Dual Frequency Data Blending in Real-Time

David Cist, PhD.

Michael Jeffords, M.S.

Geophysical Survey Systems Inc.

12 Industrial Way, Salem, N.H. 03079 USA.

David_c@geophysical.com

Abstract— A novel real-time image morphing approach has

been developed for Ground Penetrating Radar, GPR, two-

channel data collection, whereby co-located data sets are

intelligently merged to create one seamless image. High and

low frequency data are stitched together in such a way that the

shallow, high resolution information from the high frequency

antenna invisibly transitions into the more deeply penetrating,

lower resolution of the low frequency antenna. The transition

zone is not constant, and depends on the signal quality of the

higher frequency data which varies along the survey. While

morphing two images in one aids data playback and analysis,

the main benefit comes during real time data collection, where

viewing a single image streamlines interpretation and marking

for utility surveys.

Keywords-component; GPR. Dual-frequency, morph, blending,

noise transition zone, data processing, data display.

I. INTRODUCTION

Definitions of signal quality and signal to noise ratios (SNR), however complicated, invariably end with a general agreement that Signal, s, is defined as “relevant information” and Noise, n, is defined as everything else [1]. Any received GPR signal, rin ,will contain both. Noise can be “random,” including internal electronic noise (nelec), external interference, like cell phone interference etc. (nenvir). Noise can also be deterministic (nclutter) like ringing bands from metal plates or clay layers, or simply reflections from soil heterogeneities that one prefers to ignore.

SNR = |s|2 / |n|

2 (1)

rin = s + nelec + nenvir + nclutter (2)

The power density of the “random” noise remains constant with time and depth, while signal decays exponentially with depth due to factors like dispersion and soil conductivity. As a result noise, although ever present, is usually visible only after the signal strength has weakened to the point where SNR ≈ 1. This Noise Transition Zone is roughly defined as the penetration depth, which will be shallower for higher frequency antennas than for lower ones and will vary laterally depending on changing soil conditions.

Since there is always a tradeoff between penetration depth and resolution, one sometimes chooses to do the same survey twice with two antenna frequencies. The high frequency data is used to interpret shallow targets and soil horizons. Once beyond the penetration limits of the high frequency data, the low frequency (low resolution) antenna is used for mapping deeper structures.

Users might simply view these two data separately, but it is often more helpful to combine them into one image. Fusing radar data with other modalities (like EM, LIDAR etc.) is not new [2][3][4][5]. Overlaying GPR datasets of different frequencies and different polarizations also has a long history [6][7]. Overlays generally work, but suffer from the very real drawback that the better, high frequency information may get obscured too soon. Ideally, one would prefer to see the high frequency information only above the noise transition zone, (SNR ≈ 1).

Figure 1 shows the estimated noise transition zones for two co-located surveys: high (a) and low (b) frequency. The added detail (especially for the soil horizons) from the high frequency antenna is great while it lasts. But after about 1.5m, the high frequency signal starts to dip below the noise. The low frequency antenna can penetrate below 3m, resolving deeper targets that would otherwise be missed.

Figure 1 Example of high (top) and low (bottom) frequency data collection. Note the different ranges and the added detail of layers and targets in the top view. The green shaded regions show depths where SNR begins to degrade.

In figure 1, both noise transition zones become slightly deeper along the survey as soil conditions improve. This zone can in fact change rapidly over the course of complex surveys, sometimes over just a few meters. For example, a road survey interpretation over an clay creek bed, may suddenly need to rely on the low frequency data for penetration, before going back to the cleaner data from a sandy soil where the high frequency penetration is good.

II. METHODS

A. Detecting the Signal to Noise transition zone

There are several methods available for detecting the SNR transition zone [8]. The human eye can easily see when a range has been chosen that is too deep. (Figure 2) At some point down the scan, the signal starts to break down and fluctuate randomly.

Figure 2: The vertical yellow lines indicate the location of a scan, displayed in an image and as a plot. The dotted line marks the SNR transition zone, visible in both representations.

One obvious option is to look at the spectral content of each scan by segmenting several sections of each scan and characterizing the frequency content in each section. It is reasonable to suppose that the spectrum of regions with strong signal should resemble the broadband spectrum of the transmitting antenna, while the spectrum in the region of weak signal should broaden and “whiten.”

A second method uses a plot of signal strength. As the signal attenuates with depth, it will eventually sink below the level of the constant noise. The resultant change in slope marks this transition and indicates that there is no more recoverable signal.

A third method starts with the assumption that the center frequency of the antenna is known. Clearly, the zone where the signal becomes noisy is where other higher frequencies start to dominate. Mapping this transition can be achieved in a general sense by plotting the number of phase flips along the scan. As the signal becomes weaker, the number of phase flips will climb from the number of wavelengths per meter of the center frequency to something much higher as the signal degrades. Detecting the transition region will offer a general SNR transition zone.

A fourth method for determining the noise transition zone, involves quantifying signal stability. By comparing adjacent scans, one can spot the correct range to use. Automating detection of this region can be achieved by subtracting adjacent scans and then performing a mapping similar to the method described above, except that there will also be an amplitude component to the mapping. This method, essentially a high-pass filtered version of the previous

method, has the advantage of ignoring clutter, nclutter from Equation (2), from ringing or clay layers. Otherwise it would wrongly report plenty of signal over the entire range.

These implementations of identifying the noise transition zone, along with their advantages and shortcomings, give slightly different results, since each isolates slightly different aspects of the signal and noise.

B. Blending

To accurately blend data together, one first must collect co-incident data. Every scan from both antennas must be collocated exactly to produce the proper overlap. Even slight offsets will produce blending mismatches that will create problems for interpretation. The actual blending of two scans together can be performed myriad ways.

The simplest approach is to overlay both scans, taking into account different ranges, and making the high frequency data successively more transparent with depth. This would permit the low frequency data to take over as the depth increases. For example, one might mix proportions of two scans with depth, starting at the tip by no low frequency information to the High frequency data, and ending it the bottom with all low frequency data.

More involved variations on this process might limit the transition zone to start at one depth and span only a limited percent of the total range (0%, 5%, 20% etc.).

Figure 3: Comparing blend transition widths: 0%, 5%, and 20%.

This transition need not be linear over the blend width and need not be horizontal. It may, as in our case, follow the noise transition zone as it rises and falls along the survey. This makes inherent sense, since one would want the low frequency data to take over, obscuring the better high frequency information, only below the point where the high frequency signal fails to penetrate.

5 %

20 %

High

Low

High

Low

III. RESULTS

A. Noise Zone Implementation

Figure 4 Segmented spectral information. The right column shows data (300ns) chopped into four segments. The left two columns show the frequency plots for one scan and for the entire image.

We looked as several ways to characterize noise.

Examining the spectral content of successively deeper sections indeed showed the effect of starting with the broadband spectrum from the transmit pulse and progressively flattening out as the noise started to swamp the weaker signal. (Figure 4) These results were very promising at first, but although the visual results were obvious to interpret, actually automating these results in real time proved both challenging and compute intensive.

Figure 5 These plots show the log of the rectified amplitude of two scans. The place where the signal attenuates below the constant noise is clearly seen.

Mapping the amplitude seemed a more workable solution. Figure 5 shows Log(abs(Amplitude)) plots taken from same data as in Figure 4. This solution works nicely, especially for data with a high dynamic range, and especially when there is a long noise section. Where the noise runoff section is short, or in cases where signal and noise coexist over long stretches, the start of the transition zone is again difficult to identify. In these cases this method tends to overestimate the transition.

The results (Figure 6) from the both phase flip methods described above give slightly different results, since they measure slightly different noise characteristics. The downside of these methods is that the results are noisy and require some smoothing. But averaging the two results and smoothing worked acceptably well as a general and robust measure of the Noise transition zone.

And since the two methods are complimentary, measuring slightly different types of noise, averaging them together improves the reliability of the result.

Figure 6: Identifying the noise transition zone using the single scan phase flip method (red) and the differential scan phase flip method gives slightly different but valid results.

Figure 7 provides a more subtle data example. In this example, signal degradation starts well above what one might initially suppose just by looking at the gained image. However, closer examination, especially of the plot on the right, clearly shows how the combined phase flip method is able correctly to identify signal deterioration (shown in green) in its proper location. Amplitude detection misses this zone. This can be indirectly seen from the gain curve, shown in red on the right, which never quite flattens out at the bottom. This means that there is not sufficient run-off to make a reliable estimate of the transition zone by using Amplitude Mapping.

Figure 7: Another example of the phase flip methods used to determine the noise transition zone. Note that, although the signal has attenuated rapidly beneath this line, some signal and even data is evident.

However, any algorithm that attempts to delineate the zone between signal and noise must come with caveats.

1) The zone is not an exact depth, as the human eye easily confirms. There is no depth where Signal turns to Noise. Depending on soil conditions, what method you use, etc., the transition zone boundary can be sharp, diffuse, or even nonexistent (if it is beyond the range), but it is never exact.

2) Because this boundary is not precise, the results from scan to scan are inherently vague. Defining a contiguous transition zone requires some averaging over a few scans. This now makes the zone imprecise, not only vertically, but horizontally as well.

3) Targets can still appear beneath the noise transition zone, below the apparent penetration depth. A large reflector, like an underground storage tank in a utility survey, can still be resolved, even though it is completely in the zone where the noise is dominant.

4) The noise zone estimation can fail spectacularly, due to ringing, a dead antenna, a suddenly noisy environment etc. Any of these cases would skew the result. Going over a metal plate, for example, would falsely propagate “signal” down, resulting in a deep noise estimate, when in fact the penetration was zero.

5) The zone can shift due to filtering. For example smoothing, either vertical or horizontal, can reduce the number of phase flips per unit length. This noise zone drop would actually be intuitively correct, since filtering reduces noise by smoothing or stacking.

Clearly there are many ways in which noise transition zone algorithms can be fooled by effects not found in nature.

Although one should expect the noise zone to be strongly affected by the filtering methods applied to the data, it also depends on soil properties.

This has an intriguing potential side benefit to plotting the noise zone, as a method to map relative changes in soil

properties. For example in conductive soils like clay, we would expect signal to be absorbed. A pull-up in the noise zone is observed and has been used to map changes in soil conductivity. Figure 8 shows this result in a 3D survey over a test pit. The more conductive native soil on either side shows a corresponding pull-up in the noise transition zone. This means that (aside from all the caveats just listed) GPR can be used as an EM tool. Along with GPR data, one gets a conductivity map for free [9].

Figure 8: A 3D survey over a test pit filled with clean sand. The noise transition zone responds to drops in conductivity by dropping in depth. This has been used to map soil variability with promising results.

B. Overlapping and Blending two datasets

1. Overlays

Figure 9 clearly shows the problem of viewing two datasets over the same ground. Two perfectly registered high and low frequency surveys are displayed one on top of the other. Since the range of the high frequency data is naturally different, and since the resolution is naturally sharper, identifying the same targets in both becomes a challenge. The same layer looks completely different in the two images. The pipes reflect differently and the depths are visually hard to match.

Figure 9: High and low frequency data displayed on top of each other.

High

The most straightforward method for combining two data sets is simply to overlay one on top of the other (Figure 10).

Now analysis is easier with only one image. But a level overlay clips the more useful high frequency data at critical points, compromising analysis. We might rather see the sharper high frequency data (the interesting layer on the right) that gets obscured by the overlay.

NOTE: For Figures 10 through 13, gain contrast has been heightened to show differences. Compare with Figure 3.

Figure 10: High and low frequency data overlain on top of each other. The horizontal boundary is indicated at the arrow

Figure 11: High and low frequency data overlay using the noise transition zone. No blending is applied.

Overlaying along the noise transition zone (Figure 11) where the high frequency signal starts to fade essentially solves this problem. Letting the noise boundary determine the edge permits the sharp and clear high frequency data on the right side to be visible, while showing the low frequency data below this.

2. Blending

Since results from the noise transition zone experiments show that the boundary between signal and noise is not sharp, then neither should the overlay be. There is still useable high frequency signal to be seen beneath this level, which does not need to be completely obscured. Blending along this zone achieves the intended result of having the low frequency signal begin to take over in the region where the high frequency signal starts to fade.

Figure 12: High and low frequency data blended using the noise transition zone. The zone is blended over 5% of the high frequency range.

Figure 13: Same as Figure 12 but with 20% blend. Added detail is evident beneath the layer on the right at about 1.5m. NOTE: The low frequency noise transition zone has been added at the bottom just to warn the user of signal degradation.

Several different blending methods could have been used to combine datasets, but after some experimentation, linear mixing (shown above) gave acceptable results over all ranges and soil conditions.

Broadening the blending region, from 5% (Figure 12) to 20% (Figure 13), not only makes the overlapped zone less visible, it allowed useful and interesting high frequency data to mix in with the low frequency data. This benefit can be seen in Figure 13 on the far right side of the data at about 175cm. The high frequency data still has significant information content beneath its noise transition zone, even though degraded by noise. This information, within the 20% blend region, combines with the low frequency data to add details that would otherwise be lost.

IV. CONCLUSIONS

The benefits of blending data along the high frequency data’s noise transition zone are immediately clear. So long as the noise transition zone is identified correctly, information is optimally presented for both high and low frequency datasets, letting the user focus on information extraction and interpretation.

Blending over a diffuse (20%) boundary permits both datasets to contribute information into the transition region. This works only if the two surveys are exactly registered. Errors in co-location will create discontinuities, especially evident along this boundary.

The benefits of being able to do all this in real time means that decisions can be made and regions can be marked immediately in the field, rather than waiting to interpret information back at the office. So long as antenna registration is precise and the high frequency noise transition zone is accurately identified, blended data in real time has the potential to reduce errors in data analysis, improving the accuracy and speed of field interpretation.

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