically wide angular coverage which leads to significant variation in travelled distances. Inconsistent relative timing errors undoubtedly introduce artifacts in the reconstruction of the velocity fields.
Nowadays, manual picking by a well-trained human operator is still the best method to obtain reliable first-arrival times. However, some errors can result from the highly repetitive nature of the work or from inadequate working procedures. It is also a very time-consuming task. Quick, accurate first-arrival picking is of great importance when processing large data sets. Although automatic picking schemes exist, they were developed mainly for earthquake seismology and exploration seismic studies. These methods must be adapted and improved for radar applications because of the different nature of the radar wavelet and the poor signal-to-noise ratio (S/N) often encountered for large transmitter-receiver offsets.
In the framework of ground-penetrating radar (GPR) traveltime tomography, adaptations of the crosscorrelation picker are proposed by Messinger (2004) and Irving et al. (2007), whereas Tronicke (2007) devises a scheme based on a statistical criterion. Messinger (2004) proposes the combination of crosscorrelation and short-term averaging/long-term averaging (STA/LTA) techniques to design an automated picking procedure, whereas Irving et al. (2007), in a scheme also based on crosscorrelation, apply the technique to data organized in common-ray-angle gathers.
Although generally performing well, techniques based on crosscorrelation can suffer because similarity of radar waveforms is not always met. On the other hand, methods based on statistical criteria are applied on each trace individually and do not require similarity to be effective. Tronicke (2007) finds that one such criterion, the Akaike information criterion (AIC), performs well except for low S/N data and uses ad hoc time windowing based on an apparent velocity to guide the algorithm. In all cases, postprocessing quality control (QC) is required to validate the output of the picking and correct outliers manually.
In this contribution, we propose two alternative approaches to improve the accuracy of picking and decrease the number of postprocessing corrections for outliers inherent to automated methods. One method is derived from the approach of Irving et al. (2007) and is based on crosscorrelation of traces collated by ray-angle interval. To mitigate the effect of differences in waveform shape caused by late arrivals (such as waves refracted at the air-ground or saturated-unsaturated interfaces, or reflected waves) and differences in the first-break phase, a window is applied to isolate the first-break wavelet to crosscorrelate and pick only the first arrival.
The second method operates on each trace independently to bypass the restrictive criterion of waveform similarity. It is based on an improvement of the AIC picker used for P- and/or S-wave picking in seismology (Maeda, 1985) by introducing the continuous wavelet transform (CWT). The CWT acts as a band-pass filter well localized in time. The analysis of the phase part of the transform allows us to better distinguish the change of the radar wavelet phase. Our pickers are added to bh_tomo, a MATLAB borehole georadar 2D tomography package described in Giroux et al. (2007).
Modified crosscorrelation picker
The first method is based on the work of Irving et al. (2007). Irving's algorithm is based on the crosscorrelation of traces with a reference waveform for which the arrival time is known. The originality of the approach resides in the reference waveform being obtained iteratively from the data set through a specific sorting of traces.
First, the traces are aligned using crosscorrelation, with the reference trace initially being the one with the highest S/N. Then, the aligned traces are stacked to produce a new reference waveform, which is used to realign the traces. This process is repeated until all traces are aligned properly. Finally, the arrival time is picked manually on the reference trace, with the arrival times of the other traces determined from the crosscorrelation lags. The method is said to be semiautomatic because the user must pick the reference trace and intervene during the alignment of the traces to reject those that cannot be aligned properly.
To mitigate the effect of changes in the GPR phases on crosscorrelation, Irving et al. (2007) determine a number of different reference waveforms that represent ranges in transmitter-receiver angle in which the arriving pulses have a similar shape. This is achieved by gathering the traces by ray-angle intervals. As they illustrate, this step is essential to obtain high-quality results. The main assumption behind this step is that waveforms recorded at similar angles have similar shapes. Irving et al. (2007) point out clearly that significant problems might arise in situations in which this assumption is violated, such as for data collected above the water table or near the surface, where sharp velocity contrasts, refracted arrivals, and changes in antenna coupling impact greatly the waveforms and frequency content.
To overcome the latter limitation, we propose preprocessing the data in a manner that isolates the first cycle of the GPR waveform (referred to as first-cycle isolation). By doing so, waveform similarity is increased and interference with scattered arrivals during crosscorrelation can be partially, if not completely avoided. This step is applied typically to traces with moderate to high S/N because the scattered arrivals usually are not visible on traces with low S/N.
The preprocessing step proceeds as follows: First, each trace is normalized to its maximum absolute value. Then, the traces are crosscorrelated with a wavelet of the form (Arcone, 1991) (3) where f is chosen to be the dominant frequency of the signal. To automate the procedure, the beginning of the first cycle is picked at the first time lag exceeding a given crosscorrelation amplitude threshold, typically 0.25. A time window slightly wider than the wavelet of equation 3 and beginning slightly before the above time-lag datum is applied to nullify the undesirable signals (see Figure 1). In this manner, we ensure the sought onset is not altered. The time window is extended with cosine tapers at the leading and trailing edges to smooth out transitions. Note that the wavelet of equation 3 could be substituted by any other wavelet that would be more adapted to the data at hand. However, because we need to use only a time window to suppress later arrivals and do not need to determine the onset time itself, equation 3 works well enough. Once this step is completed, the procedure of Irving et al. (2007) can then be conducted using the windowed signal.
Another problem that arises when using crosscorrelation for onset picking is that when the dominant frequencies of the wavelets vary, the widths of the wavelets vary and, therefore, they differ from the reference wavelet (Figure 2a). An immediate consequence is that the crosscorrelation lags will not fall exactly at the onset, leading to an error in the picked time. To help minimize this problem, the ability to stretch the first cycles to a common length is added to the procedure. The time scale of each trace is rescaled by a ratio of , where is the dominant frequency of the trace and is the average of the dominant frequency for all traces. Because the crosscorrelation picking procedure requires that the time scales be consistent, all stretched traces must be interpolated to a common time scale. An example of the results obtained with this procedure is shown in Figure 2, illustrating the improved similarity between the rescaled traces and the reference obtained after stacking. After completing the picking procedure, one must scale back the obtained times to their original time frames.
Obviously, the quality of the time-rescaling correction depends on an accurate estimate of the dominant frequency of the first cycle of the radar wavelet. This estimation is an important task because at this step its exact location in the radargram is unknown. As a first estimate, a low-pass Chebyshev filter is typically applied before computing the frequency spectra, and the autoregressive estimator of Burg (Marple, 1987) is used on the whole trace. Autoregressive (AR), as well as moving average (MA), and autoregressive moving-average (ARMA) models are prediction models that allow relatively simple parametric descriptions of the second-order statistics of random processes, which can be used to efficiently compute their power spectral density. Spectral density estimates obtained using AR models present sharp peaks and offer good spectral resolution (Marple, 1987). In Burg's method, the power spectral density is obtained from the coefficients of an AR model that minimizes the sample-prediction-error variance in the least-squares sense. The frequency sample interval in discrete Fourier spectra is the sampling rate divided by the number of samples N used in the discrete Fourier transform. If the frequency spacing is too large, ambiguities can arise in determining the frequency content if the narrowband signal components have center frequencies that fall between the N frequency evaluation points (Marple, 1987). Hence, a potential source of error is the low resolution in estimating the dominant frequency of the radar wavelet resulting from a relatively large time discretization step and a limited number of samples. To mitigate this, we pad the ends of the traces with zeros to increase the number of points used in the Fourier transform and to decrease the frequency spacing.
The procedure to find the dominant frequency is iterative to avoid outliers that are frequent with data having a low S/N. The algorithm is initiated with the order n of the autoregressive prediction model set to two. If the frequency at the maximum energy falls outside a prescribed range (usually equal to , where is the nominal frequency of the radar antennas), the order n is incremented and the spectrum is recalculated. If a dominant frequency cannot be found for , the time rescaling correction is not performed. Note that the Chebyshev low-pass filter is applied for spectral estimation only, i.e., the picking is performed with the unfiltered traces to avoid possible bias caused by phase distortion.
In summary, the preprocessing procedure for one trace includes the following steps:
1) Low-pass filter the trace and store the original trace.
2) Apply zero padding to the trace.
3) Set the order n of the AR model to two.
4) Compute the power spectrum using Burg's algorithm.
5) Set to the frequency when the power is maximum.
6) If is outside and , where , compute the power spectrum using Burg's algorithm with the updated value of n and set to the frequency when the power is maximum.
7) The retrieve the original, unfiltered trace. If is inside , perform first-cycle isolation if desired. If time rescaling is desired, perform time-rescaling correction for the trace, tag trace as rescaled, and store for future reverse correction of picked time. Otherwise, leave the trace intact.
After applying this sequence to the whole data set, the traces are gathered by their respective associated ray angle and the picking procedure can be initiated.
AIC-CWT picker
In radar crosshole measurements, there can exist several possible paths followed by the EM energy between the transmitter (Tx) and receiver (Rx), e.g., direct, reflected, refracted, tube waves. In other words, different wave types can be present in a radar trace; therefore, similarity between traces recorded at different locations is never guaranteed. As such, it is appealing to have an automated picking method that does not rely on waveform similarity. For this reason, the AIC picker is chosen as a starting basis because of its simplicity, efficiency, and possible automatic implementation.
For any method, and for the AIC in particular, the quality of the picked times is dependent on the S/N of the recorded traces. Figure 3a shows an example of a typical radar trace and the parameters used in defining the S/N retained in this paper. First, it is necessary to define the strength of the radar signal as (4) where r is the discretized trace, std is the standard deviation, is the sample interval from to , is time index of the maximum amplitude of the radar trace, is the sampling interval, and is the dominant frequency of the trace. The S/N is defined as (5) where is the standard deviation of noise (usually calculated with the last 100 samples of the radar trace).
The distortion of the shape of the radar waveform (amplitude and phase) is caused by various phenomena and depends essentially on intrinsic ground absorption and scattering, radiation patterns and antenna coupling, wave interference (transmitted, refracted, and reflected), and Rx-Tx distance. In general, the longer the wavepath, the higher the distortion. The S/N is usually high for a small Tx-Rx angle (shorter wavepaths) and can be very low for a high Tx-Rx angle (longer wavepaths). Figure 3b shows an example of a radar trace for a high Tx-Rx angle. For this trace, the S/N is low and the radar signal is attenuated, with the frequency content different than the trace with a small Rx-Tx angle of Figure 3a.
Before picking, it is advisable to remove some noise to improve the quality of onset timing. Our experience shows that the following preprocessing steps usually work well: trend removal, data selection based on S/N level, and background noise removal by stationary wavelet transform denoising. Trend removal is carried out by linear interpolation. However, in rare cases the trend can be nonlinear and approaches such as polynomial trending or high-pass filtering should be used. After this step, all traces that have a low S/N — typically less than five — are discarded. The final preprocessing step is the translation-invariant denoising using the stationary wavelet transform (SWT) (Mallat, 1999).
The theory and numerical implementation of the discrete wavelet transform (DWT) and the SWT are well documented in the literature (Daubechies, 1992; Mallat, 1999). The DWT consists of decomposing the signal in a series of approximations and details using a filter bank and decimation. More precisely, the signal is convolved with two filters constructed from a scaling function (a low-pass filter) and from a wavelet function (a high-pass filter). The two filtered signals are decimated by suppression of one sample out of two. The high-frequency filtered signal (detail coefficients) is stored, and the process is repeated with the low-frequency filtered signal (approximation coefficients). At each level, the scale increases in a dyadic manner resulting from the decimation. In this way, the original signal is decomposed into several scales according to its frequency components.
In contrast to the DWT, the SWT is time invariant, a desirable property for signal reconstruction and denoising (Coifman and Donoho, 1995). The SWT algorithm differs from the DWT algorithm in that for each level, the decimation step is suppressed and the filter is upsampled by inserting zeros between filter coefficients. This way, the length of approximation and detail coefficients are the same as the length of the original signal. For low S/N data, the SWT denoising technique outperforms classical Fourier-based low-pass filtering when the noise variance is high near the lower cutoff frequency of the filter (Dolabdjian et al., 2002). In fact, low-pass filters typically introduce a time shift and a distortion of nonstationary signals such as radar recordings. Conversely, the SWT denoising technique is more selective: The wavelet coefficients of the radar signal are concentrated on only a few large coefficients compared to the noise, which has its energy spread over a large number of smaller coefficients. The denoising technique relies on a thresholding rule that is based on a noise model that removes the low-valued coefficients and on an inverse wavelet transform that reconstructs the radar signal with little loss of detail.
The denoising process can be summarized in three points: compute the SWT of the radar trace, apply a threshold strategy on the detail coefficients of the wavelet transform, and reconstruct the radar trace by synthesizing the denoised coefficients. The threshold strategy involves determining a base noise level in accordance with the data noise model. Coefficients below this threshold are considered noise (and should, therefore, be set to zero), with coefficients above this threshold defining the signal that should be kept and perhaps modified.
Several types of thresholding exist, with hard and soft thresholding the most common (Mallat, 1999). The hard thresholding approach we use sets the coefficients below the threshold to zero and does not modify the others. For thresholding selection rules, the universal thresholding scheme (Donoho and Johnstone, 1994) is used and nonwhite Gaussian noise assumed. Therefore, the universal threshold is calculated level by level. After several tests, a Daubechies wavelet with two vanishing moments (Mallat, 1999, p. 241) is chosen as a mother wavelet. It has a short support and permits a good reconstruction of discontinuities. The stationary wavelet transform is done using three levels of detailed decomposition.
Automatic denoising with hard thresholding does not remove residual spikes. To overcome this problem, the denoised traces are processed with a median filter of very short length, typically five samples, to preserve the radar waveform as much as possible. The result of the preprocessing sequence on a real radar trace is presented in Figure 4. The residual noise is highly smoothed and the shape of the radar waveform is well preserved.
The AIC is based on an assumption that the radar trace can be separated into locally stationary segments, each modeled as autoregressive processes. The intervals before and after the onset time are assumed to be two stationary time series. Maeda (1985) defines the AIC function as (6) where r is the discretized radar trace of N samples and var is the variance. The global minimum of the AIC function defines the onset point of the first arrival. In some cases, multiple wave arrivals can occur in a radar trace, and the AIC picker will choose the wavelet that has the strongest phase. In other words, the AIC function contains several local minima, each corresponding to the onset of a particular wavelet; but the global minimum corresponds to the wavelet that has the strongest phase (Zhang et al., 2002). Thus, we must guide the work of the AIC picker by choosing an appropriate time window that contains the onset of the first arrival. Our experience shows that for crosshole radar data, the minimum of the AIC function computed over a trace truncated in time immediately after its maximum amplitude corresponds to the first-arrival onset in most cases. We use this minimum in our algorithm.
One noticeable shortcoming of the AIC picker is that the onset time it provides is always somewhat late (or early) compared to the true time, depending on the level and frequency content of the noise. This is illustrated in Figure 5, where the relative error on the time picked with the AIC estimator increases from 0.13% for the noise-free trace to 3.29% for a trace having an S/N of 10.5. Although its performance is improved by the preprocessing steps, better picking precision should be achieved. To obtain a higher level of accuracy, we propose a correction to the AIC method based on the complex continuous-wavelet transform (CWT).
The wavelet transform of a signal allows its analysis in terms of local time-frequency compositions. This is achieved by decomposing the signal over dilated (or scaled) and translated wavelets. The CWT is different from the SWT; in SWT, the wavelet is sampled in a dyadic manner for fast multilevel evaluation. In CWT, the evaluation is performed at any desired scale. The 1D continuous wavelet transform of a radar trace can be seen as the convolution of with a scaled version of a mother wavelet that acts as a dilated band-pass filter (Mallat, 1999). Evaluated at time b and scale a, the CWT is given by (7) where is the complex conjugate of the translated and scaled wavelet.
For this application, the complex Morlet wavelet was chosen as the mother wavelet because it offers a good trade-off between time localization and frequency resolution. It is defined as (Teolis, 1998) (8) where is the bandwidth parameter and is the wavelet center frequency. The parameter is set equal to the dominant frequency of the radar trace to evaluate the CWT at the scale of the radar signal. The phase of the CWT reaches π at minima in the signal and crosses zero at the maxima. This can be seen in Figure 5a–d, which shows synthetic traces with an increasing level of noise and the corresponding phase responses of the CWT. In particular, the CWT phase response is a consistent estimator of the phase of the radar trace. Hence, the phase reaching π nearest to the AIC picker can be used as the onset of the first arrival, provided the first oscillation is positive. As shown in Figure 5, this correction improves the accuracy of the picked times; within this example, the largest relative error is 1% for the AIC-CWT method compared to 3.29% for AIC alone.
The approach can be summarized as follows:
1) After preprocessing the data, the traces are truncated in time at their maximum amplitude, the AIC is calculated on all truncated traces; the onset picking is determined by finding the AIC minima.
2) For each trace, the dominant frequency of the radar wavelet is calculated and then used to scale the complex wavelet transform. If cannot be found with the procedure, the frequency at the maximum of the amplitude spectrum is taken.
3) The position of the first break of the radar wavelet is extracted from the phase part of the complex wavelet transform. We then ensure the CWT correction falls near the AIC pick, i.e., if , the the first-arrival picking is . Otherwise, the first-arrival picking is .
4) After all traces are processed, common-receiver-gather plots with associated first-arrival picks and uncertainties are displayed for visual QC.
Synthetic data
To evaluate the performance of the proposed algorithms, we measure the accuracy of the picks and the amount of manual work required at the postprocessing QC step. To achieve this, the true traveltimes of the traces must be known. Synthetic data are generated by finite-difference time-domain (FDTD) modeling and the true traveltimes extracted from the modeled traces.
Two models are considered: the first mimics a heterogeneous saturated sand aquifer and the second includes a vadose zone and the air-ground interface (see Figure 6a and b). The physical properties (permittivity, conductivity) of both models are determined from a program developed by Giroux and Chouteau (2008). An FDTD scheme in cylindrical coordinates is then used to compute the synthetic crosshole radargrams. The source function is a Ricker source wavelet. The grid cell is , and the time step is to avoid numerical dispersion and ensure stability. Figure 6c and d shows one transmitter gather for each of the models. Traces obtained from model 1 exhibit a large similarity, whereas traces obtained from model 2 show a greater degree of dissimilarity, with superimposed arrivals related to refracted and reflected waves at the air-ground interface.
Real radar traces are contaminated by various sources of noise, the level of which obviously impacts the accuracy and reliability of any automated picking procedure. This aspect is studied independently by adding three levels of noise to the synthetic traces. Uniformly distributed pseudorandom number sets are scaled to represent noise of 0.1%, 0.2%, and 0.5% of the maximum absolute value of all traces for both data sets and are added to the traces to yield a total of eight data sets, six with noise and two without. An example of the increasing level of noise on a synthetic trace is shown in Figure 5.
The first measure of performance is the time deviation between the picking schemes relative to the true onset times. The true traveltimes are obtained from the noise-free traces by selecting the first time index in the FDTD traces at which the absolute amplitude is above zero. The FDTD time step is lower than the usual sampling frequency of field equipment. Hence, to obtain more representative results for the picking tests, the synthetic traces are downsampled to a time step (typical for field survey acquisition) from the FDTD time step. The original crosscorrelation scheme of Irving et al. (2007), labeled XC, is compared to the modified crosscorrelation with first-cycle isolation XC1, the modified crosscorrelation with first-cycle isolation and time rescaling XC2, and the AIC-CWT picker (AIC).
Figure 7 shows the time deviation relative to the true onset for two levels of noise for model 1 (the heterogeneous model). Figure 7a and b shows the time deviation versus S/N with a positive time deviation, meaning a late pick. Figure 7c and d shows the cumulative curves for absolute values of relative time deviation and S/N. The cumulative time deviation curves are asymptotic to the percentage of picked traces, i.e., the ratio of (semi)automatically picked traces over the number of traces in the data set.
From these figures, it appears that the modified crosscorrelation pickers work well for traces having both high and low S/N, with almost all traces picked with less than a 2% deviation. The modifications brought to the original crosscorrelation scheme also improve the results, although the time-rescaling step does not appear to bring significant benefit when compared to first-cycle isolation alone. This is explained by the fact that for these data sets about 95% of the traces have approximately the same dominant frequency. There is almost no dispersion, and the time-rescaling correction is not justified in this instance. Although performing well with cleaner radargrams, the accuracy of the AIC-CWT picker degrades for noisier data. For example, only 44% of the traces have less than 2% deviation on the noisier data set (Figure 7d). When comparing Figure 7a and b, one notices the AIC-CWT picker has the tendency to pick late on noisy data. This decrease in performance at low S/N is observed by Tronicke (2007).
Although the radar traces of model 1 have a high degree of similarity, the waveforms obtained with model 2 (the vadose zone model) are more disparate. Not surprisingly, the performance of the crosscorrelation pickers degrades as the similarity between the traces diminishes. This is visible in Figure 8, which shows the time deviation from the true onset for two levels of noise for model 2. There are many late outliers for all three crosscorrelation-based pickers, even at high S/N values. For most, these outliers result from unpicked air-ground refracted arrivals, which have lower amplitudes than the direct arrivals. Although easily spotted in postprocessing, these outliers require manual correction unless, of course, only direct or perhaps reflected arrivals are sought (Tronicke et al., 2001). Nevertheless, the crosscorrelation pickers have absolute deviations of less than 2% for more than 80% of the traces. Here again, there is almost no dispersion in the data, and the time-rescaling step brings no benefit. The AIC-CWT picker has the advantage of not generating outliers but shows a severe degradation of accuracy, caused by the very low overall S/N (e.g., only 13% of the traces have a S/N above 20 for 0.5% added noise level).
Tables 1 and 2 summarize the results by listing the mean and standard deviation of the timing error for both models at all noise levels. For the data set obtained with model 1, the modified crosscorrelation pickers have a clear advantage, except for the ideal, noise-free scenario when the AIC-CWT and crosscorrelation pickers perform equally well. For crosscorrelation pickers alone, the increased similarity brought by the isolation of the first cycle manifests itself by an overall improvement over the original algorithm. The results for model 2 are different. For noisy data, the mean of the deviation times is comparable for all methods. However, the AIC-CWT has an advantage, again for the noise-free scenario but also in terms of deviation around the mean, which is at worse four times lower than for the crosscorrelation pickers.
It is important to remember that in processing the arrival times with the crosscorrelation methods, the user can reject the traces that cannot be aligned properly because of a strong dissimilarity with other traces in the common-ray-angle gather. This is done to improve the shape of the stacked reference trace, which impacts the precision of the picks. These rejected traces can be processed manually afterward. On the other hand, the AIC-CWT picker processes all of the traces but sometimes generates outliers for low S/N traces. These outliers must be discarded after visual inspection or picked manually. With the AIC-CWT picker, very noisy traces are rejected on the basis of their S/N by fixing a rejection S/N threshold, and many picking runs can be carried out to choose the best threshold.
For all methods, the accuracy of the picks can be unsatisfying and can also be adjusted manually in postprocessing. A certain degree of manual intervention is needed for all automatic picking methods, which should be as low as possible. Hence, the second measure of performance relates to the number of automatically processed traces and to the manual work needed to achieve the final results.
Tables 3 and 4 list the percentages of automatically or semiautomatically processed traces, manually adjusted picks, and overall processed traces. The results are comparable for all methods, except for the AIC-CWT picker on the noisier data sets in which more manual postprocessing is needed. It is worth noting, however, that the crosscorrelation methods are semiautomatic and require some level of processing by the user — hence, having an advantage over the AIC-CWT picker in manual postprocessing alone.
Field data
To confirm the conclusions obtained from the synthetic data, the algorithms are tested further with two sets of data collected in the field. The first was obtained in a limestone quarry where a large campaign was carried out to delineate clay-filled karsts. This data set exhibits a very low overall S/N, with only 25% of the traces having a S/N larger than 20. The shape of the radar waveforms in this example have little distortion, and only some traces show the superposition of waves and interference.
The second data set was acquired on a concrete structure (Giroux et al., 2006). In contrast to the limestone quarry data set, it is characterized by heavy distortion of the shape of the radar wavelet. The disparity in radar waveforms is caused mainly by the intrinsic dispersive proprieties of the concrete at the site, in which electrical resistivity measurements performed on 66 coring samples yielded an average of . The disparity is also caused by the presence of reinforcement bars and other reflectors. The second data set is also fairly noisy, with low-frequency and inductive wow events of small to moderate amplitudes, in addition to the usual high-frequency noise. With this data set, a high S/N (as defined in equation 5) can be misleading because the low-frequency noise tends to be interpreted as a signal. A RAMAC system from Malå was used, with antennas having nominal frequencies of 250 and for the first and second data collections, respectively.
Figure 9 shows the time deviations of the automated picking methods from manually picked onsets for the two data sets, which are considered the correct arrival times. Initially, 68.1% of the total number of traces could be correctly picked manually for the limestone quarry data set. This percentage is only 44.3% for the concrete structure data set. The accuracy of our performance criterion is reduced because the automated methods might pick onsets rejected by the operator during manual picking (it happened for the AIC-CWT picker, as reflected with percentages above 100% in Table 5). Hence, some of the eventually correct picks might not be included in the results shown in Figure 9 because of the absence of reference data. Although not rigorously verifiable, we expect this effect to be marginal.
For the limestone quarry data set, all automated pickers perform equally well, with the modified crosscorrelation methods picking more than 81.5% of the traces with less than a 2% deviation; the AIC-CWT lags slightly behind, with 68.2% of the traces having the same precision. Here, the percentages are calculated with respect to the number of manually picked traces. Therefore, in terms of all available data (including traces not picked manually), the percentages are lower, i.e., on the order of 55% and 46% for the modified crosscorrelation and AIC-CWT pickers, respectively.
In agreement with the results obtained with the synthetic data, the AIC-CWT method is affected more by low S/N than the other methods, as shown in Figure 9a. Also of interest is the fact that the time-rescaling correction improves the results significantly below 4% deviation, i.e., XC2 picked 10% more traces with less than 2% deviation than XC1. This is explained by the strong dispersion observed in the data, as shown in Figure 10.
For the concrete structure data set, the crosscorrelation methods do not appear appropriate. For these schemes, the time deviations are below 2% for at best 24.5% of the manually picked traces. The poor performance of the crosscorrelation pickers is explained by the fact that sorting into common-ray-angle gathers fails to guarantee waveform similarity. Although an improvement over the original crosscorrelation scheme, the first cycle detector used in the XC1 amd XC2 approaches fails to isolate the first wavelet oscillation in a sufficient number of cases, even with high S/N data, as seen in Figure 9b. This is caused by the presence of a highly distorted and relatively low-amplitude first arrival on a significant number of traces. Figure 11 illustrates the traces corresponding to ray angles between 7.5° and 12.5°. On the concrete structure data set, the AIC-CWT picker performs better. It picked about 61% of first arrivals within 2% of manual picks, as seen in Figure 9d.
With regard to the amount of manual postprocessing work performed, Table 5 illustrates the performance statistics in terms of the percentage calculated with respect to the number of manually picked traces. For the limestone data set, the amount of postprocessing work is relatively similar for all methods and the modified crosscorrelation pickers required slightly less manual work than the AIC-CWT method for a slightly lower final amount of picked traces.
The situation is different for the concrete data set. For the crosscorrelation pickers, a large number of traces had to be rejected manually in the semiautomated phase of the processing. Because of the lack of similarity within the common angle gathers, it was difficult to obtain a satisfying reference waveform from the stacking procedure. This is reflected in the percentages of automatically picked traces for the XC, XC1, and XC2 pickers, which are 67%, 82%, and 76%, respectively. A considerable amount of manual work is also needed in postprocessing to pick the rejected traces and correct the outliers.
The situation is different for the AIC-CWT approach, in which the percentage of automatically picked traces is higher than the amount of manually picked traces (120%). In postprocessing, only 26% of the traces were adjusted manually, which is 50% less than the crosscorrelation pickers. For a large proportion of these traces, they were discarded, as reflected by the final number of picked traces reaching a value of 113%. The concrete structure data set is an example in which the AIC-CWT method presents a clear advantage over the crosscorrelation methods.
Two new algorithms have been developed to automate first-break picking of crosshole radar data, each having its own strengths and deficiencies. In the first algorithm, a technique based on crosscorrelation of traces sorted into common ray-angle gathers was modified to incorporate a detector designed to isolate the first cycle of the radar signal and a time-rescaling operator to stretch the isolated wavelets to a common length in time. First-cycle isolation improves the results in all tests performed. On the other hand, the time-rescaling correction proves useful only when strong dispersion is observed in the data. The modified crosscorrelation picker is very accurate, even for data with low S/Ns, as long as the shapes of the radar waveform are not too disparate. In such situations, the second algorithm, based on AIC with a correction derived from the CWT, is more robust.
The only drawback of the AIC-CWT picker is the performance degradation at moderately low S/N. Both methods require careful postprocessing QC to correct for the outliers resulting from the automated procedures. Based on a relatively short experience with the new algorithms, we estimate that, postprocessing included, the gain in processing time with respect to manual picking is about three to four times better for the crosscorrelation pickers and perhaps one order of magnitude better for the AIC-CWT picker.
One shortcoming of the modified crosscorrelation picker is the inefficiency of the first-cycle detector in highly distorted data sets. Possible improvements could be the development of pattern recognition criteria to define the degree of similarity between the traces. Sorting the radar traces in groups following these criteria rather than by ray angle is susceptible to produce better results. We are investigating the advantages of a first-cycle detector based on the AIC-CWT picker. As a final note, both proposed methods require an estimate of the dominant frequency of the radar signal and some form of band-pass filtering. This leads us to suggest that a relatively high time sampling rate should be used when performing data acquisition to achieve a high resolution of the frequency spectra.
This material is based on work supported, in part, by the Natural Sciences and Engineering Research Council of Canada (operating grant RGPIN848 from M.C.), and by the Fonds québécois de la recherche sur la nature et les technologies under contract ER-115473. The authors thank Anaïs Chabagno for testing the algorithms and the associate editor and three anonymous reviewers for feedback that greatly improved the manuscript.
- Received September 18, 2008.
- Revision received December 22, 2008.


text: We are very excited to be offering headshots to all our clients. We were recently invited to photograph the good folks at Roche. The annual conference was held at the QT hotel on the Gold Coast which is just fantastic. We had heaps of fun and enjoyed photographing the delegates for their promotional materials and social media sites. Here is a few samples of the headshots we took.


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{enjoy the silence at Wordless Wednesday}
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p.s. I know this is supposed to be wordless, but when I took Sam outside that morning and saw these spiderwebs all over the grass (there were at least five), I thought it was the beginning of "The Mist" or something, lol. Luckily this past summer I've made great progress in learning to live with spiders and bees.


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Where is the wisdom of Solomon when you need it? And most desperately do we need it when it comes to athletes who may or may not be cheating with performance-enhancing drugs. The latest case of the world champion British triathlete, Tim Don, who missed three drug tests in the past 18 months and is now serving a three-month ban, is a classic cautionary tale. Did he do it? Is he innocent? Are the rules negligent or bordering on the criminally insane? If you were the judge, what would you do: reach for the black cap or wave the magic wand of exoneration?
These are the facts. After missing the three tests, Don supplied his reasons/excuses to UK Sport, Britain's anti-doping authority. They were considered unacceptable. A hearing was convened at which he was deemed guilty only of forgetfulness and a possible two-year ban was commuted to three months. He will only miss three competitions but his UK Sport funding has been withdrawn for the duration of the ban. He has accepted his punishment.
In person, he is a chirpy character, slim and small. His hair seems to weigh more than he does. His gold medal from the World Championships in Lausanne hangs casually on a cupboard door. This is at home in Loughborough, where he lives with his girlfriend, Kelly, about 10 minutes from the university.
"It wasn't really expected," he is saying of his big win in Switzerland last month. "I'd been racing well, but only in smaller races. It was great, but the missed tests have got more publicity. I was in The Sun. Triathletes are never in The Sun. The headline was 'Don And Dusted!'." He laughs, clearly neither traumatised nor made taciturn by recent events.
One of the central tenets of his defence was the fact that he had been tested nine times in the same year he missed three tests. He disappears and returns bearing a clutch of forms that prove he was tested at certain competitions including the World Cup in Beijing last month and the World Championships in Switzerland. The Swiss, typically efficient, sent him a letter to tell him he was clean. Usually he hears nothing. Unless, as with the missed tests, there is a problem.
In a box on some forms he has to write what drugs he has taken in the last seven days. On one he admits to Vitamin C tablets, zinc, iron and a sleeping pill (administered by the team doctor). In all, he can recall nine tests, six of them at competitions.
The three missed tests were all out-of-competition tests and these were his given reasons. 1) Sept 13 2005: "We'd been competing at the World Championships in Japan. We were staying in a Japanese hotel, sleeping on the floor, no one spoke English. We had to fly out a translator in the end. No way could I have updated my whereabouts on a computer. There was none of that there. I did the event and collapsed of heat exhaustion. The performance director had to stop me swallowing my tongue. Two days later we flew to Beijing and that's when I missed the test. I had completely and utterly forgotten to update the information in the system and the testers were looking for me at a swimming pool in Loughborough."
2) Feb 21 2006: "We were competing at the South African Championships and the computers crashed at the hotel where we were staying. I thought, 'Cool, no worries. I'll update it tomorrow'. But then I did the race. Collapsed with heat exhaustion again and the next day we flew to Australia for our preparations for the Commonwealth Games. The day after the flight I missed the test, but to be honest, updating my whereabouts was the last thing on my mind. The testers went to Loughborough again."
3) June 7 2006: "There was a good standard track and field meet here in Loughborough. Some of Kelly's friends were running and I wanted to check out some possible training partners, so I went along to watch. It over-ran, as these meetings usually do. I wasn't thinking about any possible drug test and when I got back home at 10.10pm, the testers had left 10 minutes ago."
There we are. It is hard to believe that someone with two missed tests, teetering on the brink of damnation, could be so airily negligent of timing. On the other hand, it has to be said that some athletes do a tremendous job of projecting an image of dopiness (no pun intended). Don reliably informed me that he and Kelly often go out together and come back a few hours later only to find their key still in the front door. The scale of his irresponsibility is admittedly staggering, so much so that it is either endearingly nutty or suspicious. To recap: athletes are required to spell out their whereabouts for one hour per day, five days per week. This is so that drug testers can find them. Don claims to have forgotten to do this. On those occasions when he did remember he said he could not get on to a computer. If he did, he said the system was too complicated to access. So why didn't he use a phone?
"He misunderstood that," explained Norman Brook, chief executive of the British Triathlon Association. "He said that at the hearing as well, that he couldn't use a phone. I corrected him. In fact, there is a free phone number you can use home and abroad, though I'm not sure how easy it would have been to use a phone from South Africa. All this confusion is about the message and whether athletes are absorbing and understanding the message. We've got to revisit the message. We've got to deliver it more strongly."
According to Don, his induction into the new whereabouts system in the summer of 2005 consisted of a crowd of athletes huddling round a demonstrator and her laptop, which initially would not work. People had homes to go to, he said, their brains were switched off. He is not sure he fully understood the campaign. He produces a plastic red key ring from UK Sport with phone numbers written in such tiny lettering they were barely legible. They are thinking of fridge magnets and mobile stickers next, presumably in bigger print.
But the point is, Don missed three out-of-competition tests in a row, yet has been treated very leniently. Perhaps because he had the backing of his sport; perhaps because to meet him is to like him. He is friendly, cheerful, even giggly. The tribunal gave him the benefit of the doubt, and had a harsh word to say about the system. They concluded he was a preoccupied lad with other things on his mind. He is either that or a very good actor. But there is a serious point here to make about out-of-competition tests. They are the only reliable guide to cheating, as UK Sport are the first to admit.
"What's important is the unpredictability," a spokesman said. "To test at an event or a couple of days before or after an event is not as effective because it doesn't take rocket science to work out that an athlete can come off drugs for a competition. The cornerstone of our system is out-of-competition testing. It is imperative as a deterrent, to prove innocence and to catch cheats."
That is why when Don explains he has been tested nine times, those at events are less relevant. That leaves three. One was four days before the World Championships, conducted by the International Triathlon Union, and another three days afterwards – Don is not sure by whom. That leaves one. On Aug 9 2006 and conducted by UK Sport. It must have been negative or he would have heard otherwise by now.
So we are where we are, in a thoroughly indecisive situation. You have to feel sympathy for British triathlon, a minority sport that has somehow managed to produce six world champions at different disciplines. For its size, the sport is punching well above its weight. Brook is now begging for a harmonisation of rules worldwide that would make the system for his athletes less confusing. "I'm sure Tim is innocent," he said. "If I didn't think that I would have to question why I was in the sport at all." He pointed to the inconsistencies. For instance, the ITU operate a system where athletes have to identify their whereabouts for two hours instead of one. WADA, the World Anti-Doping Agency, allow drug-control officers to phone their quarry to find out where they are. Their British counterparts turn up, wait an hour and go. All this is indeed a wretched maelstrom of red tape, useful though if you are looking for a loophole to avoid prosecution. Drugs in sport have made cynical sleuths of the majority.
That does not include everybody. Don's father, Phillip, the former football referee, is not remotely angry with his son. "No, Dad's not cross at all. He said, 'Well, bloody hell, of course you're going to forget things like that.' He can see that maybe UK Sport took this system live a little bit early, before all the problems were ironed out." UK Sport can counter that criticism. "At the end of the day, grown adults in receipt of a lot of public funding have to take responsibility," said the spokesman. "It drives us mad." They are not the only ones. The wider public have every reason to be driven mad with rules that do not dovetail and missed tests that result in inconclusive punishments. Tim Don, in effect, has been half-damned. He has definitely committed a doping violation. He has a stain on his record. But he alone will know whether that stain should go deeper and ban him from all future Olympic competition or whether it should be washed clean away.
One significant fact, however, should emerge from this hopelessly chaotic muddle. Tribunals should look very closely, not merely at missed tests but the pattern in which they fall. Don was not tested out of competition from September 2005 to August 2006. That was a long time. If he is innocent, the system has done him wrong by not proving him so. If he is guilty, he got lucky.
This is not, by the way, a campaign against a truly affable competitor whose performances this year ought to act as an inspiration.
Nor is it against a sport in which Britain is excelling. It is merely an example, a case study, of the fine old mess we're in. It ought to be fixed. Bring out the stickers, lay on the text numbers, and next time an athlete misses three out-of-competition tests in a row without a totally compelling reason, ban them for two years.
Don's case is the warning. There really is no excuse after this.
Perhaps the last word belongs with the Don himself. "It was a pure case of not understanding the system and forgetfulness. I suppose I'm lucky in some ways that the sentence was quite light, but it's the stigma that goes with it. That's all it takes. Just three missed tests and it can put your career in tatters. For me, how do I remember 2006? The year I won the World Championships or the year they tried to do me for drugs?"
Testing times
MISSED OUT-OF-COMPETITION TEST (in transit to Beijing)
2 25.9.05
In-competition test (won Newcastle Duathlon, Australia)
3 21.2.06
MISSED OUT-OF-COMPETITION TEST (just arrived in Australia)
4 24.3.06
In-competition test (4th in Commonwealth Games)
5 15.5.06
In-competition test (racing for French team, Beauvais)
6 7.6.06
MISSED OUT-OF-COMPETITION TEST (late from Loughborough track meet)
7 2.7.06
In-competition Test (racing in Beauvais)
8 9.8.06
Out-of-competition test (by UK Sport)
9 30.8.06
Out-of-competition test (four days before World Championships)
10 3.9.06
In-competition test (1st in World Championships)
11 6.9.06
Out-of-competition test (three days after World Championships)
12 24.9.06
In-competition test (Beijing World Cup triathlon)