the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Apr 2022
3D geological modelling of igneous intrusions in LoopStructural v1.4.4
Abstract. Over the last two decades, there have been significant advances to improve the 3D modelling of geological structures by incorporating geological knowledge into the model algorithms. These methods take advantage of different structural data types and do not require manual processing, making them robust and objective. Igneous intrusions have received little attention in 3D modelling workflows, and there is no current method that ensures the reproduction of realistic intrusion shapes. Existing techniques are strongly dependent on the availability of data and manual processing to refine models. Intrusions are usually partly or totally covered, making the generation of realistic 3D models challenging without the modeller’s intervention. In this contribution, we present a method to stochastically model intrusions based on the Object-Distance Simulation Method. We adapted this method considering typical datasets and rules of intrusion emplacement mechanisms. Using the geometric elements of intrusions (inflation direction, propagation direction) and stochastic simulations of intrusion thickness, we can generate realistic intrusions shapes while honouring observations and accounting for the spatial variability in thickness. The method is tested in synthetic and real-world case studies and the results indicate that the method can reproduce expected geometries without manual processing. A comparison with Radial Basis Function (RBF) interpolation shows that our method can better reproduce intrusion shapes, particularly when considering scenarios with sparse datasets.
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RC1: 'Comment on gmd-2022-88', Anonymous Referee #1, 15 Jun 2022
The manuscript 2022-88 addresses an interesting subject and topic, which perfectly fits the scope of GMD, and proposes an interesting idea. I have, however, major concerns that should be addressed before considering the paper for publication, meaning, a second review would probably be required after revision. To make a summary: the paper is messy, with repetitive parts, superficial explanations of references used in it, sometimes inappropriate words and fuzzy vocabulary are used; the objects of interest (igneous intrusion) are hardly presented; It also lacks details concerning the algorithm, and the analysis of the results remains superficial, and some aspects of the approach are completely let apart in the result analysis. I am not sure the paper and method could be followed by someone who does not already know the references and approaches. Figures are not always legible, it lacks some additional illustrations, and there are some duplicated references. In the following, I develop all these points.
The paper is messy and should completely be re-organised and re-structured. In the present state, the section titles do not reflect what they content. To start, the introduction does not present the object of interest, the igneous intrusions, and they are hardly presented in the section 3, which mixes in each sub-section theorical description and algorithmic proposals. The algorithm description is dispersed and repeated in several parts of the manuscript: part 2.1, then lines 151- 172 in part 3.1, then 182 to 191, and they are mixed with results presentations in sections 4. Section 6, which is supposed to present a “discussion” presents again some results, supposed to be in section 5. The paper should be re-written and ordered following the classical introduction – methods – results- discussion – conclusion plan, which, in the present case would be easy to follow and sounds.
To write their introduction, authors could get inspiration from this reference: Claerbout, J. F. (1991). A scrutiny of the introduction. The Leading Edge, 288–291. And both these references are also advised for paper : Sudarshan Iyengar. (2013, May). How to Write a Great Research Paper. Strunk, W., & White, E. B. (n.d.). The Elements of Style.
In more details, Introduction should here 1) present igneous intrusions, from a geological/descriptive point of view, with figures showing the diversity of encountered shapes, and explaining the processes of formation. Then, 2) clearly explain why these shapes cannot be reproduced easily and automatically by existing geomodelling approaches (going deeper in the geomodelling concepts than just saying “it is hard to do it” : explain why (superposition and lateral continuity principles that constitute a pillar of existing appraoches, management of unconformities, etc)). 3) then, present papers that treat similar questions of highly convoluted shapes and explain their limitations considering the author’s specific question: I do not know works on igneous intrusions, but there are on salt tectonic features. For ex. the authors cite Clausolles et al., 2019, but hardly in the part 2 (for the SGS parametrization in the ODSIM process (?)) while they are close to the present contribution (salt diapirs modelling with an approach inspired by ODSIM). The authors should explain the differences and demonstrate the originality and plus-value of their own contribution. 4) finish with the plan of the paper.
On the contrary, fuzzy focuses are made on “structural frames” in the introduction (lines 25-35) and the section 2.2. In both cases, the link with the present work is hardly understandable and so many details for fold-frame and fault-frame seem useless to understand the contribution of this paper. Section 2.2 could be removed and lines 25-35 limited to one citation.
Vocabulary is not appropriate: “anisotropies” is the general term used by the authors to describe apparently faults and stratigraphic surfaces, and it is not right.
Concerning the method [which should be presented from a general point of view, not on particular CS] :
- Path search algorithm:
- This step is not clearly explained and illustrated: The figure 4 is not clear enough and too small. Points are below the stratigraphic surfaces but then a value seems affected to this surface. Ic and IF are not explained in the text and the way they are mixed is not clear. The position and meaning of Jout is unclear.
- Its plus-value and interest are not demonstrated as it is only used in 1 simple and theoretical CS. In other cases, the user chooses the “skeleton” surfaces and we do not understand why not doing this in this first simple example.
- They refer all time to Borghi et al., but:
- the latter were looking for linear paths between 2 points, here the authors search surfaces, which is not the same. How to pass from several lines to surfaces? It is not clear at all.
- Borghi takes its inspiration from Henrion et al. 2007, 2008 (Henrion, V., Pellerin, J., & Caumon, G. (2008). A stochastic methodology for 3d cave system modelling. In G. Ltd (Ed.), 8th Geostatistics Congress (pp. 525–533). Santiago, Chili.), and Henrion et al. already took inspiration from the main path search proposed by Vitel et al to identify main path in fracture networks (Vitel, S. (2007). Méthodes de discrétisation et de changement d’échelle pour les réservoirs fracturés 3D. Institut National Polytechnique de Lorraine. // Vitel, S. (2006). Fast Transmissibility Upscaling Technique for NFR. In 26th Gocad Meeting (pp. 1–18).). One difference was that they use FMA instead of A* algorithm. It conducts me to the following point:
- searching for a best path between two points is not a contribution of Borghi, it is a standard and several algorithms exist for a long time. This should be the main references. Also, why using Fast marching (FMA)? Why not Djikstra ? Why not A*? etc. These points should be discussed and argued. Here, you are not looking from a path between 2 points, but from surfaces of circulation between areas. You could free yourself of this redundant reference about karsts (who is not the only one nor the first to propose it), just say that a similar approaches were proposed for karstic networks by Henrion et aL, Borghi et al., Collon et al; Paris et al., etc (and also for other types of systems perhaps?), but here you are dealing differently in a different context.
- to use FMA, one need to choose velocity values. Everything will depend on that. The choice of these values is also hardly discussed, not illustrated (no values are provided for the case studies) and no sensibility analysis is made.
- On the “structural frame”
- Beside the fact that it is presented several times (3.2 and 4), each time incompletely, the necessity of this step is unclear. Demonstrating the interest of these 3 directions by comparing with a more classic approach without this structural frame but an anisotropic 3D variogram (like in Clausolles et al., 2009) would be more convincing.
- The time and user expertise needed to perform so many steps should be discussed
- The way this step is incorporated in the global workflow was unclear to me. I “guess” it replaces the distance field computed in ODSIM, but it is never really said, and it remains unclear why this step is changed.
- On the 4.2.2 “ODSIM-inspired” part
- The difference between the distance field and the random field is not clear in the text while it is a crucial point for the reader to understand.
- Distance field does not need to be Euclidean (see Rongier et al). This could be, at least, said, and discussed later in the discussion part. If I guess right and the 1 distance field is replaced by the “structural frame”, this should be better explained and the motivations behind this choice should be given.
- For the SGS generating the random field:
- why using an isotropic variogram? especially when asymmetric shapes are searched?
- Why an infinite range? Does it have any sense from a geostatistical point of view in a SGS? I don’t think so
- How do you infer the histogram parameters for running the SGS? No demonstration is provided from the data
- Why not using Gibbs sampler when you want to fit data? The part about data fitting is quite unclear
- How do you managed data which are not located on the envelope of the intrusion but inside or outside?
- How do you manage data that say “no intrusion here”?
- One point of ODSIM is that the SGS generates a random field, and thus, when you mix the distance field with the random one, you obtain several equiprobable realizations: it is stochastic. Here the stochasticity is not presented in the results, only one result is each time presented. And the interest of this stochasticity is not really highlighted.
Results [they should incorporate the presentation of the CS (not introduced earlier, as the method part should be general) and the results obtained on it]:
- Igneous intrusion shapes:
- only sills are presented while the introduction speaks of sill, plutons, dikes, laccoliths. Several examples should be provided and compared with what is obtained with other methods
- especially, a conceptual model is presented for pluton, but not really illustrated
- if only sill and plutons are considered, this should be clearly stated in the title, abstract and introduction. And this limitation should be discussed and presented as a future work in conclusion.
- The case studies should incorporate the demonstration of the variogram and histogram definition from the data
- CS3: why so much data? where should they come from in general cases?
- ODSIM can generate shapes in the absence of observation points. Here no results are provided in the absence of points indicating the position of the intrusion contour. This should be rectified.
- One realization, coming from a stochastic process is compared to the solution of a deterministic approach (the RBF-based), and to the “ideal” solution:
- stochastic processes do not aim to find “the solution” but a range of realistic solutions which embraces the possibilities given the non-completeness of data. In that sense, at least several realizations (10-50-100?) should be considered and compared to the “solution”
- the variability of the realizations should be estimated and in several context of data: the variability should reduce with increasing data
- it is strange to compare a deterministic solution (RBF) with 1 realisation of as tochastic method which do not use the same input data… You can say that they are usable with different input data, but it is difficult to be objective here.
Discussion:
- The influence of variogram and histogram used for the random field generation has been demonstrated crucial (Henrion et al 2008, Clausolles et al 2019). This should be discussed with the help of a small sensitivity analysis, trying various variogram settings.
- The stochasticity should be discussed and the comparison with RBF should consider the fact that RBF is deterministic.
- The capacity of the method to reduce uncertainties as the amount of data increase should be discussed
- the computing time should be given and discussed
- the results concerning the shapes should be discussed as compared to the one proposed in other contexts (eg salt diapirs or karsts anisotropic shapes like in Rongier et al 2014). In particular, the interest of the structural frame compared to the simple introduction of an “standard object” as a skeleton and an adapted distance field (I guess the advantages, but the authors say nothing about it and demonstrate nothing)
- Is it possible to combine several types of intrusion in one model?
- Current limitations (considered shapes, grid requirements, …)
“Minor” comments:
- Abstract: lines 9-11 : “existing technics are strongly dependant on the availability of data” : isn’t the case of all methods including yours ? => better remove this sentence
- L53: “estimation”: of what ? a volume ? For what point?
- “realistic” is said several times: what is a “realistic shape”? An un-realistic one? Do you have a specific criterion in particular?
- L70: I am not sure ODSIM has been applied on meandering channels: to check
- Section 2.1: should better be understandable with a figure
- L76-l84: completely out of the scope of ODSIM. Should be removed. It lost the reader here as the point of the path search is different (it is to create a skeleton, ODSIM starts from the skeleton.)
- L84-87: not clear. Especially, l86, no, the geological body is not defined by the isovalue of lambda, but by the surface given by the difference between D(p) and Phi(P) (as you said 2 lines below).
- Section 2.2: as already said, I would remove this part, I found it completely useless for understanding this paper (and often quite fuzzy)
- L161: “observation points” meaning? on seismic? On well? what kind of data exactly?
- L162: what do you mean “simulate anisotropies”? Also simulating faults is not the same than horizons.
- L165: what assumptions? What do you mean by “mechanical anisotropy”? it is quite fuzzy
- Figure 1: not really clear. What kind of observation points? What mean intrusion network surfaces? Are they determined by the geologist knowledge? If the magma comes from below, the faults should potentially have been a vector of it? Why are they not considered here in their lower part?
- Figure 2: light the colours. Please add g, p and l on the figure. For case (a) please explain the context to allow the reader understanding what have guided the definition of the three axes in this case.
- L205: no literature describing quantitatively the igneous shapes and proposing geometrical description?
- Figure 3: use it to explain roof and floor. In the legend it is written g(p,l), should it not be (g,p,l) like in the text ? For sill why using a regular parallelepiped and not a one which become thinner along one direction?
- 1: in the current form, the title suggests the method will depend on considered shapes. If the authors change the structure of the paper, this confusion should disappear.
- L276: unclear
- Figure 5 and CS2: is the final shape known from seismic?
- Figure 5: if we only have points and horizontal strata, how was p and l chosen? On the figure it is hardly understandable. Perhaps it is a problem relative to the view angle
- L361: give the distribution. Explain what are the “values” that you put in this distribution. How do you compute them? It is unclear.
- Figure 6: is it specific to this case study?
- Figure 7: show several realizations. Could you colour the result depending on Z or use contour lines to help the reader see the relief?
- Figure 9: a is not readable. Points are all mixed we do ot see anything.
- L435-438: what justify the choices made (so many points, why selecting some specific locations, etc)
- L461: distribution used in entry?
- Figure 10: we can’t distinguish between constraints.
- Figure 11: why only A and C?
- Figure 14: I do not understand what is presented in the graphs
- L568-570: not demonstrated
- L571: references are not enough to demonstrate what is “natural intrusion geometries”, you should be more precise, what is not usually good and is here?
- L575: “sparse dataset”: with more than 100 data points, regularly sampled, do you really think it has demonstrated the ability to deal with sparse and irregular datasets?
To conclude, this paper proposes a workflow to facilitate/automate the 3D modelling of igneous intrusions. I do not know works having specifically addressed this question, while the specific geometries encountered in such context could be, indeed, difficult to represent with the existing software. Thus, the subject is relevant and that is why, despite the important limitations that I detailed above, I think it could, after an in-depth revision, constitute an interesting publication for GMD.
CODE EVALUATION:
The paper refers to a Zenodo deposit and the LoopStructural project. On Zenodo, only a zip file can be downloaded, but there is also a link to a github deposit : https://github.com/Fer071989/loopstructural_intrusions_paper/tree/loopstructural .
As zip files are a vector for viruses, I would rather put the link to the github repo in the paper than the zenodo one : it allows just to consult the content and, if we want, to download only the parts we want.Note that the specific code described in the paper is indeed not presented in the zenodo file. The package, on both platforms, contains data used in the paper and 4 jupyter notebooks corresponding to the examples. The code presented in the paper has been directly integrated in LoopStructural.
I encountered some problems to install LoopStructural and was already late to send my review. Thus I finally abandoned the idea to test the notebooks… I am really sorry for that.
Citation: https://doi.org/10.5194/gmd-2022-88-RC1 -
AC1: 'Reply on RC1', Fernanda Alvarado-Neves, 22 Jul 2022
Dear Referee #1,
Thank you for the feedback and the suggested references. Please find below our response to your comments:
The paper is messy and should completely be re-organised and re-structured. In the present state, the section titles do not reflect what they content. To start, the introduction does not present the object of interest, the igneous intrusions, and they are hardly presented in the section 3, which mixes in each sub-section theorical description and algorithmic proposals. The algorithm description is dispersed and repeated in several parts of the manuscript: part 2.1, then lines 151- 172 in part 3.1, then 182 to 191, and they are mixed with results presentations in sections 4. Section 6, which is supposed to present a “discussion” presents again some results, supposed to be in section 5. The paper should be re-written and ordered following the classical introduction – methods – results- discussion – conclusion plan, which, in the present case would be easy to follow and sounds. To write their introduction, authors could get inspiration from this reference: Claerbout, J. F. (1991). A scrutiny of the introduction. The Leading Edge, 288–291. And both these references are also advised for paper: Sudarshan Iyengar. (2013, May). How to Write a Great Research Paper. Strunk, W., & White, E. B. (n.d.). The Elements of Style.
In more details, Introduction should here 1) present igneous intrusions, from a geological/descriptive point of view, with figures showing the diversity of encountered shapes, and explaining the processes of formation. Then, 2) clearly explain why these shapes cannot be reproduced easily and automatically by existing geomodelling approaches (going deeper in the geomodelling concepts than just saying “it is hard to do it” : explain why (superposition and lateral continuity principles that constitute a pillar of existing approaches, management of unconformities, etc)). 3) then, present papers that treat similar questions of highly convoluted shapes and explain their limitations considering the author’s specific question: I do not know works on igneous intrusions, but there are on salt tectonic features. For ex. the authors cite Clausolles et al., 2019, but hardly in the part 2 (for the SGS parametrization in the ODSIM process (?)) while they are close to the present contribution (salt diapirs modelling with an approach inspired by ODSIM). The authors should explain the differences and demonstrate the originality and plus-value of their own contribution. 4) finish with the plan of the paper. On the contrary, fuzzy focuses are made on “structural frames” in the introduction (lines 25-35) and the section 2.2. In both cases, the link with the present work is hardly understandable and so many details for fold-frame and fault-frame seem useless to understand the contribution of this paper. Section 2.2 could be removed and lines 25-35 limited to one citation.
We will restructure the paper following the classical introduction – methods – results- discussion – conclusion. A more thorough description of igneous intrusions and current challenges to model them will be included. Regarding the structural frames, we will clarify the importance of using a structural frame for the approach, and if it seems reasonable to improve the quality of the text, we will remove the details of fold and fault frames.
Vocabulary is not appropriate: “anisotropies” is the general term used by the authors to describe apparently faults and stratigraphic surfaces, and it is not right.
Anisotropies of the host rock has been described by previous authors as major controls on igneous intrusions emplacement, such as Clemens and Mawer (1992), Hogan and Gilbert (1995), Vigneresse et al., (1999), Cruden and Weinberg (2018), Schofield et al., (2012).
Clemens, J. D. and Mawer, C. K.: Granitic magma transport by fracture propagation, 204, 339–360, https://doi.org/10.1016/0040-1951(92)90316-X, 1992
Cruden, A. R. and Weinberg, R. F.: Mechanisms of Magma Transport and Storage in the Lower and Middle Crust—Magma Segregation, Ascent and Emplacement, in: Volcanic and Igneous Plumbing Systems, Elsevier, 13–53, https://doi.org/10.1016/B978-0-12-809749-6.00002-9, 2018
Hogan, J. P. and Gilbert, M. C.: The A-type Mount Scott Granite sheet: Importance of crystal magma traps, J. Geophys. Res. Solid Earth, 100, 15779–15792, https://doi.org/10.1029/94JB03258, 1995.
Schofield, N. J., Brown, D. J., Magee, C., and Stevenson, C. T.: Sill morphology and comparison of brittle and non-brittle emplacement mechanisms, J. Geol. Soc. London., 169, 127–141, https://doi.org/10.1144/0016-76492011-078, 2012.
Vigneresse, J. L., Tikoff, B., and Améglio, L.: Modification of the regional stress field by magma intrusion and formation of tabular granitic plutons, 302, 203–224, https://doi.org/10.1016/S0040-1951(98)00285-6, 1999.
Concerning the method [which should be presented from a general point of view, not on particular CS]
We will restructure the description of the methods section so it is presented in a general way and Case Studies will be presented in results.
Regarding your suggestions for the path search algorithm, we will consider removing the shortest path algorithm as the same results can be achieved without this step. We will refer to the suggested references if we keep the description of the shortest path algorithm.
On the “structural frame”: Beside the fact that it is presented several times (3.2 and 4), each time incompletely, the necessity of this step is unclear. Demonstrating the interest of these 3 directions by comparing with a more classic approach without this structural frame but an anisotropic 3D variogram (like in Clausolles et al., 2009) would be more convincing. The time and user expertise needed to perform so many steps should be discussed. The way this step is incorporated in the global workflow was unclear to me. I “guess” it replaces the distance field computed in ODSIM, but it is never really said, and it remains unclear why this step is changed.
The structural frame replaces the skeleton of the ODSIM, so the threshold values are distances to the axes of the structural frame. This allows us to simulated distances to constrain the thickness of the intrusion, and distances to constrain the width of the intrusion. The intrusion network (originally built using shortest path algorithm) is essentially a way to generate more value constraints for the Coordinate G of the structural frame, with the particularity that these constraints honour the anisotropies of the host rock involved in the emplacement of the intrusion. These value constraints are points that approximate the location of the roof or floor contact. The structural frame can be also constrained with other field measurements (inflation vector and flow direction vector) that cannot be used by interpolation algorithms (RBF, co-kriging, DSI). The structural frame is also used to parameterise simple conceptual models and adapt them for complex intrusion shapes. For example, with the structural frame, a sill complex with steps and sill fragmentation can be modelled as a one simple parallelepiped within the coordinates of the structural frame. Without the structural frame, the conceptual model would be significantly complex. We will include a figure showing more clearly how we use the structural frame coordinates to parametrise the conceptual models.
Regarding the reviewer’s suggestion about demonstrating the interest of these 3 directions by using an anisotropic 3D, we believe this will not be helpful because the anisotropic variogram does not provide a tool to parameterise the conceptual models. The authors believe the conceptual models are a key part of the workflow since they allow us to incorporate interpretations of the intrusion geometry in a traceable and repeatable way.
On the “ODSIM-inspired” part: The difference between the distance field and the random field is not clear in the text while it is a crucial point for the reader to understand. Distance field does not need to be Euclidean (see Rongier et al). This could be, at least, said, and discussed later in the discussion part. If I guess right and the 1 distance field is replaced by the “structural frame”, this should be better explained and the motivations behind this choice should be given. For the SGS generating the random field, why using an isotropic variogram? especially when asymmetric shapes are searched? Why an infinite range? Does it have any sense from a geostatistical point of view in a SGS? I don’t think so
We will clarify that the simulated random fields represent the difference between the conceptual models and the intrusion contact that is being modelled (we called these ‘residual values’). Two groups of random fields are used: one for the lateral contact (width of the intrusion) and one for the vertical contact (thickness of the intrusion). Isotropic variograms and infinite ranges are used so these random fields (i.e. the difference with the conceptual model) are relatively constant and with no sharp changes throughout the model. Sharp changes in the intrusion geometry such as sills or pluton steps are controlled by the structural frame, and therefore there is no need to achieve this in the simulations. Furthermore, as suggested by the second referee, we will assess the use of an exact interpolation method instead of simulations.
How do you infer the histogram parameters for running the SGS? No demonstration is provided from the data
Why not using Gibbs sampler when you want to fit data? The part about data fitting is quite unclear.
We will include how the histograms are calculated, and we will clarify that the data conditioning is reached using Sequential Gaussian Simulations.
How do you managed data which are not located on the envelope of the intrusion but inside or outside?
How do you manage data that say “no intrusion here”?
Data points that are not located in the intrusion contact are not used but will be considered for further improvements of the method. This will be discussed in the text.
One point of ODSIM is that the SGS generates a random field, and thus, when you mix the distance field with the random one, you obtain several equiprobable realizations: it is stochastic. Here the stochasticity is not presented in the results, only one result is each time presented. And the interest of this stochasticity is not really highlighted.
We will discuss briefly the usefulness of doing stochastic simulations, however, presenting in the text more than one model for each Case Study is outside the scope of this work. Since the simulation outcomes represent the differences with respect to the conceptual model constrained by the data, we expect the coarse scale geometry of the intrusions should not differ significantly, and we will evaluate to include as supplementary material different realizations of the case studies.
Results [they should incorporate the presentation of the CS (not introduced earlier, as the method part should be general) and the results obtained on it]:
Igneous intrusion shapes: only sills are presented while the introduction speaks of sill, plutons, dikes, laccoliths. Several examples should be provided and compared with what is obtained with other methods especially, a conceptual model is presented for pluton, but not really illustrated. If only sill and plutons are considered, this should be clearly stated in the title, abstract and introduction. And this limitation should be discussed and presented as a future work in conclusion.
Sills and plutons 3D models are presented in the case studies. Presenting these case studies is sufficiently illustrative enough because even though such intrusions differ significantly in nature, the modelling workflow is the same, the main difference being the conceptual model defined for each case. Examples of conceptual models are presented for both sills and plutons in Figure 3. The authors will discuss whether adding conceptual models of laccoliths and dykes will anything significant. If not, we will highlight that their tabular morphologies are similar to sills or tablet-shape plutons.
The case studies should incorporate the demonstration of the variogram and histogram definition from the data
We will include the variogram and histogram definition for case studies.
CS3: why so much data? where should they come from in general cases?
The Case Study 3 has 0.1% of the original contact points dataset. Even though the dataset is dense, the objective of this examples is comparing the results with RBF interpolation. A typical dataset for modelling intrusions is described in the introduction.
ODSIM can generate shapes in the absence of observation points. Here no results are provided in the absence of points indicating the position of the intrusion contour. This should be rectified.
Generating models with no data is beyond the scope of this paper.
One realization, coming from a stochastic process is compared to the solution of a deterministic approach (the RBF-based), and to the “ideal” solution:
stochastic processes do not aim to find “the solution” but a range of realistic solutions which embraces the possibilities given the non-completeness of data. In that sense, at least several realizations (10-50-100?) should be considered and compared to the “solution”. The variability of the realizations should be estimated and in several context of data: the variability should reduce with increasing data. Tt is strange to compare a deterministic solution (RBF) with 1 realisation of as tochastic method which do not use the same input data… You can say that they are usable with different input data, but it is difficult to be objective here.
The comparison with RBF is performed because RBF is one of the interpolation techniques used to model igneous intrusions in 3D in currently available modelling packages. While the authors understand the reviewer’s concern about comparing one solution of a stochastic process with the outcome of a deterministic process, we believe our approach is valid because the whole aim of the stochastic simulation is to better constrain the intrusion contact surface. In the models built using the proposed workflow, the intrusion contact is given by the isovalue 0 of a scalar field. This scalar field is computed so the intrusion contact given by the simulations (i.e., contact = conceptual model – residual distances) is the isovalue 0 of the scalar field. For the purpose of this workflow, the simulations can be replaced by interpolating the residual values (i.e., distances between the data and the conceptual model). This will be implemented and discussed.
The contact data points used for models A, C and D are the same, the only difference is that models C and D also include propagation and inflation vector data, while model A includes planar constraints. The input dataset for Model B has around 5 times the number of data points compared with the other models. This was done to illustrate that RBF can reproduce more realistic geometries (compared to what was mapped in the seismic survey, Figure 9) when dense datasets and gradient constraints are provided. Event though the input data are not exactly the same (because both method do not use the same type of input data), we believe the comparison is fair as models A, C and D use similar amount of value and planar constraints.
Discussion: The influence of variogram and histogram used for the random field generation has been demonstrated crucial (Henrion et al 2008, Clausolles et al 2019). This should be discussed with the help of a small sensitivity analysis, trying various variogram settings.
We believe a sensitivity analysis to assess the influence of the variogram is out of the scope of the paper. We will reference previous works (e.g. Henrion et al., 2010, Clausolles, et al., 2019). As mentioned before, and as suggested by the second referee, we will implement exact interpolation to replace the use of stochastic simulations.
The stochasticity should be discussed and the comparison with RBF should consider the fact that RBF is deterministic. The capacity of the method to reduce uncertainties as the amount of data increase should be discussed. the computing time should be given and discussed. The results concerning the shapes should be discussed as compared to the one proposed in other contexts (eg salt diapirs or karsts anisotropic shapes like in Rongier et al 2014). In particular, the interest of the structural frame compared to the simple introduction of an “standard object” as a skeleton and an adapted distance field (I guess the advantages, but the authors say nothing about it and demonstrate nothing)
We will discuss the stochasticity and comparison with the deterministic approach, the capacity of the method to reduce the uncertainties (however, the quantification of the uncertainties is out of the scope of this paper), the computing time, and the advantages of using structural frames.
Is it possible to combine several types of intrusion in one model?
More than one intrusion can be modelled in one 3D model as independent objects. This is showed in case study 1 and will be stated in the text
Current limitations (considered shapes, grid requirements, …)
Limitation of the method are described in the last paragraph of the discussion section
Regarding the minor comments, these will be addressed to improve the quality of the text.
Code evaluation: Yes, the links are links to the examples. We will fix the link to the LoopStructural python library.
Citation: https://doi.org/10.5194/gmd-2022-88-AC1
- Path search algorithm:
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RC2: 'Comment on gmd-2022-88', Italo Goncalves, 29 Jun 2022
The manuscript presents a novel methodology to model the geometry of igneous intrusions. Developments from previous works are employed along an adaptation of the ODSIM algorithm. External knowledge can be inputed through parametric functions.
The first reviewer already made substantial points about the work's structure, clarity, and methodology. My contributions are the following:
Major comments:I believe the authors should try to isolate the strengths, limitations, and benefits of the three main components of the proposed methodology, namely the use of (i) strucural frames, (ii) ODSIM, and (iii) parametric conceptual models. Experiments using (i) and (ii), (i) and (iii), just (i), etc. would be too much work perhaps, but their isolated effects and their contribution to the final result must be measured somehow. It might be that one of the three is completely unnecessary or redundant, at least for the case studies provided.
Please clarify the mathematical notation. It is common to use lowercase for scalars, bold lowercase for vectors, and bold uppercase for matrices.
Section 2.1 - A figure with a conceptual explanation would be interesting. If a 3D example becomes too convoluted, cross-sections or a 2D example can be used.
It is not clear whether the g, p, and l fields are scalar or vector fields. Lines 314-326 present some ambiguity in this regard. The text mentions isovalues, supporting the notion of scalar fields, but it also mentions orthogonality between p and l, suggesting that they are in fact vectors. Do you mean orthogonality between their gradients? If g, p, and l were in fact vector fields, then one would have to interpolate 9 variables instead of 3.
Why use simulations? Wouldn't it be possible to use kriging or RBF (even if you must compute normal scores first) to obtain a "mean" surface?
Section 5.1 and lines 473-477 - For the sake of fairness to RBF, you could employ an elliptical conceptual model in this case as well. It should be simple to define a parametric base field and subtract it from the signed distances data.
Figures 7, 8, 10c, and 10d: please discuss the possible causes for the jagged aspect of the models. I suspect it has to do with the use of simulations.
Lines 555-556: I see it as an advantage, rather than a limitation. User input in this form allows for more flexible and realistic models. It may require extra work and thought, but that is why professionals are trained.
Minor comments:
Figure 3 - do you mean (g, p, l) or g(p, l)?
Figure 4, legend - "The stating points for the search is the shortest path is J_in"; please rephrase
Section 4.2.1 - The gradients of the g, p, and l fields have a constant direction? I assume that this is the case in the presented example, but not a requirement for the methodology to work.
Line 309: "The gradient of this scalar field is a normalized vector parallel to the propagation direction of the intrusion." Does this mean that the field p is linear? Looking at Figure 5 the direction of the gradient appears to be constant, but the slope seems variable (for instance, the green region is thicker than the cyan one). This might be an artifact of the color scale. I recommend the use of visually uniform color maps (Crameri et al., 2020)
Lines 339-344: The text seems to repeat the explanation of lines 350-356 after the equation.
Line 361: What to you mean by a variogram of infinite range? A range larger than the extent of the g, p, l coordinates?
Figure 7, legend: "sills" -> "sill's"; "shows" -> "show"
Line 455: Do you mean Figure 10d?
Figure 11: In the first line, Vb is equal to model volume. It this correct?
Figure 14, legend: "thought" -> "through"
Line 569: "realization" -> "realizations"
Line 576: "restricted" -> "constrained"
References:Crameri, F., Shephard, G. E., & Heron, P. J. (2020). The misuse of colour in science communication. Nature Communications, 11(1), 1–10. https://doi.org/10.1038/s41467-020-19160-7
Citation: https://doi.org/10.5194/gmd-2022-88-RC2 -
AC2: 'Reply on RC2', Fernanda Alvarado-Neves, 22 Jul 2022
Dear Italo,
Thank you for your feedback. Please, see below our response to your comments:
I believe the authors should try to isolate the strengths, limitations, and benefits of the three main components of the proposed methodology, namely the use of (i) strucural frames, (ii) ODSIM, and (iii) parametric conceptual models. Experiments using (i) and (ii), (i) and (iii), just (i), etc. would be too much work perhaps, but their isolated effects and their contribution to the final result must be measured somehow. It might be that one of the three is completely unnecessary or redundant, at least for the case studies provided.
An assessment of the benefits and limitation of each of the three main components (structural frames, ODSIM, and parametric conceptual models) sounds interesting, however we agree that various experiments to isolate their advantages will be outside of the scope of this paper. We propose to discuss the expected effects on removing each of the component and qualitatively assess their contribution to the method.
Please clarify the mathematical notation. It is common to use lowercase for scalars, bold lowercase for vectors, and bold uppercase for matrices.
We will fix the mathematical notation as suggested.
Section 2.1 - A figure with a conceptual explanation would be interesting. If a 3D example becomes too convoluted, cross-sections or a 2D example can be used.
We will include a figure of the ODSIM workflow, and tentatively we will make a figure showing how intrusions frame are incorporated in the ODSIM workflow.
It is not clear whether the g, p, and l fields are scalar or vector fields. Lines 314-326 present some ambiguity in this regard. The text mentions isovalues, supporting the notion of scalar fields, but it also mentions orthogonality between p and l, suggesting that they are in fact vectors. Do you mean orthogonality between their gradients? If g, p, and l were in fact vector fields, then one would have to interpolate 9 variables instead of 3.
g, p, and l are scalar fields and the orthogonality is between their gradients. We will clarify this in the text.
Why use simulations? Wouldn't it be possible to use kriging or RBF (even if you must compute normal scores first) to obtain a "mean" surface?
We will evaluate using exact interpolation methods instead of simulations. We mainly used simulations following the ODSIM proposal, however, our method does not aim to generate several realizations of each model, so using interpolation would probably be a simpler way of computing the distances thresholds along the frame axes.
Section 5.1 and lines 473-477 - For the sake of fairness to RBF, you could employ an elliptical conceptual model in this case as well. It should be simple to define a parametric base field and subtract it from the signed distances data.
Regarding CS3 and its RBF 3D models, the authors will create the 3D models using an elliptical conceptual model to make a fairer comparison.
Figures 7, 8, 10c, and 10d: please discuss the possible causes for the jagged aspect of the models. I suspect it has to do with the use of simulations.
The jagged aspect of the models in Figures 7, 8, and 10 is because of the grid. It will be discussed, and we will run the models with a finer grid for the figures.
Lines 555-556: I see it as an advantage, rather than a limitation. User input in this form allows for more flexible and realistic models. It may require extra work and thought, but that is why professionals are trained.
This is true, thanks for the comment, we will rephrase this part of the discussions.
Regarding the minor comments, these will be addressed to improve the quality text.
Citation: https://doi.org/10.5194/gmd-2022-88-AC2
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AC2: 'Reply on RC2', Fernanda Alvarado-Neves, 22 Jul 2022
Interactive discussion
Status: closed
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RC1: 'Comment on gmd-2022-88', Anonymous Referee #1, 15 Jun 2022
The manuscript 2022-88 addresses an interesting subject and topic, which perfectly fits the scope of GMD, and proposes an interesting idea. I have, however, major concerns that should be addressed before considering the paper for publication, meaning, a second review would probably be required after revision. To make a summary: the paper is messy, with repetitive parts, superficial explanations of references used in it, sometimes inappropriate words and fuzzy vocabulary are used; the objects of interest (igneous intrusion) are hardly presented; It also lacks details concerning the algorithm, and the analysis of the results remains superficial, and some aspects of the approach are completely let apart in the result analysis. I am not sure the paper and method could be followed by someone who does not already know the references and approaches. Figures are not always legible, it lacks some additional illustrations, and there are some duplicated references. In the following, I develop all these points.
The paper is messy and should completely be re-organised and re-structured. In the present state, the section titles do not reflect what they content. To start, the introduction does not present the object of interest, the igneous intrusions, and they are hardly presented in the section 3, which mixes in each sub-section theorical description and algorithmic proposals. The algorithm description is dispersed and repeated in several parts of the manuscript: part 2.1, then lines 151- 172 in part 3.1, then 182 to 191, and they are mixed with results presentations in sections 4. Section 6, which is supposed to present a “discussion” presents again some results, supposed to be in section 5. The paper should be re-written and ordered following the classical introduction – methods – results- discussion – conclusion plan, which, in the present case would be easy to follow and sounds.
To write their introduction, authors could get inspiration from this reference: Claerbout, J. F. (1991). A scrutiny of the introduction. The Leading Edge, 288–291. And both these references are also advised for paper : Sudarshan Iyengar. (2013, May). How to Write a Great Research Paper. Strunk, W., & White, E. B. (n.d.). The Elements of Style.
In more details, Introduction should here 1) present igneous intrusions, from a geological/descriptive point of view, with figures showing the diversity of encountered shapes, and explaining the processes of formation. Then, 2) clearly explain why these shapes cannot be reproduced easily and automatically by existing geomodelling approaches (going deeper in the geomodelling concepts than just saying “it is hard to do it” : explain why (superposition and lateral continuity principles that constitute a pillar of existing appraoches, management of unconformities, etc)). 3) then, present papers that treat similar questions of highly convoluted shapes and explain their limitations considering the author’s specific question: I do not know works on igneous intrusions, but there are on salt tectonic features. For ex. the authors cite Clausolles et al., 2019, but hardly in the part 2 (for the SGS parametrization in the ODSIM process (?)) while they are close to the present contribution (salt diapirs modelling with an approach inspired by ODSIM). The authors should explain the differences and demonstrate the originality and plus-value of their own contribution. 4) finish with the plan of the paper.
On the contrary, fuzzy focuses are made on “structural frames” in the introduction (lines 25-35) and the section 2.2. In both cases, the link with the present work is hardly understandable and so many details for fold-frame and fault-frame seem useless to understand the contribution of this paper. Section 2.2 could be removed and lines 25-35 limited to one citation.
Vocabulary is not appropriate: “anisotropies” is the general term used by the authors to describe apparently faults and stratigraphic surfaces, and it is not right.
Concerning the method [which should be presented from a general point of view, not on particular CS] :
- Path search algorithm:
- This step is not clearly explained and illustrated: The figure 4 is not clear enough and too small. Points are below the stratigraphic surfaces but then a value seems affected to this surface. Ic and IF are not explained in the text and the way they are mixed is not clear. The position and meaning of Jout is unclear.
- Its plus-value and interest are not demonstrated as it is only used in 1 simple and theoretical CS. In other cases, the user chooses the “skeleton” surfaces and we do not understand why not doing this in this first simple example.
- They refer all time to Borghi et al., but:
- the latter were looking for linear paths between 2 points, here the authors search surfaces, which is not the same. How to pass from several lines to surfaces? It is not clear at all.
- Borghi takes its inspiration from Henrion et al. 2007, 2008 (Henrion, V., Pellerin, J., & Caumon, G. (2008). A stochastic methodology for 3d cave system modelling. In G. Ltd (Ed.), 8th Geostatistics Congress (pp. 525–533). Santiago, Chili.), and Henrion et al. already took inspiration from the main path search proposed by Vitel et al to identify main path in fracture networks (Vitel, S. (2007). Méthodes de discrétisation et de changement d’échelle pour les réservoirs fracturés 3D. Institut National Polytechnique de Lorraine. // Vitel, S. (2006). Fast Transmissibility Upscaling Technique for NFR. In 26th Gocad Meeting (pp. 1–18).). One difference was that they use FMA instead of A* algorithm. It conducts me to the following point:
- searching for a best path between two points is not a contribution of Borghi, it is a standard and several algorithms exist for a long time. This should be the main references. Also, why using Fast marching (FMA)? Why not Djikstra ? Why not A*? etc. These points should be discussed and argued. Here, you are not looking from a path between 2 points, but from surfaces of circulation between areas. You could free yourself of this redundant reference about karsts (who is not the only one nor the first to propose it), just say that a similar approaches were proposed for karstic networks by Henrion et aL, Borghi et al., Collon et al; Paris et al., etc (and also for other types of systems perhaps?), but here you are dealing differently in a different context.
- to use FMA, one need to choose velocity values. Everything will depend on that. The choice of these values is also hardly discussed, not illustrated (no values are provided for the case studies) and no sensibility analysis is made.
- On the “structural frame”
- Beside the fact that it is presented several times (3.2 and 4), each time incompletely, the necessity of this step is unclear. Demonstrating the interest of these 3 directions by comparing with a more classic approach without this structural frame but an anisotropic 3D variogram (like in Clausolles et al., 2009) would be more convincing.
- The time and user expertise needed to perform so many steps should be discussed
- The way this step is incorporated in the global workflow was unclear to me. I “guess” it replaces the distance field computed in ODSIM, but it is never really said, and it remains unclear why this step is changed.
- On the 4.2.2 “ODSIM-inspired” part
- The difference between the distance field and the random field is not clear in the text while it is a crucial point for the reader to understand.
- Distance field does not need to be Euclidean (see Rongier et al). This could be, at least, said, and discussed later in the discussion part. If I guess right and the 1 distance field is replaced by the “structural frame”, this should be better explained and the motivations behind this choice should be given.
- For the SGS generating the random field:
- why using an isotropic variogram? especially when asymmetric shapes are searched?
- Why an infinite range? Does it have any sense from a geostatistical point of view in a SGS? I don’t think so
- How do you infer the histogram parameters for running the SGS? No demonstration is provided from the data
- Why not using Gibbs sampler when you want to fit data? The part about data fitting is quite unclear
- How do you managed data which are not located on the envelope of the intrusion but inside or outside?
- How do you manage data that say “no intrusion here”?
- One point of ODSIM is that the SGS generates a random field, and thus, when you mix the distance field with the random one, you obtain several equiprobable realizations: it is stochastic. Here the stochasticity is not presented in the results, only one result is each time presented. And the interest of this stochasticity is not really highlighted.
Results [they should incorporate the presentation of the CS (not introduced earlier, as the method part should be general) and the results obtained on it]:
- Igneous intrusion shapes:
- only sills are presented while the introduction speaks of sill, plutons, dikes, laccoliths. Several examples should be provided and compared with what is obtained with other methods
- especially, a conceptual model is presented for pluton, but not really illustrated
- if only sill and plutons are considered, this should be clearly stated in the title, abstract and introduction. And this limitation should be discussed and presented as a future work in conclusion.
- The case studies should incorporate the demonstration of the variogram and histogram definition from the data
- CS3: why so much data? where should they come from in general cases?
- ODSIM can generate shapes in the absence of observation points. Here no results are provided in the absence of points indicating the position of the intrusion contour. This should be rectified.
- One realization, coming from a stochastic process is compared to the solution of a deterministic approach (the RBF-based), and to the “ideal” solution:
- stochastic processes do not aim to find “the solution” but a range of realistic solutions which embraces the possibilities given the non-completeness of data. In that sense, at least several realizations (10-50-100?) should be considered and compared to the “solution”
- the variability of the realizations should be estimated and in several context of data: the variability should reduce with increasing data
- it is strange to compare a deterministic solution (RBF) with 1 realisation of as tochastic method which do not use the same input data… You can say that they are usable with different input data, but it is difficult to be objective here.
Discussion:
- The influence of variogram and histogram used for the random field generation has been demonstrated crucial (Henrion et al 2008, Clausolles et al 2019). This should be discussed with the help of a small sensitivity analysis, trying various variogram settings.
- The stochasticity should be discussed and the comparison with RBF should consider the fact that RBF is deterministic.
- The capacity of the method to reduce uncertainties as the amount of data increase should be discussed
- the computing time should be given and discussed
- the results concerning the shapes should be discussed as compared to the one proposed in other contexts (eg salt diapirs or karsts anisotropic shapes like in Rongier et al 2014). In particular, the interest of the structural frame compared to the simple introduction of an “standard object” as a skeleton and an adapted distance field (I guess the advantages, but the authors say nothing about it and demonstrate nothing)
- Is it possible to combine several types of intrusion in one model?
- Current limitations (considered shapes, grid requirements, …)
“Minor” comments:
- Abstract: lines 9-11 : “existing technics are strongly dependant on the availability of data” : isn’t the case of all methods including yours ? => better remove this sentence
- L53: “estimation”: of what ? a volume ? For what point?
- “realistic” is said several times: what is a “realistic shape”? An un-realistic one? Do you have a specific criterion in particular?
- L70: I am not sure ODSIM has been applied on meandering channels: to check
- Section 2.1: should better be understandable with a figure
- L76-l84: completely out of the scope of ODSIM. Should be removed. It lost the reader here as the point of the path search is different (it is to create a skeleton, ODSIM starts from the skeleton.)
- L84-87: not clear. Especially, l86, no, the geological body is not defined by the isovalue of lambda, but by the surface given by the difference between D(p) and Phi(P) (as you said 2 lines below).
- Section 2.2: as already said, I would remove this part, I found it completely useless for understanding this paper (and often quite fuzzy)
- L161: “observation points” meaning? on seismic? On well? what kind of data exactly?
- L162: what do you mean “simulate anisotropies”? Also simulating faults is not the same than horizons.
- L165: what assumptions? What do you mean by “mechanical anisotropy”? it is quite fuzzy
- Figure 1: not really clear. What kind of observation points? What mean intrusion network surfaces? Are they determined by the geologist knowledge? If the magma comes from below, the faults should potentially have been a vector of it? Why are they not considered here in their lower part?
- Figure 2: light the colours. Please add g, p and l on the figure. For case (a) please explain the context to allow the reader understanding what have guided the definition of the three axes in this case.
- L205: no literature describing quantitatively the igneous shapes and proposing geometrical description?
- Figure 3: use it to explain roof and floor. In the legend it is written g(p,l), should it not be (g,p,l) like in the text ? For sill why using a regular parallelepiped and not a one which become thinner along one direction?
- 1: in the current form, the title suggests the method will depend on considered shapes. If the authors change the structure of the paper, this confusion should disappear.
- L276: unclear
- Figure 5 and CS2: is the final shape known from seismic?
- Figure 5: if we only have points and horizontal strata, how was p and l chosen? On the figure it is hardly understandable. Perhaps it is a problem relative to the view angle
- L361: give the distribution. Explain what are the “values” that you put in this distribution. How do you compute them? It is unclear.
- Figure 6: is it specific to this case study?
- Figure 7: show several realizations. Could you colour the result depending on Z or use contour lines to help the reader see the relief?
- Figure 9: a is not readable. Points are all mixed we do ot see anything.
- L435-438: what justify the choices made (so many points, why selecting some specific locations, etc)
- L461: distribution used in entry?
- Figure 10: we can’t distinguish between constraints.
- Figure 11: why only A and C?
- Figure 14: I do not understand what is presented in the graphs
- L568-570: not demonstrated
- L571: references are not enough to demonstrate what is “natural intrusion geometries”, you should be more precise, what is not usually good and is here?
- L575: “sparse dataset”: with more than 100 data points, regularly sampled, do you really think it has demonstrated the ability to deal with sparse and irregular datasets?
To conclude, this paper proposes a workflow to facilitate/automate the 3D modelling of igneous intrusions. I do not know works having specifically addressed this question, while the specific geometries encountered in such context could be, indeed, difficult to represent with the existing software. Thus, the subject is relevant and that is why, despite the important limitations that I detailed above, I think it could, after an in-depth revision, constitute an interesting publication for GMD.
CODE EVALUATION:
The paper refers to a Zenodo deposit and the LoopStructural project. On Zenodo, only a zip file can be downloaded, but there is also a link to a github deposit : https://github.com/Fer071989/loopstructural_intrusions_paper/tree/loopstructural .
As zip files are a vector for viruses, I would rather put the link to the github repo in the paper than the zenodo one : it allows just to consult the content and, if we want, to download only the parts we want.Note that the specific code described in the paper is indeed not presented in the zenodo file. The package, on both platforms, contains data used in the paper and 4 jupyter notebooks corresponding to the examples. The code presented in the paper has been directly integrated in LoopStructural.
I encountered some problems to install LoopStructural and was already late to send my review. Thus I finally abandoned the idea to test the notebooks… I am really sorry for that.
Citation: https://doi.org/10.5194/gmd-2022-88-RC1 -
AC1: 'Reply on RC1', Fernanda Alvarado-Neves, 22 Jul 2022
Dear Referee #1,
Thank you for the feedback and the suggested references. Please find below our response to your comments:
The paper is messy and should completely be re-organised and re-structured. In the present state, the section titles do not reflect what they content. To start, the introduction does not present the object of interest, the igneous intrusions, and they are hardly presented in the section 3, which mixes in each sub-section theorical description and algorithmic proposals. The algorithm description is dispersed and repeated in several parts of the manuscript: part 2.1, then lines 151- 172 in part 3.1, then 182 to 191, and they are mixed with results presentations in sections 4. Section 6, which is supposed to present a “discussion” presents again some results, supposed to be in section 5. The paper should be re-written and ordered following the classical introduction – methods – results- discussion – conclusion plan, which, in the present case would be easy to follow and sounds. To write their introduction, authors could get inspiration from this reference: Claerbout, J. F. (1991). A scrutiny of the introduction. The Leading Edge, 288–291. And both these references are also advised for paper: Sudarshan Iyengar. (2013, May). How to Write a Great Research Paper. Strunk, W., & White, E. B. (n.d.). The Elements of Style.
In more details, Introduction should here 1) present igneous intrusions, from a geological/descriptive point of view, with figures showing the diversity of encountered shapes, and explaining the processes of formation. Then, 2) clearly explain why these shapes cannot be reproduced easily and automatically by existing geomodelling approaches (going deeper in the geomodelling concepts than just saying “it is hard to do it” : explain why (superposition and lateral continuity principles that constitute a pillar of existing approaches, management of unconformities, etc)). 3) then, present papers that treat similar questions of highly convoluted shapes and explain their limitations considering the author’s specific question: I do not know works on igneous intrusions, but there are on salt tectonic features. For ex. the authors cite Clausolles et al., 2019, but hardly in the part 2 (for the SGS parametrization in the ODSIM process (?)) while they are close to the present contribution (salt diapirs modelling with an approach inspired by ODSIM). The authors should explain the differences and demonstrate the originality and plus-value of their own contribution. 4) finish with the plan of the paper. On the contrary, fuzzy focuses are made on “structural frames” in the introduction (lines 25-35) and the section 2.2. In both cases, the link with the present work is hardly understandable and so many details for fold-frame and fault-frame seem useless to understand the contribution of this paper. Section 2.2 could be removed and lines 25-35 limited to one citation.
We will restructure the paper following the classical introduction – methods – results- discussion – conclusion. A more thorough description of igneous intrusions and current challenges to model them will be included. Regarding the structural frames, we will clarify the importance of using a structural frame for the approach, and if it seems reasonable to improve the quality of the text, we will remove the details of fold and fault frames.
Vocabulary is not appropriate: “anisotropies” is the general term used by the authors to describe apparently faults and stratigraphic surfaces, and it is not right.
Anisotropies of the host rock has been described by previous authors as major controls on igneous intrusions emplacement, such as Clemens and Mawer (1992), Hogan and Gilbert (1995), Vigneresse et al., (1999), Cruden and Weinberg (2018), Schofield et al., (2012).
Clemens, J. D. and Mawer, C. K.: Granitic magma transport by fracture propagation, 204, 339–360, https://doi.org/10.1016/0040-1951(92)90316-X, 1992
Cruden, A. R. and Weinberg, R. F.: Mechanisms of Magma Transport and Storage in the Lower and Middle Crust—Magma Segregation, Ascent and Emplacement, in: Volcanic and Igneous Plumbing Systems, Elsevier, 13–53, https://doi.org/10.1016/B978-0-12-809749-6.00002-9, 2018
Hogan, J. P. and Gilbert, M. C.: The A-type Mount Scott Granite sheet: Importance of crystal magma traps, J. Geophys. Res. Solid Earth, 100, 15779–15792, https://doi.org/10.1029/94JB03258, 1995.
Schofield, N. J., Brown, D. J., Magee, C., and Stevenson, C. T.: Sill morphology and comparison of brittle and non-brittle emplacement mechanisms, J. Geol. Soc. London., 169, 127–141, https://doi.org/10.1144/0016-76492011-078, 2012.
Vigneresse, J. L., Tikoff, B., and Améglio, L.: Modification of the regional stress field by magma intrusion and formation of tabular granitic plutons, 302, 203–224, https://doi.org/10.1016/S0040-1951(98)00285-6, 1999.
Concerning the method [which should be presented from a general point of view, not on particular CS]
We will restructure the description of the methods section so it is presented in a general way and Case Studies will be presented in results.
Regarding your suggestions for the path search algorithm, we will consider removing the shortest path algorithm as the same results can be achieved without this step. We will refer to the suggested references if we keep the description of the shortest path algorithm.
On the “structural frame”: Beside the fact that it is presented several times (3.2 and 4), each time incompletely, the necessity of this step is unclear. Demonstrating the interest of these 3 directions by comparing with a more classic approach without this structural frame but an anisotropic 3D variogram (like in Clausolles et al., 2009) would be more convincing. The time and user expertise needed to perform so many steps should be discussed. The way this step is incorporated in the global workflow was unclear to me. I “guess” it replaces the distance field computed in ODSIM, but it is never really said, and it remains unclear why this step is changed.
The structural frame replaces the skeleton of the ODSIM, so the threshold values are distances to the axes of the structural frame. This allows us to simulated distances to constrain the thickness of the intrusion, and distances to constrain the width of the intrusion. The intrusion network (originally built using shortest path algorithm) is essentially a way to generate more value constraints for the Coordinate G of the structural frame, with the particularity that these constraints honour the anisotropies of the host rock involved in the emplacement of the intrusion. These value constraints are points that approximate the location of the roof or floor contact. The structural frame can be also constrained with other field measurements (inflation vector and flow direction vector) that cannot be used by interpolation algorithms (RBF, co-kriging, DSI). The structural frame is also used to parameterise simple conceptual models and adapt them for complex intrusion shapes. For example, with the structural frame, a sill complex with steps and sill fragmentation can be modelled as a one simple parallelepiped within the coordinates of the structural frame. Without the structural frame, the conceptual model would be significantly complex. We will include a figure showing more clearly how we use the structural frame coordinates to parametrise the conceptual models.
Regarding the reviewer’s suggestion about demonstrating the interest of these 3 directions by using an anisotropic 3D, we believe this will not be helpful because the anisotropic variogram does not provide a tool to parameterise the conceptual models. The authors believe the conceptual models are a key part of the workflow since they allow us to incorporate interpretations of the intrusion geometry in a traceable and repeatable way.
On the “ODSIM-inspired” part: The difference between the distance field and the random field is not clear in the text while it is a crucial point for the reader to understand. Distance field does not need to be Euclidean (see Rongier et al). This could be, at least, said, and discussed later in the discussion part. If I guess right and the 1 distance field is replaced by the “structural frame”, this should be better explained and the motivations behind this choice should be given. For the SGS generating the random field, why using an isotropic variogram? especially when asymmetric shapes are searched? Why an infinite range? Does it have any sense from a geostatistical point of view in a SGS? I don’t think so
We will clarify that the simulated random fields represent the difference between the conceptual models and the intrusion contact that is being modelled (we called these ‘residual values’). Two groups of random fields are used: one for the lateral contact (width of the intrusion) and one for the vertical contact (thickness of the intrusion). Isotropic variograms and infinite ranges are used so these random fields (i.e. the difference with the conceptual model) are relatively constant and with no sharp changes throughout the model. Sharp changes in the intrusion geometry such as sills or pluton steps are controlled by the structural frame, and therefore there is no need to achieve this in the simulations. Furthermore, as suggested by the second referee, we will assess the use of an exact interpolation method instead of simulations.
How do you infer the histogram parameters for running the SGS? No demonstration is provided from the data
Why not using Gibbs sampler when you want to fit data? The part about data fitting is quite unclear.
We will include how the histograms are calculated, and we will clarify that the data conditioning is reached using Sequential Gaussian Simulations.
How do you managed data which are not located on the envelope of the intrusion but inside or outside?
How do you manage data that say “no intrusion here”?
Data points that are not located in the intrusion contact are not used but will be considered for further improvements of the method. This will be discussed in the text.
One point of ODSIM is that the SGS generates a random field, and thus, when you mix the distance field with the random one, you obtain several equiprobable realizations: it is stochastic. Here the stochasticity is not presented in the results, only one result is each time presented. And the interest of this stochasticity is not really highlighted.
We will discuss briefly the usefulness of doing stochastic simulations, however, presenting in the text more than one model for each Case Study is outside the scope of this work. Since the simulation outcomes represent the differences with respect to the conceptual model constrained by the data, we expect the coarse scale geometry of the intrusions should not differ significantly, and we will evaluate to include as supplementary material different realizations of the case studies.
Results [they should incorporate the presentation of the CS (not introduced earlier, as the method part should be general) and the results obtained on it]:
Igneous intrusion shapes: only sills are presented while the introduction speaks of sill, plutons, dikes, laccoliths. Several examples should be provided and compared with what is obtained with other methods especially, a conceptual model is presented for pluton, but not really illustrated. If only sill and plutons are considered, this should be clearly stated in the title, abstract and introduction. And this limitation should be discussed and presented as a future work in conclusion.
Sills and plutons 3D models are presented in the case studies. Presenting these case studies is sufficiently illustrative enough because even though such intrusions differ significantly in nature, the modelling workflow is the same, the main difference being the conceptual model defined for each case. Examples of conceptual models are presented for both sills and plutons in Figure 3. The authors will discuss whether adding conceptual models of laccoliths and dykes will anything significant. If not, we will highlight that their tabular morphologies are similar to sills or tablet-shape plutons.
The case studies should incorporate the demonstration of the variogram and histogram definition from the data
We will include the variogram and histogram definition for case studies.
CS3: why so much data? where should they come from in general cases?
The Case Study 3 has 0.1% of the original contact points dataset. Even though the dataset is dense, the objective of this examples is comparing the results with RBF interpolation. A typical dataset for modelling intrusions is described in the introduction.
ODSIM can generate shapes in the absence of observation points. Here no results are provided in the absence of points indicating the position of the intrusion contour. This should be rectified.
Generating models with no data is beyond the scope of this paper.
One realization, coming from a stochastic process is compared to the solution of a deterministic approach (the RBF-based), and to the “ideal” solution:
stochastic processes do not aim to find “the solution” but a range of realistic solutions which embraces the possibilities given the non-completeness of data. In that sense, at least several realizations (10-50-100?) should be considered and compared to the “solution”. The variability of the realizations should be estimated and in several context of data: the variability should reduce with increasing data. Tt is strange to compare a deterministic solution (RBF) with 1 realisation of as tochastic method which do not use the same input data… You can say that they are usable with different input data, but it is difficult to be objective here.
The comparison with RBF is performed because RBF is one of the interpolation techniques used to model igneous intrusions in 3D in currently available modelling packages. While the authors understand the reviewer’s concern about comparing one solution of a stochastic process with the outcome of a deterministic process, we believe our approach is valid because the whole aim of the stochastic simulation is to better constrain the intrusion contact surface. In the models built using the proposed workflow, the intrusion contact is given by the isovalue 0 of a scalar field. This scalar field is computed so the intrusion contact given by the simulations (i.e., contact = conceptual model – residual distances) is the isovalue 0 of the scalar field. For the purpose of this workflow, the simulations can be replaced by interpolating the residual values (i.e., distances between the data and the conceptual model). This will be implemented and discussed.
The contact data points used for models A, C and D are the same, the only difference is that models C and D also include propagation and inflation vector data, while model A includes planar constraints. The input dataset for Model B has around 5 times the number of data points compared with the other models. This was done to illustrate that RBF can reproduce more realistic geometries (compared to what was mapped in the seismic survey, Figure 9) when dense datasets and gradient constraints are provided. Event though the input data are not exactly the same (because both method do not use the same type of input data), we believe the comparison is fair as models A, C and D use similar amount of value and planar constraints.
Discussion: The influence of variogram and histogram used for the random field generation has been demonstrated crucial (Henrion et al 2008, Clausolles et al 2019). This should be discussed with the help of a small sensitivity analysis, trying various variogram settings.
We believe a sensitivity analysis to assess the influence of the variogram is out of the scope of the paper. We will reference previous works (e.g. Henrion et al., 2010, Clausolles, et al., 2019). As mentioned before, and as suggested by the second referee, we will implement exact interpolation to replace the use of stochastic simulations.
The stochasticity should be discussed and the comparison with RBF should consider the fact that RBF is deterministic. The capacity of the method to reduce uncertainties as the amount of data increase should be discussed. the computing time should be given and discussed. The results concerning the shapes should be discussed as compared to the one proposed in other contexts (eg salt diapirs or karsts anisotropic shapes like in Rongier et al 2014). In particular, the interest of the structural frame compared to the simple introduction of an “standard object” as a skeleton and an adapted distance field (I guess the advantages, but the authors say nothing about it and demonstrate nothing)
We will discuss the stochasticity and comparison with the deterministic approach, the capacity of the method to reduce the uncertainties (however, the quantification of the uncertainties is out of the scope of this paper), the computing time, and the advantages of using structural frames.
Is it possible to combine several types of intrusion in one model?
More than one intrusion can be modelled in one 3D model as independent objects. This is showed in case study 1 and will be stated in the text
Current limitations (considered shapes, grid requirements, …)
Limitation of the method are described in the last paragraph of the discussion section
Regarding the minor comments, these will be addressed to improve the quality of the text.
Code evaluation: Yes, the links are links to the examples. We will fix the link to the LoopStructural python library.
Citation: https://doi.org/10.5194/gmd-2022-88-AC1
- Path search algorithm:
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RC2: 'Comment on gmd-2022-88', Italo Goncalves, 29 Jun 2022
The manuscript presents a novel methodology to model the geometry of igneous intrusions. Developments from previous works are employed along an adaptation of the ODSIM algorithm. External knowledge can be inputed through parametric functions.
The first reviewer already made substantial points about the work's structure, clarity, and methodology. My contributions are the following:
Major comments:I believe the authors should try to isolate the strengths, limitations, and benefits of the three main components of the proposed methodology, namely the use of (i) strucural frames, (ii) ODSIM, and (iii) parametric conceptual models. Experiments using (i) and (ii), (i) and (iii), just (i), etc. would be too much work perhaps, but their isolated effects and their contribution to the final result must be measured somehow. It might be that one of the three is completely unnecessary or redundant, at least for the case studies provided.
Please clarify the mathematical notation. It is common to use lowercase for scalars, bold lowercase for vectors, and bold uppercase for matrices.
Section 2.1 - A figure with a conceptual explanation would be interesting. If a 3D example becomes too convoluted, cross-sections or a 2D example can be used.
It is not clear whether the g, p, and l fields are scalar or vector fields. Lines 314-326 present some ambiguity in this regard. The text mentions isovalues, supporting the notion of scalar fields, but it also mentions orthogonality between p and l, suggesting that they are in fact vectors. Do you mean orthogonality between their gradients? If g, p, and l were in fact vector fields, then one would have to interpolate 9 variables instead of 3.
Why use simulations? Wouldn't it be possible to use kriging or RBF (even if you must compute normal scores first) to obtain a "mean" surface?
Section 5.1 and lines 473-477 - For the sake of fairness to RBF, you could employ an elliptical conceptual model in this case as well. It should be simple to define a parametric base field and subtract it from the signed distances data.
Figures 7, 8, 10c, and 10d: please discuss the possible causes for the jagged aspect of the models. I suspect it has to do with the use of simulations.
Lines 555-556: I see it as an advantage, rather than a limitation. User input in this form allows for more flexible and realistic models. It may require extra work and thought, but that is why professionals are trained.
Minor comments:
Figure 3 - do you mean (g, p, l) or g(p, l)?
Figure 4, legend - "The stating points for the search is the shortest path is J_in"; please rephrase
Section 4.2.1 - The gradients of the g, p, and l fields have a constant direction? I assume that this is the case in the presented example, but not a requirement for the methodology to work.
Line 309: "The gradient of this scalar field is a normalized vector parallel to the propagation direction of the intrusion." Does this mean that the field p is linear? Looking at Figure 5 the direction of the gradient appears to be constant, but the slope seems variable (for instance, the green region is thicker than the cyan one). This might be an artifact of the color scale. I recommend the use of visually uniform color maps (Crameri et al., 2020)
Lines 339-344: The text seems to repeat the explanation of lines 350-356 after the equation.
Line 361: What to you mean by a variogram of infinite range? A range larger than the extent of the g, p, l coordinates?
Figure 7, legend: "sills" -> "sill's"; "shows" -> "show"
Line 455: Do you mean Figure 10d?
Figure 11: In the first line, Vb is equal to model volume. It this correct?
Figure 14, legend: "thought" -> "through"
Line 569: "realization" -> "realizations"
Line 576: "restricted" -> "constrained"
References:Crameri, F., Shephard, G. E., & Heron, P. J. (2020). The misuse of colour in science communication. Nature Communications, 11(1), 1–10. https://doi.org/10.1038/s41467-020-19160-7
Citation: https://doi.org/10.5194/gmd-2022-88-RC2 -
AC2: 'Reply on RC2', Fernanda Alvarado-Neves, 22 Jul 2022
Dear Italo,
Thank you for your feedback. Please, see below our response to your comments:
I believe the authors should try to isolate the strengths, limitations, and benefits of the three main components of the proposed methodology, namely the use of (i) strucural frames, (ii) ODSIM, and (iii) parametric conceptual models. Experiments using (i) and (ii), (i) and (iii), just (i), etc. would be too much work perhaps, but their isolated effects and their contribution to the final result must be measured somehow. It might be that one of the three is completely unnecessary or redundant, at least for the case studies provided.
An assessment of the benefits and limitation of each of the three main components (structural frames, ODSIM, and parametric conceptual models) sounds interesting, however we agree that various experiments to isolate their advantages will be outside of the scope of this paper. We propose to discuss the expected effects on removing each of the component and qualitatively assess their contribution to the method.
Please clarify the mathematical notation. It is common to use lowercase for scalars, bold lowercase for vectors, and bold uppercase for matrices.
We will fix the mathematical notation as suggested.
Section 2.1 - A figure with a conceptual explanation would be interesting. If a 3D example becomes too convoluted, cross-sections or a 2D example can be used.
We will include a figure of the ODSIM workflow, and tentatively we will make a figure showing how intrusions frame are incorporated in the ODSIM workflow.
It is not clear whether the g, p, and l fields are scalar or vector fields. Lines 314-326 present some ambiguity in this regard. The text mentions isovalues, supporting the notion of scalar fields, but it also mentions orthogonality between p and l, suggesting that they are in fact vectors. Do you mean orthogonality between their gradients? If g, p, and l were in fact vector fields, then one would have to interpolate 9 variables instead of 3.
g, p, and l are scalar fields and the orthogonality is between their gradients. We will clarify this in the text.
Why use simulations? Wouldn't it be possible to use kriging or RBF (even if you must compute normal scores first) to obtain a "mean" surface?
We will evaluate using exact interpolation methods instead of simulations. We mainly used simulations following the ODSIM proposal, however, our method does not aim to generate several realizations of each model, so using interpolation would probably be a simpler way of computing the distances thresholds along the frame axes.
Section 5.1 and lines 473-477 - For the sake of fairness to RBF, you could employ an elliptical conceptual model in this case as well. It should be simple to define a parametric base field and subtract it from the signed distances data.
Regarding CS3 and its RBF 3D models, the authors will create the 3D models using an elliptical conceptual model to make a fairer comparison.
Figures 7, 8, 10c, and 10d: please discuss the possible causes for the jagged aspect of the models. I suspect it has to do with the use of simulations.
The jagged aspect of the models in Figures 7, 8, and 10 is because of the grid. It will be discussed, and we will run the models with a finer grid for the figures.
Lines 555-556: I see it as an advantage, rather than a limitation. User input in this form allows for more flexible and realistic models. It may require extra work and thought, but that is why professionals are trained.
This is true, thanks for the comment, we will rephrase this part of the discussions.
Regarding the minor comments, these will be addressed to improve the quality text.
Citation: https://doi.org/10.5194/gmd-2022-88-AC2
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AC2: 'Reply on RC2', Fernanda Alvarado-Neves, 22 Jul 2022
Data sets
Case studies 1,2 and 3 datasets and Jupyter notebooks Fernanda Alvarado-Neves, Laurent Ailleres, Lachlan Grose, Sandy Cruden, Robin Armit https://doi.org/10.5281/zenodo.6381034
Model code and software
LoopStructural Lachlan Grose, Laurent Ailleres, Gautier Laurent, Mark Jessel https://doi.org/10.5281/zenodo.6381007
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