[GPlates-discuss] Estimating uncertainty in plate positions and motion paths

[Eglington, Bruce]

Hi Ben
  Agreed that one can calculate something. The issue is what it means. Yes, to illustrate variability between models but, if none of them are correct, there is no way to assess this. However, just doing the calculations forces us all to think of what we want or mean to portray so the exercise is valuable. A simple illustration from an area I am more at home with is: the average age of the Earth is about 2000 Ma, based on available geochronology but this does not tell us anything useful. Working through the data does, however, show where we might have bias, uneven data distribution and a host of other information.

Chris Scotese showed a comparison of various global models at the RFG conference a year or so ago, using spots for various major cities on different continents. It was very interesting because it showed similarities between some models and vast differences for others, all of which highlighted areas and time intervals requiring research and I think that much of what you are doing will be of similar use. Go for it and show us how to develop methodology for when better data are available.

Bruce


Bruce Eglington (Ph.D.)
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Geological Sciences
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From: GPlates-discuss <gplates-discuss-bounces at mailman.sydney.edu.au> On Behalf Of Ben Mather
Sent: Monday, October 7, 2019 16:15
To: Sabin Zahirovic <sabin.zahirovic at sydney.edu.au>; gplates-discuss at mailman.sydney.edu.au; mdarin at uoregon.edu
Subject: Re: [GPlates-discuss] Estimating uncertainty in plate positions and motion paths

Hi all,

Great discussion! But just to clear up any confusion: the parameter uncertainty problem is less complicated than the inference problem some are alluding to. If you want the total uncertainty of the model given the data, then a likelihood function would need to be constructed that links a reconstruction to a set of observations (palaeomagnetic stripes, fossil records, etc.) and compares the misfit. From there you would sample the posterior probability, using a MCMC algorithm, and build up an ensemble of realisations until you can extract the posterior uncertainty. A frequentist approach may be preferable in some linear cases e.g. anomaly picks - thanks for the reading material, Douwe. Alas, as Sabin pointed out, all of this is outside the scope of what can be achieved short term.

Rather than finding the posterior uncertainty, you can compare a suite of reconstructions using all the different rotation files available and quantify their collective uncertainty through time. The uncertainty on Arabia-Eurasia convergence will not reflect the total uncertainty of the model given the data, but it will reflect the uncertainty between rotation files. Admittedly, this is far from perfect, given the small set of reconstructions we have available and the weighting bias I mentioned earlier, but it's a start...

I hope that gives a bit more insight into what I had in mind. Hopefully this will provide a better framework to assess and compare models - and, as Bruce suggests - illustrate where and when certain models are thought to be better constrained than other parts.

Cheers,
Ben

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On 2019-10-07 21:43:42+11:00 GPlates-discuss wrote:
Hi Mike and team,

I agree with Bruce, using alternative models is not likely going to capture the uncertainty present in the Arabia-Eurasia convergence. If one is just looking at the Arabia-Eurasia convergence rate during a time where Atlantic seafloor spreading is occurring, then one probably wouldn’t need to take into account the absolute reference frame, but just evaluate the uncertainties across the relative plate motion hierarchy (Arabia – Africa – North America – Eurasia). However, as Bruce pointed out, other constraints might be useful, especially if intraplate deformation is significant. The reality at the moment is that this is not easy to do, and would generally need to be done on a case-by-case basis, by trawling back through the rotation file and checking whether uncertainty ellipses are published for the poles used, and so on. Would be cool to have this in GPlates one day! In terms of Ben’s suggestion, it might be interesting to see what different models propose/predict for the Arabia-Eurasia convergence. There’s a bunch of models to download from here: https://protect-au.mimecast.com/s/_d9UCnxyErCYqx7jCZ9zFv?domain=earthbyte.org (EarthByte models, Chris Scotese model, etc.), and I think Douwe van Hinsbergen and team have some GPlates-related files here: https://protect-au.mimecast.com/s/XfLFCoVzGQi0L8rZTOy7Aj?domain=geologist.nl

Cheers,
Sabin

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From: GPlates-discuss <gplates-discuss-bounces at mailman.sydney.edu.au<mailto:gplates-discuss-bounces at mailman.sydney.edu.au>> on behalf of "Eglington, Bruce" <bruce.eglington at usask.ca<mailto:bruce.eglington at usask.ca>>
Reply-To: GPlates general discussion mailing list <gplates-discuss at mailman.sydney.edu.au<mailto:gplates-discuss at mailman.sydney.edu.au>>
Date: Monday, 7 October 2019 at 8:21 am
To: GPlates general discussion mailing list <gplates-discuss at mailman.sydney.edu.au<mailto:gplates-discuss at mailman.sydney.edu.au>>, "mdarin at uoregon.edu<mailto:mdarin at uoregon.edu>" <mdarin at uoregon.edu<mailto:mdarin at uoregon.edu>>
Subject: Re: [GPlates-discuss] Estimating uncertainty in plate positions and motion paths

Hi
 The issue is actually much more difficult to conceptualise because different parts of different models are variably uncertain and there is no reason to assume that the average of available models is any closer to reality. I doubt that motion paths are going to resolve better models from worse, other than to identify plate motions that are too fast, etc. In order to better constrain models, we will needs to have far more comprehensive data sets that can be ‘draped’ over the kinematic blocks to assess matches and mismatches. One can already start some of this with data like palaeomagnetics, geochronology, etc and, to a limited extent geochemistry and geology. In most cases, though, we need data sets with much better temporal and spatial resolution than are currently available. There are lots of ways in which machine learning and AI could help, if only we had better organised, structured and relevant data.

The best that can be said at present seems to be that each model can be tested for validity with localised data sets where sufficient detail is available, from which we can start to improve models.

None of this is to say that we should not attempt to develop ways to test model comparisons in anticipation of improved data compilations. By doing so, we will have a better idea of how to assess and compare models. It would also be useful to somehow be able to illustrate which parts of individual models are thought to be better constrained than other parts (time, polygons, motion, etc). Something like this would certainly help address the very real need to quantify model uncertainties to help potential end users.

Bruce Eglington

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From: GPlates-discuss <gplates-discuss-bounces at mailman.sydney.edu.au<mailto:gplates-discuss-bounces at mailman.sydney.edu.au>> on behalf of Ben Mather <ben.mather at sydney.edu.au<mailto:ben.mather at sydney.edu.au>>
Sent: Saturday, October 5, 2019 4:39:49 AM
To: gplates-discuss at mailman.sydney.edu.au<mailto:gplates-discuss at mailman.sydney.edu.au> <gplates-discuss at mailman.sydney.edu.au<mailto:gplates-discuss at mailman.sydney.edu.au>>; mdarin at uoregon.edu<mailto:mdarin at uoregon.edu> <mdarin at uoregon.edu<mailto:mdarin at uoregon.edu>>
Subject: Re: [GPlates-discuss] Estimating uncertainty in plate positions and motion paths

Hi Mike,

Thanks for reaching out.

In principle, if you had enough reconstructions (rotation files) you could build up an ensemble of plate models that would enable you to interrogate uncertainty information from (standard deviation, confidence intervals, etc.), but one of the key problems is it's unclear how to weight each reconstruction. For instance, one could always argue that the latest reconstruction is the "best" because it's the result of painstaking tweaks and adjustments of all those that came before it as a product of additional geological constraints.
Nonetheless, if you see beyond this caveat, a qualitative comparison between the different models is still useful and some quantitative metrics can also be employed. Comparing the plate velocities and cumulative plate distance is relatively simple to do with motion paths, but it can give the false impression that the plate reconstructions do not agree at all. A test we are working on is to place a bunch of points equally spaced across the globe and measure the distance between these points through time for different rotation files. Essentially this is just comparing multiple motion paths across the globe. From there you would calculate (pseudo-)uncertainty maps of where the reconstructions agree and where they do not.

This workflow is particularly suitable for pyGPlates because swapping rotation files a breeze, and it's easy to import other python modules that deal with statistical analysis. Once we have something in place (that works!) I'll send you the python scripts so you can customise it to your problem. Is that OK? Let me know if you have any other suggestions and if you would like to be involved with testing.

Best regards,
Ben
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On 2019-10-05 05:25:49+10:00 GPlates-discuss wrote:
Hello,
I'm using GPlates to reconstruct the Arabia-Eurasia collision zone and to make a plot showing Total Arabia-Eurasia Relative Motion vs. Time. To do this, I fixed the Eurasia plate and then created a set of motion paths for points on Arabia. This worked great, as I was then able to export a text file containing the coordinates of each reference point at different time steps, which allowed me to calculate the distance that Arabia had traveled between each time step.
However, there must be some uncertainty in the rotation model that is not currently reflected in the generated motion paths. I am wondering if and how I could generate error ellipses in map view for the motion paths, which would allow me to add error bars to each point on the plots that reflect the uncertainties in the locations of each reference point through time? This doesn't seem straightforward to me, so I am reaching out to the discussion list for suggestions. ​
Thank you,
Mike
Michael H. Darin, Ph.D.
Postdoctoral Research Associate
Department of Earth Sciences
University of Oregon
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