I am not familiar with the references you cite and am unable to access them. I am familiar with the KUT methods in gamma-ray spectrometry.

There are two issues to address. The first issue is zero and negative values. You did not say how you obtained zero and negative values. Do these come from background subtract or corrections of regions, like, subtracting uranium influence from the thorium region?

When a zero or negative result is obtained you have a problem with too much precision. This is also true with small positive values. You have too much precision because the value is below the detection limit. What you have is a small number with large uncertainty. Any attempt to use the number mathematically will result in even larger uncertainty.

The second issue is the use of ratios. Ratios are not linear. A ratio diverges as the difference between the numerator and denominator increases. It is necessary to perform some type of normalization when ratios are compared. One type of normalization is to sum the numerator and denominator and divide the sum into the numerator.

Нажаль я не є фахівець з цієї проблеми

Thank you, Mr. Alvarez. However, I did not follow your normalization. Is it like that?

Example:

(eU/eTh normalization): (eU + eTh) / eTh

The references I cited are these:

1)

Article Short note: On the use of radioelement ratios to enhance gam...

and

2) https://inis.iaea.org/collection/NCLCollectionStore/_Public/22/072/22072114.pdf

The zeros and negative values are from K (%), eU (ppm) and eTh (ppm) channels of an airborne geophysical survey. They were processed for all the corrections known for gamma-ray spectrometry data (background and others). The second reference explains that values below 0.25% could indicate the presence of water (p.52 of reference 2) and some normalization should be applied.

In reference 1 there is a example of a normalization as follows:

Ratio = (10 + s*eTh_normalized)/(10 + K_normalized)

s is a arbitrary value and could be 0.5, 1 or 2.

However, the author cited that you should normalize the eTh and K in the above equation according to the reference 2 (sum all the adjacent values that I mentioned before). I want to know how can I apply this method or if there is a better one I should use.

In our lab, we check the minimum value of a grid (e.g. K channel) and add a value that will give a minimum value of 0.01 for the grid.

Example:

K channel gridded minimum value: -0.43 %

Math grid: K_grid+0.44

Final K channel gridded minimum value: 0.01%

This avoids zero and negative values for the ratios. Nevertheless, I think this method could mask important data of the survey.

The normalization is eTh/(eU + eTh). This will ensure that no ratio is greater than one. If you do the inverse you will get 1 + R, where R is the unnormalized ratio.

The best method to have a well-behaved grid is to perform a running average along a gridline for each K, eTh, and eU value. Example: Start with the first value in the gridline and sum the first 10 K values and divide by 10. Make this average your first point along the line, but placed at position 10. Next, start at the second value in the gridline and sum the next 10 K values and place at position 11.

This will greatly reduce the noise and increase the sensitivity. Zeros are OK in the sum, but all minus values should be replaced with zeros. There will be no information loss.

Thank you for your reply, Mr. Alvarez. I will try this method.

First, negative values in AGRS are not unusual

(even for well collected and processed surveys).

IMO, the reason is impossibility to keep the survey and

processing conditions in nominal requisitions.

Therefore negative values are normal (in a sense) and no

math tricks can make them meaning.

Second, if one have to avoid empty places of ratio or similar

parameters some math tricks can help.

Just try to apply them in areas with negative values, not positive.

So, simple lifting of all values is not a good decision.

While lifting the negative values up to some tolerance level (e.g. 0.25%)

is an acceptable decision.

Minty(2011) ratio = (10+s*Tn)/(10+Kn) is unnecessarily complicated:

normalized variables have mean=0 and standard=1.0,

therefore s*Tn

Dear Vinicius,

as Eugene Druker is suggesting, negative values in AGRS are not unusual. Raw counts collected by AGRS are positive (or null) but contain some inherent statistical noise due to the nature of radioactive decay. This noise level is not very well represented in low count values, and as you process the data, and apply corrections, the noise envelope will likely widens and 'deform', potentially leading to negative values. Furthermore, if your processing parameters are slightly off, it can bring low values in the negative, while sometime it gets compensated back by further steps in the processing stream. but not always.

Our approach with AGRS data processing has been to keep negative values up to the end, and assess the final data. If all your calibrations has been done properly, and your processing parameters are sound, negative values in the end results are related to low counts in the raw data and therefore, related to measurements with a low significance. By a proper inspection of the data you can evaluate a threshold under which to mask the data. That will also prevent ratios to be thrown to extreme values.

hope this helps,

Richard Fortin

Geological Survey of Canada

Vinicius

As Fortin and Druker say small and negative values are noise in the process. As I stated in the first answer they are the result of too much precision. You could calculate a detection limit for the stripping process, summing all the uncertainty. The detection limit will give you an idea of the amount of precision that is useful. There is no data loss in values lower than the useful precision. Adding or subtracting numbers smaller than the useful precision will make no difference.

Dear Eugene Druker,

Thank you for you response.

Let’s see if I understand what you have told me. I should try to lift all my negative values up to some tolerance level (e.g. 0.25%).

Given the example below:

Value of K in one point of the line: -4.5 %

Value of eU in the same point: -2 ppm

Value of eTh in the same point: 3 ppm

New value of K: 0.25 %

New value of eU: 2500 ppm (0.25% = 2,500 ppm) OR -2 ppm?

New value of eTh: 3 ppm OR 2500 ppm?

My question is: if I have negative values for one of the radioelements, should I lift up K, eU and eTh to the threshold value or just work with the negative numbers?

Dear Richard,

Thank for you reply.

Would you mind telling me which method do you use to evaluate a threshold value to mask the data?

Vinicius,

This would be by trial and errors. Find threshold values for K, U and Th that eliminates these low areas, but still retain a useful coverage. Refer to the raw values in cps to help.

But it is probably possible to relate to some statistical parameters to quantify the estimation of these threshold values.

I'd like to add that if you have a lot of negative values in your final data, you may want to verify your processing parameters to make sure that it is not overcorrecting somewhere, especially for background removal.

hope this helps,

Richard

The threshold values should not be trial and error. Threshold values are easily calculated. It is simple to alter your stripping algorithm to indicate the detection limit.

Joseph,

In a controlled environment, indeed, you can easily detemine a detection limit. In a geophysical airborne survey, the "background" de-facto change from point to point, making this calculation not trivial at all.

This is why a fits-all approach has appeared to practitioners as a totally appropriate and practical way of getting to usefull data, at the risk of having a few outliers...

Richard

Richard

Indeed, the background does change, but the stripping algorithm can easily incorporate the detection limit for each point.

What is a fits-all if you are doing trial and error?

Joe

Joe,

"fits-all", here, means at the scale of a survey.

I still think the best approach is to let the negative values run to the end, and then mask the data that is below a certain noise level. How this noise level is determined is what we are debating.

A "trial-and-error" approach has the benefit of being easy to accomplish, and will implicitely cover for any uncertainties encountered in the processing and in the procesesing parameters calculations. It is still based on a quantitative observations of the data. A good starting point is to look at stretches of data over water. - as a matter of fact, for Vinicius benefits, if all, or a large proportion of data over water is negative that may point more to a background overestimation or a filtering step that is too heavy, and less to a weak signal issue.

cheers,

RIchard

I recommend to use artificial intelligence techniques. You can put your desired constraints on the calculated values using these techniques. You can see your answer in my recent publications.

Regards,

Hadi

Vinicius Antunes

Richard Fortin

Joseph L Alvarez

Eugene Druker

Hadi Shahabinejad

Hello everyone!

With respect to this discussion, and in the case of gamma-ray surveys, I have to add that one of the first things you should observe is your statistics. Yes, negative values ​ exist, but they tend to not be that frequent.. A quick analysis on the database histogram will show you that the proportion of negative values ​​compared to your total database is really low.

At least here in Brazil, regarding to the airborne geophysical data from the Geological Survey of Brazil, these values ​​usually represent a tiny 1% of the total data. The spatial distribution of these "incoherent" data is another factor to be considered. If the data is spread over a large area, it can represent mere noise. There are also drainage sites, dams, large rivers and lakes, where values ​​tend to fluctuate between 0. Another factor to take into account is if only one of the channels has this "incoherent" value for the point or all channels (K, Th, U) have it, because if it is only one channel, the most likely hypothesis is that it is just a noise or "fluctuation" of detected values close to zero ... In these cases you can declare the points as DUMMY and just move on in your data processing flow.

If the negative points are represented in all your channels at the same time and for the same coordinates, and are spatially concentrated in the same region... Well.. in this case you must investigate the cause. However, this will rarely be the case.

If your "inconsistent" values ​​represent somewhere between 5 - 10% of your database, probably something in the QA / QC during the data acquisition occurred, I mean, some technical failure or difficulty. In this case, the data set is under suspicion. It does not mean that the entire database would be useless, but it does mean that your analysis needs to take this factor into account when drawing conclusions or making predictions.

Another factor that can make negative values ​​appear on your maps, even if you are careful to@ declare values ​​as DUMMY in your database, is the interpolation method. Imagine two points close to zero and the interpolator, to "connect" them, does it by means of a polynomial curve of degree 2 instead of a straight line. Somewhere the curve may fluctuate to negative values ​​... and then there may be some remnants on your map. In this case, check the map statistics (histogram) and review the possibility of declaring the inconsistent points as DUMMY.

Best regards,

Frederico Sousa

Researcher in Geosciences - Geophysicist

Geological Survey of Brazil