3D trace elements-- how does the internal standardization calculation work?

edmarshall

I would like to use the 3D Trace Elements DRS, as it seems to outperform the older Longerich et al. (1996)-based trace elements DRS, but I'm having trouble understanding how the new data reduction scheme works. Maybe this is a good venue to ask this question.

In Paul et al. (2023), which describes the 3D trace elements approach, the first step of calculations seems to be creating a calibration curve for each standard block, concentration against intensity, and then extrapolating the calibration curves between the blocks to cover the sample data. The paper also seems to describe the older Longerich-based calculation method as a "single point calibration curve". As you all know well, laser ICPMS data doesn't work well with calibration curves because of drift, changes in laser settings between spots, matrix effects between phases, etc. The Longerich-approach sidesteps calibration curves by using internal standardization, so it is confusing to me that it is described as a "single point calibration curve", and thus very confusing to me that the 3D trace elements data reduction scheme is described as a multi-reference material calibration curve that is extrapolated through time. How does it actually work? How does internal standardization work with this approach?

Is there somewhere where the calculation procedure is explicitly written out? Thanks for your help!

Bence

Hi @edmarshall

This a good question. I started writing a reply here but it started to get a bit long. So I've turned it into a blog post:

https://notes.iolite.xyz/posts/tes_combined/

If you have any questions after reading that, or if you spot any errors, please feel free to post here.

Kind regards,
Bence

edmarshall

Thanks so much for answering this question. After posting it, I had decided that the question was too onerous, and had deleted it and started working through the DRS code myself. This has been slow going and I really appreciate you dredging it back up and answering it fully.

I guess a point of confusion was that the calculation process is described as a two step process. The code does work this way, so it's certainly accurate to describe it this way. But let me try to describe it as if it were a single step process, and see if this is correct:

The Longerich equation is (using the variable names from your blog post):

And because sensitivity is defined:

Then, by substitution we could rewrite the Longerich equation to be:

Within this way of thinking about it, the biggest difference between the older Trace Elements approach and the new 3D Trace Elements approach is that the sensitivities for the RMs are calculated very differently. In the old trace elements DRS they were calculated from measurements of a single RM, and then (if I understand correctly) the sensitivities at each time point are given by a chosen function (spline, linear fit, mean, whatever). However, in the new 3D trace elements DRS, the sensitivities are produced from linear concentration-intensity fits of each block of standard data (if the fits are forced through zero, then the sensitivity is the slope of the fit line). These fits are then extrapolated through time (using splines, linear fit, mean, whatever) allowing sensitivity to be calculated from the fits at each time point.

So unless I messed up somewhere, this means that essentially the 3D trace elements DRS is creating sensitivities for each element by averaging together (well not really averaging, fitting is not averaging-- but not sure what to call it) the sensitivities of several different standards. This is a super cool way to do it!

Thanks again!

BTW-- some equations in your blog post are a bit messed up on my end. Here's what I see (tried in Chrome and in Edge):

Bence

edmarshall I really appreciate you dredging it back up and answering it fully.

Not a problem! We are very keen to ensure that iolite is not a "black box" and that interested and inquisitive folks such as yourself can really drill down into what iolite is doing. And if you find an error, or a better way of doing it, we can incorporate those changes and make iolite better in the process 😃

I would agree with the equation you show for Li, which is just the count rate of the sample divided by the sensitivity of the RM (this is the same as dividing by the slope in the more traditional calibration curve approach), and then multiplying this by a sensitivity ratio for the Int stds between the RM and the sample. I would just rearrange it to:

to make it clear that you're dividing the count-rate by the sensitivity and then multiplying that by a correction factor... but it's exactly the same as the way you put it.

edmarshall In the old trace elements DRS they were calculated from measurements of a single RM, and then (if I understand correctly) the sensitivities at each time point are given by a chosen function (spline, linear fit, mean, whatever).

Yes, this is correct.

edmarshall in the new 3D trace elements DRS, the sensitivities are produced from linear concentration-intensity fits of each block of standard data (if the fits are forced through zero, then the sensitivity is the slope of the fit line).

You are correct that the sensitivity is the slope of the fit to the RMs, but this is always the case whether the fit is forced through zero or not. Remember sensitivity is just the slope of the line in the tradtional calibration curve plot: steeper line means better sensitivity and vice versa. I tend to avoid the confusion between "sensitivity = slope of calibration plot line" vs "sensitivity = R / c" by referring to the latter as "yield". They're the same if you assume zero intercept and use a single RM, but if you're using a fit to multiple RMs, it's the slope of that line.

edmarshall These fits are then extrapolated through time (using splines, linear fit, mean, whatever) allowing sensitivity to be calculated from the fits at each time point.

💯 We interpolate the slope and intercept of the calibration plot so that at any point in time you could reconstruct an interpolated calibration plot.

edmarshall this means that essentially the 3D trace elements DRS is creating sensitivities for each element by averaging together (well not really averaging, fitting is not averaging-- but not sure what to call it) the sensitivities of several different standards. This is a super cool way to do it!

Yes, exactly. Fitting a line to multiple RMs is what I would describe it as.

The only wrinkle in this approach that is (slightly?) ignored by previous attempts at multi-RM calibration for LA-ICP-MS is that your calibration curve may be affected by the different ablation properties of your RMs. For example, if you use NIST glasses and basalt glasses, as we did in our paper, you can see very slight differences in the yield of each. There's a yield correction built into the calibration curve where you select a primary RM and then all the other RMs yields are adjusted relative to that, but it might not be necessary if you're using all the same matrix type RMs and discussing that correction could perhaps be another post by itself!

Thanks for asking probing questions, and thanks for the heads up about the equations in the Note.

Bence

Geonostalgia

There's a yield correction built into the calibration curve where you select a primary RM and then all the other RMs yields are adjusted relative to that, but it might not be necessary if you're using all the same matrix type RMs and discussing that correction could perhaps be another post by itself!

Just following this conversation now and really enjoying it - I'd like to keep this part going! What are the considerations for choosing to use primary RM yield calibration correction (or not)?

For example, in the 2023 paper for the NIST-basalt glasses example (Figure 2), it didn't make as much of a difference whether or not yield normalization was used or not so long as an internal standard was used (relative to other options), though in the absence of internal standard usage, yield normalizing certainly gave big improvements. That is all based on the sum of absolute % difference however, and individual elements may actually be better suited to a strategy that has "worse" sum of absolute % difference as a whole, but does better for that element in particular (which may be key for the study at hand). I'm finding this in my own data and not always sure what to do - is it better to go with what most accurately represents the performance of the RM(s) as a whole (or is that uncritical), or for the element of interest (or is that cherry-picking)?

Furthermore, for other datasets of mine, yield normalization with no internal standard gives roughly the same results as internal standards without yield normalization - is one more "defensible" than the other? Particularly given the fact that lack of internal standard usage often labels the analysis as "semi-quantitative" (which seems to unfairly degrade confidence in the result), does use of yield normalization alleviate that? If not mathematically, then at least in terms of community acceptance?

Thanks for having a space for us to ask these kind of questions!

Bence

Geonostalgia is it better to go with what most accurately represents the performance of the RM(s) as a whole (or is that uncritical), or for the element of interest (or is that cherry-picking)?

That is a really good question, and one that I'd be keen to hear what others think too.

My opinion is that if it's a choice between RM-normalisation and Int Std use, it's more important to optimise for the elements of interest instead of the overall performance. This is not necessarily cherry-picking because the two normalisations are slightly different. One uses all elements (RM-normalisation) which may include poorly constrained RM values, or inaccurately measured elements. The Int Std correction however, can be more targeted, which is why it might give better results in some situations. I think it really depends on the setup, and if you choose one over the other, you should be able to justify to a peer-reviewer as to the choice.

Regarding yield normalisation being semi-quantitative... I would say that if your sample matches your primary RM (i.e. the one everything else is normalised to) then it's approximately equivalent to using an internal standard with the same elements. That's probably why you're seeing roughly the same results: it might be just a slight difference in the elements used for normalisation.

What do others think?

sunguochao

Bence Hi, Bence. After reading that 2023 (JAAS) article, I still don't fully understand the computational principles behind Primary RM. The paper said "The latter option calculates yield normalisation factors for each calibrating RM relative to a selected ‘primary’ RM. This process only uses elements where there is an accepted value for both RMs. A median yield factor is then applied to all measured elements for the RM. The algorithm calculates a median yield correction factor based on the elements in common and applies that factor to all results for this RM." My question is how to calculate the median yield factor using the Primary RM. And how to use the yield the norm factor to the other RMs. When i see the code of 3D trace elements I found that " M[row][col] = (groupResult/groupRMValue) / (masterGroupResult/masterGroupRMValue)“ ,but this seems to not calculate the median yield.

Bence

Hi sunguochao

Very sorry for the late reply to your question.

I will try to explain the median yield normalisation process a little better. Let's say you have two RMs you want to calibrate with: RM1 and RM2. They have the following accepted concentration values (please ignore units, I've just used numbers that are easy to comprehend):

Element RM1 RM2
Mg 10 1
Si 30 50
Sr 0.8 3
Th 1 -
U - 0.01

The elements in common are Mg, Si and Sr. We don't have Th values for RM2 or U values for RM1, so we can't calculate yields for those elements and they will be omitted from the yield normalisation process.
Then we work out the yield for each element, for each RM, using the average baseline-subtracted count rates for all analyses of that element, remembering that yields is CPS / concentration.

Element Yield RM1 RM2
Mg 1 1.2
Si 3 3.7
Sr 0.8 1.1

We can then look at the ratio of yields. Let's say that RM1 is the ref mat we want to normalise to. We would get the following yield ratios:

Yield Ratio (RM2/RM1)
Mg 1.2/1
Si 3.7/3
Sr 1.1/0.8

The median ratio here would be about 1.2, so we now know from multiple elements that the yield of RM2 is about 1.2 times that of RM1, so we need to divide the count rate of RM2 results by 1.2 before including them in our calibration curve.

Note that we use the median value because there will be elements of very low concentration and therefore lower accuracy included in the yield calculation, so we want to minimise the effect of outliers.

I hope this clarifies the process. Please let me know if you have any other questions.

Kind regards,
Bence

edmarshall

Thanks again Bence for your detailed response. Sorry, I didn't give a reply sooner. I would be really interested in learning more about the math behind the yield correction/yield normalization-- I agree with @sunguochao that it isn't super explicitly explained in the 2023 paper either.

To give my own opinion on internal standardization vs yield normalization with no internal standard. To me, it all comes down to the quality of the secondary reference materials measured. Regardless of the calibration approach, one needs to prove to users and peer reviewers that the calculated values are accurate, and this can only be done with quality secondary RMs. I think that sum normalization would be more criticized by reviewers simply because it is an atypical approach-- at least in the geochemistry culture that I operate in.

A worry I have about 3D Trace Elements is that because there are many more "knobs to turn" (compared to the TEs DRS) one could change the calibration approach until the error from the true secondary RM composition is minimized. This is the correct approach if the secondary RM matrix is identical to that of the samples, but if it is different from the samples (for example, measuring minerals but using NIST or USGS glasses as secondary RMs) then fitting your calibration to the secondary RM could result in an overconfident appraisal of accuracy. Potentially, mediocre data could be fiddled with until looks like good data.

I guess my point here is that, whatever calibration approach you choose, it is very important to have well-matched secondary RMs to definitively validate your analyses (even if only for a few elements). The point I raised is also true for the old Longerich (1996) internal standardization calibration method though, so nothing new I suppose.

Geonostalgia

edmarshall - that's an interesting perspective. With the sulfides I work with, even the quality of primary standards can be an issue, which is why I think multi-RM calibration is such a useful approach, since you can cobble together the strengths of different RMs as needed. As you rightly point out though, there are more knobs to turn generally with 3DTE, and if you're trying to be "creative" (as I am), it becomes far more difficult to succinctly convey what steps were taken and why. There have been some efforts to show what's going on "under the hood" (Herzog et al. 2024 had a good appendix on this), but it still falls short for easy reproducibility in an age where electronic appendices seem to be an easy answer for this question. Another reason why mass-export of calibration settings for 3D-TE-DRS would be nice to "drop and go" for accountability on this.

Another question for @Bence on this - what happens in the software when only some selections have an internal standard value set, but others do not? Is the calculation performed separately for each selection, either with the IS or not?

Bence

Geonostalgia what happens in the software when only some selections have an internal standard value set, but others do not? Is the calculation performed separately for each selection, either with the IS or not?

Short answer: if the "Use internal standards" option has been checked and a selection does not have an Int Std value, there will be no concentration data calculated for that selection.

Slightly longer answer:
iolite creates a channel called ISValue and fills it with blank (NaN) values. When the DRS is crunched, for each selection the DRS fills the channel with the Int Std value over that selection's interval. Then the channel is used in the concentration calculation. Because it's a channel, with as many values as the measurements, we can calculate a concentration for each data point.

I haven't forgotten about creating a better export of DRS settings for 3D Trace Elements. The issue is that the settings are spread across a couple of different places:

general DRS settings (whether to apply masking to results),
individual channel settings such as what RMs are used to calibrate it,
individual selection settings (e.g. Int Std values) and,
group settings (ablation mass settings for total ablated mass calculations as discussed here).

I don't mention that to bamboozle anyone, just to explain why it's taking a little bit to get it all together 🙂 .

I hope to have something to report soon.

Bence

edmarshall

Geonostalgia Yes, if I understand you correctly, my opinion would be that your approach here is problematic. I can't say that it would yield worse absolute results, but it certainly yields results where the accuracy is not fairly estimated. I also do sulfide analyses, and I know the sulfide standards are less well characterized, more heterogeneous, and more poorly matrixed matched compared to silicate glass standards. It is just harder to make homogenous standards for sulfides than for silicate glasses, which makes it harder to prove that your analyses are accurate. So if you tune your analyses to these secondary reference materials, you generate results that will underestimate the uncertainties-- In essence, just drawing the target around the arrow. I think what you are saying is more defensible when you have perfect matrix matches between sample, calibration material, and reference material, but otherwise I would not do this.

Anda

I'm currently working with the 3D Trace Elements DRS and have encountered a puzzling issue when trying to replicate iolite's FQ (Fully Quantified) results manually. I'm hoping someone here might be able to shed some light on what I might be missing.

Background:
I've been following the calculation logic in the 3D Trace Elements Python code, specifically this section:

for c in data.timeSeriesList(data.Output):
    d = c.data()*norm
    c.setData(d)

Based on my understanding, the FQ concentration should be calculated as: c(FQ) = c(SQ) × norm.
Where:

c(SQ) is the concentration without internal standard correction (Don't Use internal standards)
norm is the normalization factor derived from the internal standard

My test setup:
I extracted the following parameters from my iolite4 results table: RelativeYield(Use internal standards)、c(SQ)(Don't Use internal standards)
Since norm = 1/RelativeYield, my manual calculation for FQ was: FQ (manual) = c(SQ) × (1/RelativeYield)

The problem:
However, when I compare my manually calculated values with the FQ values exported directly from iolite, there's a substantial discrepancy. The following table cannot be displayed properly, so it will be shown like this for now.

| Fe57_ppm               | Calculation formula     | sel_rm_00     | sel_rm_01     | sel_rm_02     |
| ---------------------- | ------------------------| ------------- | ------------- | ------------- |
| FQ (by-iolite4)        | ?                       | 469.478       | 514.661       | 516.005       |
| FQ (by-manual)         | c(FQ) = c(SQ) * norm    | 419.601       | 465.430       | 454.026       |
| RelativeYield          | RY = 1 / norm           | 0.684215      | 0.683864      | 0.709730      |
| SQ (by-iolite4)        | c(SQ)：UseIntStds=false | 287.097       | 318.291       | 322.236       |

My question:

What could be causing this 10-12% difference? Is my understanding of the FQ calculation incomplete? Are there additional correction factors applied in the DRS that aren't captured by the simple c(SQ) × norm relationship? Could there be some channel-specific scaling or unit conversion happening behind the scenes?

I'd really appreciate any insights from those more familiar with the 3D Trace Elements internals. I'm trying to fully understand the quantification process rather than just treating iolite as a black box, so any pointers would be very helpful.

Thanks in advance!

Anda

Anda
Supplementary information:
For the results table exported from iolite4, the interface settings are as follows:

Single external standard
Normalize yields to external standard = true
Model = ODR
Zero = true
Frac. correction = false
Spline type = meanmean
Stat. = mean
Use internal standards (either = true, with only a single internal standard's Element, Value, and Units set; or = false)
All other parameters remain unset.

Bence

Hi @Anda

Would you mind sending your .io4 and any calculations you've done to the iolite support email address? It's difficult to see what the differences might be from your post (i.e. without seeing the data). However, your understanding appears to be correct, so it might be something else.

Kind regards,
Bence

Geonostalgia

edmarshall --- Sorry Ed, but I'm not sure I follow you precisely: what part of the approach specifically seems problematic? Not disagreeing per se, just not sure I understand your point fully.

edmarshall

Geonostalgia Calibrating reference materials (RMs) are what is used to calculate concentration. Secondary RMs are measured as unknowns in order to check that the calculated concentrations are accurate. Samples are also measured, but these are true unknowns and so are not helpful for quality control. But, what is important in analysis is that the samples have accurate concentration measurements. This is evaluated using secondary RMs, and fundamentally based on the calibrating RM.

To take a step back for a moment--- if you try a "standards run" (where you measure only reference materials, and you can freely use one RM to calculate concentrations against the other RMs) what you will find is that reference materials do not perfectly predict the concentrations of one another. Inaccuracies related to poor characterization aside, this is largely due to different matrix effect behaviors between standards. Matrix effects are caused by a variety of different things during ablation: differences of laser coupling to the surface, differential condensation of elements in matrix material after ablation, differential transport of elements away from the ablation site, the size distribution of particles entering the plasma, and more. So, when you choose RMs, it is important to pick RMs that have similar matrices so that their elemental fractionations during analysis will be similar and yield similar, comparable results.

The issue is that with sulfides, we are typically ablating minerals like pyrite or sphalerite, but our RMs are things like MASS-1, FES-1, or STDGL3-- with matrices totally dissimilar to natural sulfide minerals. The matrix effects are not small-- for example, the paper that introduces STDGL3 (https://onlinelibrary.wiley.com/doi/full/10.1111/ggr.12512) finds large matrix effects, and proposes correction factors for different elements and matrices.

The issue is that if your samples have a very different matrix than the secondary RM (again common in sulfides), they may not be very useful in determining the accuracy of your calibration for your samples except in a "ballpark" sense.

So, if you are using 3D trace elements to tune your calibration to make your secondary RM replicate the published values, without good matrix matching between the secondary RM and the samples, the changes that you make to improve your secondary RM concentration data do not necessarily result in more accurate sample concentration data.

However, like I said, this isn't really a 3D trace element issue specifically. It is also possible to make the same mistake in the Longerich method by switching calibrating RMs until the secondary RM looks better.

If you are in the situation where you don't have good matches between your RMs and your samples, like for sulfides, I've found it most helpful to compare the probe data for the samples rather than rely so heavily on the secondary RM. For example, magnetite doesn't have great RM matches for LA-ICPMS, but if my V and Ti data fall along a 1:1 line with the probe V and Ti data, then I am happy.

Geonostalgia

edmarshall --- Thank you for the clarification, and I 100% agree; 3DTE gives more versatility in matching a secondary RM when constructing the calibration curve, but it does not supersede the fundamental matrix relationship between all RMs used, whether secondary or primary. That's why STDGL3 has been such a boon in our analyses - it doesn't solve everything of course, but it is a great step forward.