Constraining stochastic 3-D structural geological models with topology information using approximate Bayesian computation in GemPy 2.1

Schaaf, Alexander; de la Varga, Miguel; Wellmann, Florian; Bond, Clare E.

doi:https://doi.org/10.5194/gmd-14-3899-2021

Articles | Volume 14, issue 6

https://doi.org/10.5194/gmd-14-3899-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-14-3899-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 14, issue 6

Development and technical paper

|

28 Jun 2021

Development and technical paper |

| 28 Jun 2021

Constraining stochastic 3-D structural geological models with topology information using approximate Bayesian computation in GemPy 2.1

Alexander Schaaf, Miguel de la Varga, Florian Wellmann, and Clare E. Bond

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Final revised paper (published on 28 Jun 2021)
Preprint (discussion started on 18 Aug 2020)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Referee Comment', Ashton Krajnovich, 17 Oct 2020
- AC1: 'Authors response to Review #1', Alexander Schaaf, 17 Nov 2020
RC2: 'Constraining stochastic 3-D structural geological models with topology information using Approximate Bayesian Computation using GemPy 2.1', Anonymous Referee #2, 21 Oct 2020
- AC2: 'Authors response to Review #2', Alexander Schaaf, 17 Nov 2020

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Alexander Schaaf on behalf of the Authors (25 Nov 2020) Author's response

ED: Referee Nomination & Report Request started (05 Mar 2021) by Thomas Poulet

RR by Anonymous Referee #2 (11 Mar 2021)

Suggestions for revision or reasons for rejection

I am recommending a few technical corrections. I originally advised minor revision based on the following three concerns:

1) Many sentences are poorly worded.

2) The term 'likelihood-free' and its implications are presented inconsistently and in a very misleading way.

3) Terms like observation, prior and likelihood are applied in an unclear manner often contradicting convention.

I considered these minor because my suggestions for addressing them were simple and did not require additional data analysis or significant writing. For #1, the manuscript is still reads like a draft version, but I'm not going to ask for more changes relating to this. #2 has been addressed. #3 this has been ignored. The comments below detail the main remaining issues.

Specific Comment 3)

"We have referred to the initial topology graph as an observation, as this is the terminology used in literature. We understand that this could potentially lead to certain confusion with the reader. We have thus added the clarification to the manuscript, that we treat our subjectively chosen topology graph as the observation in the terminology of ABC."

I could not find the place in the revised manuscript where this change was made.

Specific Comment 4)

This comment has not been addressed. All I asked is that you state that the initial graph is what is treated as an observation even though its derivation includes significant subjective steps. This ties in with specific comment 3 as the procedure behind the observation was never properly discussed.

P2L5)

"learn our input data parameter (prior) distributions"

Still incorrect as I stated in the previous annotated document.

P2L25)

"Likelihood functions essentially represent information in a probabilistic mathematical form. This information can be available numerical data, such as information about the range of possible layer thicknesses in a depositional setting."

Likelihood relates data to model parameters. This reads if the likelihood function is that data. The function is a relation not data in itself.

P3L10)

Using ABC to indirectly specify a likelihood function is your choice. The claim that obtaining such a function is intractable us untrue for the one you use.

If 'theta' is the model parameters and 'y' is the initial graph. Define a binary statistic of 'theta', call it 'x', as true if the topology graph of 'theta' is within distance 'iota' of 'y', and false otherwise. If we then formulate the likelihood in terms of 'x' being the observation 'f(x|theta)' and sample from posterior 'p(theta|x)', this samples from the same posterior as what your ABC method does in algorithm 1 and approximates in algorithm 2. Replacing data with a statistic of it to simplify a problem is a very old practice. So I will repeat this, the claim that the use of ABC solves an intractable likelihood specification is not true for this specific work.

P7L5)

The definition of model parameters is still too vague and poorly written. The author conflates parameters with probability distributions as I pointed out in the previous annotated document.

P14L10)

"chosen emperically" how?

P18L18)

"while reducing the number of required iterationsthrough use of advanced sampling techniques."

Sampling technique efficiency was not presented as the focus in the preceding parts of this paper and should not as there is very little here on that topic.

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RR by Ashton Krajnovich (24 Mar 2021)

ED: Publish subject to minor revisions (review by editor) (24 Mar 2021) by Thomas Poulet

AR by Alexander Schaaf on behalf of the Authors (13 May 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (24 May 2021) by Thomas Poulet

AR by Alexander Schaaf on behalf of the Authors (26 May 2021)

Short summary

Uncertainty is an inherent property of any model of the subsurface. We show how geological topology information – how different regions of rocks in the subsurface are connected – can be used to train uncertain geological models to reduce uncertainty. More widely, the method demonstrates the use of probabilistic machine learning (Bayesian inference) to train structural geological models on auxiliary geological knowledge that can be encoded in graph structures.