New Advances of the Multiscale Approach for the Analyses of InSAR Ground Measurements: The Yellowstone Caldera Case-Study
Round 1
Reviewer 1 Report
Dear Authors
The proposed paper has its scientific soundness, mainly as regard the sections describing the different methods and their integration in the multiscale approach, and its application to synthetic/real deformation patterns
Anyway, the focus of the paper is not very clear to me.
The proposed approach models, among other things, the ground deformations, using the InSAR measurements as a constraint only in the third case. I understand what you mean with the sentence "for modeling InSAR measurement" in the title, but, in this form, this could lead to misunderstanding.
In other words, you are deepening the integrated multiscale approach for modeling relatively complex volcanic scenarios, but you are using SAR displacements/velocities just in one case study, which is not the real core of the paper. The main issue seems to be related with the potentialities of the proposed approach, and not the modeling of SAR measurements.
In the light of this, I suggest to review the the structure of the paper to better match what you state in the title, or better focus what you want to show with this research.
Also some minor changes are required in Fig. 3 (a-b-c-d-f), where you should add ticks near the coordinate labels or a grid to make more clear the extension of the area.
Author Response
Comment
Dear Authors,
The proposed paper has its scientific soundness, mainly as regard the sections describing the different methods and their integration in the multiscale approach, and its application to synthetic/real deformation patterns. Anyway, the focus of the paper is not very clear to me. The proposed approach models, among other things, the ground deformations, using the InSAR measurements as a constraint only in the third case. I understand what you mean with the sentence "for modeling InSAR measurement" in the title, but, in this form, this could lead to misunderstanding. In other words, you are deepening the integrated multiscale approach for modeling relatively complex volcanic scenarios, but you are using SAR displacements/velocities just in one case study, which is not the real core of the paper. The main issue seems to be related with the potentialities of the proposed approach, and not the modeling of SAR measurements. In the light of this, I suggest to review the structure of the paper to better match what you state in the title, or better focus what you want to show with this research.
Reply
We thank the reviewer for her/his interesting analysis concerning our submitted paper. To better highlight which are the main issues of our proposed research, we have applied several changes in the main text: a new title has been conceived that is more apt to describe the matter of the work (lines 2-4); we have added some sentences in the Abstract at lines 10-14 and in the Introduction at lines 55-60; in the Materials and Methods a new structure has been proposed and other subparagraphs have been considered; we have reported in different Results subparagraphs the integrated multiscale application to simulated and real deformation patterns; some sentences have been added also to Discussion and Conclusions section (lines 381-385). Accordingly, the revised version of the paper has now a focus that is more shifted from the modeling of the InSAR measurements to the presentation/discussion of multi-scale approach potentialities, already presented in previous works and here further improved. Finally, we want to specify that the Materials and Methods section has been improved with some new parts (text, equations, figures, and tables) to take into account the Reviewer #2’s suggestions.
Comment
Minor Comment
Also some minor changes are required in Fig. 3 (a-b-c-d-f), where you should add ticks near the coordinate labels or a grid to make more clear the extension of the area.
Reply
We want to thank the reviewer for this observation. We added clear ticks in all the maps reported in this figure, which is renamed as Figure 2 in the new version of the submitted manuscript.
Reviewer 2 Report
The study presents a method based on Euler deconvolution used in potential field geophysics to infer the shapes of sources, but applied to InSAR deformation data of Yellowstone caldera. The method has been widely used in exploration geophysics but its use in volcano geodesy is very new. I am not an expert on potential field geophysics so I only reviewed the sections pertinent to my expertise which is InSAR and volcano geodesy. In general the paper is well written and structured, so I recommend minor revisions aside from the detail analysis of the multiscale approach.
Line 19: the episode of uplift lasted from 2004 to 2009, not 2005-2007
Line 37: true that models are based on linear elasticity
Lime 46-47: the big problem is that for volcano deformation a priori information does not exist, except from inferring the shape of the deformation source with a regular shaped model (Okada, Mogi, Yang, etc).
Lines 48-63: the authors should state that they are using techniques similar to an Euler deconvolution that were developed inferring the shape of sources that can explain potential field data like gravity and magnetics
Line 73-74: It’s better to state that there is no need to assume the elastic parameters of the medium, which have to be assumed for the use of a Yang/Okada model.
Lines 97-98: the Yellowstone source models are indeed different but they are not conflicting in the sense that all of them identify a source below the resurgent domes (regardless of its shape) and another source below the Norris Geyser basin. The implications of all these models are the same because they require in one way or the order the transport of fluids across the caldera.
L 235-238: State that track 48 is from the IM1 and has much fewer acquisitions than tracks 320 IM2, and track 41 is from the IM2 beam. If track 48 has fewer data than track 320, why did you choose it?
L 239-261: this section lacks a lot of detail on how the interferograms were processed, filtered, unwrapped, chosen for time series and so on. For example, the time series in figure 3 is heavily filtered but the authors do not explain why. I’d think that the lowpassed the data to remove uncorrected atmospheric phase delays. So the authors should expand this and also show the chosen interferograms because a strict SBAS processing is not possible at Yellowstone. THis is due to the large temporal and spatial baselines of SLCs that result in cobherent interferograms.
L256-261: what is the point of simulating the displacement of the North America plate. Is it much simpler just to remove a ramp to every interferogram to reference them to a stable non-defirming area?
L 268: describe the signals observed in the time series and ground deformation maps. This is in section 3.2 but should be moved upwards.
Line 345: typo “Both orbits…”
Line 347: the caldera uplift is highly non-linear, so is this rate representative of the full episode of uplift or of just a single year period?
Line 354: note that Delgado and Grandin 2021 obtained ~25 cm, 5 cm more than the authors because the former used data from ascending track 320 IM2 which does sustain the coherence atop the SC dome during the whole episode of uplift.
L 403: typo “objective way of the source ”
L 473: there is no need to confirm that a single source can explain the deformation below the caldera. This has been known since the study of Chang et al., 2007.
L 516: I think active is the wrong term. Try something like “the areas of maximum uplift”.
L522: it could also be that the magma flux is stronger below SC instead of it being the most active area just because it is shallower.
L 524: provided that the source is not a monopole as in Line 77.
Figure 3: panel e). The time series are heavily filtered. This is fine, but it should be stated somewhere in the main text.
Figure 5. Add the outline of the sill geometry of either Chang et al., 2007,2010 and/or Delgado and Grandin 2021 for visual comparison.
Author Response
Comment
The study presents a method based on Euler deconvolution used in potential field geophysics to infer the shapes of sources, but applied to InSAR deformation data of Yellowstone caldera. The method has been widely used in exploration geophysics but its use in volcano geodesy is very new. I am not an expert on potential field geophysics so I only reviewed the sections pertinent to my expertise, which is InSAR and volcano geodesy. In general, the paper is well written and structured, so I recommend minor revisions aside from the detail analysis of the multiscale approach.
Reply
We thank the reviewer for her/his positive comments. To meet the relevant observations, we improved the Materials and Methods section by adding some new parts (text and equations highlighted in yellow, Figure 1 and Table 1). We expect that these additional details could allow for a better understanding of the proposed/adopted methodology.
Comment
Line 19: the episode of uplift lasted from 2004 to 2009, not 2005-2007
Reply
Corrected.
Comment
Line 37: true that models are based on linear elasticity
Reply
Done.
Comment
Lime 46-47: the big problem is that for volcano deformation a priori information does not exist, except from inferring the shape of the deformation source with a regular shaped model (Okada, Mogi, Yang, etc).
Reply
We want to thank the reviewer for this observation. We would like to clarify that with “a priori information” we refer not only to the shape of the deformation source but also to any model parameter that is inferred by the operator during the inverse procedures.
Comment
Lines 48-63: the authors should state that they are using techniques similar to a Euler deconvolution that were developed inferring the shape of sources that can explain potential field data like gravity and magnetics.
Reply
We modified this sentence in the revised main text by adding this statement at lines 44-45.
Comment
Line 73-74: It’s better to state that there is no need to assume the elastic parameters of the medium, which have to be assumed for the use of a Yang/Okada model.
Reply
We applied some changes at lines 60-67 to integrate the main text with the proposed suggestion.
Comment
Lines 97-98: the Yellowstone source models are indeed different but they are not conflicting in the sense that all of them identify a source below the resurgent domes (regardless of its shape) and another source below the Norris Geyser basin. The implications of all these models are the same because they require in one way or the order the transport of fluids across the caldera.
Reply
We agree with the reviewer. Accordingly, we rephrased the sentence as at lines 80-82.
Comment
L 235-238: State that track 48 is from the IM1 and has much fewer acquisitions than tracks 320 IM2, and track 41 is from the IM2 beam. If track 48 has fewer data than track 320, why did you choose it?
Reply
We thank the reviewer for this observation. Our choice was mostly dictated by the need to have a balanced number of SAR images in the ascending and descending SAR tracks from to avoid/reduce undesired unbalancing effects when the system of equations representing the LOS-projected time-series are combined to recover the 2-D ground displacement time-series, see [53,54]. This part of the work is intended as a sort of further investigation of the work shown in Tizzani et al. (2015). So, we took that data track (descending, 27 images) results as they were and searched for a “freely-available” set of ascending SAR data consisting with a balanced number of SAR data (32 images). Eventually, the discriminated Up-Down and East-West ground displacement time-series were produced with a consistent/suitable and rather regular time sampling with 59 acquisitions. Of course, we agree with the reviewer that alternative solutions such as the joint processing of several independent SAR data tracks could possibly have been adopted, but we followed such a strategy. We hope that the reviewer could be understood our point of view.
Comment
L 239-261: this section lacks a lot of detail on how the interferograms were processed, filtered, unwrapped, chosen for time series and so on. For example, the time series in figure 3 is heavily filtered but the authors do not explain why. I’d think that the lowpassed the data to remove uncorrected atmospheric phase delays. So the authors should expand this and also show the chosen interferograms because a strict SBAS processing is not possible at Yellowstone. This is due to the large temporal and spatial baselines of SLCs that result in cobherent interferograms.
Reply
We thank the reviewer for this valuable comment. In the revised manuscript, some additional details on the InSAR processing of the available datasets have been included for the readers’ sake of convenience. We would like to stress that the generation of the ground displacement time-series for the descending data track was already addressed in a previous publication. Here, as stated before, the focus has been more on the generation of the “decomposed” East-West and Up-Down ground displacement time-series than the generation of the SBAS-driven LOS-projected ground displacement time-series. Accordingly, just for this reason, we initially did not put in the text several details on the processing. However, now, following the reviewer’s suggestion, we have included more details in the revised manuscript (see lines 233-305).
We would like to stress that in our work we did not simply apply a strict/regular SBAS processing on the selected SAR datasets. First, the multi-look interferograms were generated after applying the space-time noise-filtering method, known as Enhanced Multi-Temporal InSAR (E-MTInSAR) Noise-Filtering Algorithm and fully detailed in the relevant publications [49]. Such a method can allow to reduce the impact of the decorrelation artifacts in sequences of multi-temporal SAR interferograms by jointly using all information coming from multiple sets of multi-look interferograms. It has been applied in several context and it is also integrated in the EMCF-SBAS processing chain developed for the processing of Sentinel-1 data, see [49-51].
Subsequently, we would like to clarify that the 2-D ground displacement time-series were generated in correspondence to locations were both ascending and descending LOS-projected time-series were correctly obtained by applying the post-processing method, known in the literature as Minimum Acceleration combination (MinA) method, which is fully detailed in the references [54-55]. Accordingly, the presented results are not simply the products, in the Line-of-Sight direction, that usually can be obtained by applying the SBAS algorithm (or similar short-baseline methods) to sequences of SAR data. In particular, the MinA method was applied to the sets of LOS-projected time-series to recover the East-West and Up-Down ground displacement time-series. This method, similarly to other alternative ones (such as the M-SBAS method), relies on the solution of a regularized system of linear equations where regularizations is weighted through a coefficient. The optimal value of this parameter is usually obtained by considering an L-curve method of optimization, and its application leads to the effect that has been observed by the reviewer. Such an effect is expected and can be emphasized/de-emphasized using different values of the mentioned coefficient. The selected value is suitable considering the good fit between the available GPS measurements and the reconstructed Up-Down and East-West ground displacement time-series. Of course, different values of that coefficient could be used to reduce the effect of “heavy” filtering but this was not intentionally done, because we wanted to exclude the possibility to introduce in the analysis of the obtained 2-D maps spurious (time) high-frequency signals related to uncompensated APS and/or other noise sources. Interested readers can refer to [54-55] to have additional clarifications on the applied multi-platform MinA method. See also the revised paragraph 2.8 of the submitted manuscript.
Comment
L256-261: what is the point of simulating the displacement of the North America plate. Is it much simpler just to remove a ramp to every interferogram to reference them to a stable non-deforming area?
Reply
We agree with the reviewer that a simpler solution could have been to remove a ramp from every interferogram but also orbital artefacts are correlated with ramps. Note also that this present work has to be seen as a further investigation following the work presented in Tizzani et al. (2015) and for one orbit the same LOS-projected SBAS-driven results were used. So, we adopted the same strategy to recover and compensate for the high spatial-frequency displacements of the North American Plate in the generated ground displacement maps.
Comment
L 268: describe the signals observed in the time series and ground deformation maps. This is in section 3.2 but should be moved upwards.
Reply
We would like to thank the reviewer for this valuable suggestion. Accordingly, we moved the subparagraph 3.2 in the Materials and Methods sections.
Comment
Line 345: typo “Both orbits…”
Reply
Done.
Comment
Line 347: the caldera uplift is highly non-linear, so is this rate representative of the full episode of uplift or of just a single year period?
Reply
We thank the reviewer for this interesting observation. We selected, in the framework of the same uplift event (i.e., 2004-2009), the time interval characterized by the greatest rate of deformation, which occurred during the 2005 – 2007 temporal period. In this way, the selected rate distinguishes itself also for the high signal-to-noise ratio and, since it falls within the 2004 – 2009 uplift episode without any greater deformation rate variations in the framework of the same event, the selected rate can be considered representative of the observed fluid/magma injection phenomenon.
Comment
Line 354: note that Delgado and Grandin 2021 obtained ~25 cm, 5 cm more than the authors because the former used data from ascending track 320 IM2 which does sustain the coherence atop the SC dome during the whole episode of uplift.
Reply
We thank the reviewer for this comment. We want to clarify that in our paper we do not refer to strictly-speaking LOS-projected maps obtained from the analysis of single interferograms, but we discriminated and analyzed the vertical and East-West ground displacement time-series in correspondence to location of points that were seen coherent (and well processed) by both ascending and descending orbits. The MinA method has the advantage to increase the temporal sampling of the observations because the 2-D time-series are available on the whole set of ascending+descending time acquisition and can further reduce the impact of decorrelation noise and APS with respect to single interferograms. On the other hand, the number of well processed points could be reduced with respect to the analysis of single interferograms and/or single data tracks. Besides, suitably large values of the temporal coherence threshold (i.e., 0.6) have been considered to have sounder results at the expenses of a more reduced spatial coverage of the analysis. The direct comparison between the LOS-projected measurements shown for instance in Delgado and Grandin 2021 and the vertical displacement values shown in our work can be misleading. Indeed, here, we refer to 20 cm of uplift along the vertical direction (i.e., vertical component of the ground deformation field), while Delgado and Grandin 2021 have highlighted 25 cm of deformation along the satellite Line Of Sight directions. We applied some changes to the text at line 301-302 to avoid this misunderstanding for the readers.
Comment
L 403: typo “objective way of the source”
Reply
Done.
Comment
L 473: there is no need to confirm that a single source can explain the deformation below the caldera. This has been known since the study of Chang et al., 2007.
Reply
We thank the reviewer for this clarification about the number of sources at Yellowstone caldera. We specify that, although there is no need to confirm the presence of a single source from a volcanic point of view, several authors, after the work of Chang et al. (2007), have instead highlighted the presence of two sources from a geodetic point of view. However, we have made some changes in this sentence (lines 445-446).
Comment
L 516: I think active is the wrong term. Try something like “the areas of maximum uplift”.
Reply
Done.
Comment
L522: it could also be that the magma flux is stronger below SC instead of it being the most active area just because it is shallower.
Reply
We thank the reviewer for this comment; however, our work cannot prove this hypothesis.
Comment
L 524: provided that the source is not a monopole as in Line 77.
Reply
We specify that your highlighted aspect is already reported at lines 396-398 of the same paragraph, i.e., Discussion and Conclusion, therefore, we have avoided to repeat it again in the framework of the same section and of general conclusive sentences.
Comment
Figure 3: panel e). The time series are heavily filtered. This is fine, but it should be stated somewhere in the main text.
Reply
We added some new sentences in the main text also according to your previous comment.
Comment
Figure 5. Add the outline of the sill geometry of either Chang et al., 2007,2010 and/or Delgado and Grandin 2021 for visual comparison.
Reply
We integrated Figure 5 (that is renamed Figure 6 in the new version of the manuscript) with the sill geometry of Delgado and Grandin (2021).
Reviewer 3 Report
Comments on the paper
Integrated Multiscale Approach for Modeling InSAR Measurements at Yellowstone Caldera
By Andrea Barone, Antonio Pepe, Pietro Tizzani, Maurizio Fedi and Raffaele Castaldo
The paper is devoted to a highly specialized audience, as it addresses the comparison – or integration – between different mathematical approaches to the “inversion problem” in volcanic areas. Volcanic areas are characterized by large spatial gradients and – in addition - by conspicuous eventual changes in time, related to volcanic activity.
I am not a specialist in these specific computational items, mostly concerned with mathematical procedures.
From a physical viewpoint, the most important observational matter-of-fact is the deformation of the surface as it is monitored by satellite monitoring (SAR technique) that detects line-of-sight deformation – to be eventually separated in vertical deformation and horizontal displacement.
Other information can be given by profiles carried out by active seismometry, or by magnetic or MT surveys that, in any case, apply to linear sections of the area of investigation and can hardly provide with detailed 2D mapping.
In addition, these additional monitoring techniques can hardly monitor the time changes of structures, as they require an intrinsic long time for operation.
A more effective analysis can be performed by means of the GRACE satellites – that seem not to be considered in the present paper. This is not - however – a criticism.
The next step is to envisage a “reasonable” source underground to be associated (by any mean) with every observed effect. This is the classical “inversion problem” that, per se, has not a unique solution. A solution can be inferred upon considering reasonable assumptions that, is some way, are related to principles of mathematical simplicity.
Several algorithms were therefore proposed in the literature, and all of them give a solution, while different methods provide results that in some way resemble each other, although – in general – with some large discrepancies that depend on the arbitrary assumptions of every algorithm.
It is important to implement joint methods that, in some way, take into account the assumptions of different algorithms, and in this way optimize the result by reducing the discrepancy implied by different “reasonable” approaches.
There is nothing “magic”, however, as the inversion problem is intrinsically indeterminate. However, these improved algorithms are a step forward in the search for a better “reasonable” modeling of the underground ongoing processes.
This paper is a proposal in this direction.
I have no adequate background in this special computational area in order to express any appreciation or criticism of the mathematical algorithms. Only a restricted set of insiders can express a competent evaluation. I would not be honest to express any judgement on something that I cannot fully understand.
My approach, as a geophysicists, is to accept the results and consider how they can fit into some general model on the origin of volcanism, etc.
In this respect, I guess that the best judgment on the effectiveness of the method that is proposed by this paper will be possible when it will be eventually applied to several volcanoes and to repeated epochs on every volcanic area. I mean that all indeterminacies and arbitrariness that are implicit in every method can find support by how reasonable are the inferences derived in different case histories.
Owing to these reasons, I cannot compare my evaluation with the review made by a specialist of the restricted set of insiders.
To my understanding, the paper is well written, even though – according to my feeling – it is biased by the “fashion “ of journals that require short papers. In general, I prefer to read a smaller number of long papers than a set of short papers. The communication between interdisciplinary experts suffers by this “fashion”, because only insiders of selected ensembles of specialists can talk with each other. This is a bias for the development of understanding.
As a practical personal suggestion, I like to see - at the end of every paper - a list of acronyms, as this may help the non-specialist reader the get a better understanding. However, this is only a personal feeling.
As far as I can understand, the paper can be published as it is.
It is obvious that everything can always be improved. However, the scientific progress occurs through an effective exchange of ideas. Communication is fundamental for the scientific debate, and discussion – and discussion and eventual controversies are the true seeds for the progress of science.
Author Response
Comment
The paper is devoted to a highly specialized audience, as it addresses the comparison – or integration – between different mathematical approaches to the “inversion problem” in volcanic areas. Volcanic areas are characterized by large spatial gradients and – in addition - by conspicuous eventual changes in time, related to volcanic activity. I am not a specialist in these specific computational items, mostly concerned with mathematical procedures. From a physical viewpoint, the most important observational matter-of-fact is the deformation of the surface as it is monitored by satellite monitoring (SAR technique) that detects line-of-sight deformation – to be eventually separated in vertical deformation and horizontal displacement. Other information can be given by profiles carried out by active seismometry, or by magnetic or MT surveys that, in any case, apply to linear sections of the area of investigation and can hardly provide with detailed 2D mapping. In addition, these additional monitoring techniques can hardly monitor the time changes of structures, as they require an intrinsic long time for operation. A more effective analysis can be performed by means of the GRACE satellites – that seem not to be considered in the present paper. This is not - however – a criticism. The next step is to envisage a “reasonable” source underground to be associated (by any mean) with every observed effect. This is the classical “inversion problem” that, per se, has not a unique solution. A solution can be inferred upon considering reasonable assumptions that, is some way, are related to principles of mathematical simplicity. Several algorithms were therefore proposed in the literature, and all of them give a solution, while different methods provide results that in some way resemble each other, although – in general – with some large discrepancies that depend on the arbitrary assumptions of every algorithm. It is important to implement joint methods that, in some way, take into account the assumptions of different algorithms, and in this way optimize the result by reducing the discrepancy implied by different “reasonable” approaches. There is nothing “magic”, however, as the inversion problem is intrinsically indeterminate. However, these improved algorithms are a step forward in the search for a better “reasonable” modeling of the underground ongoing processes. This paper is a proposal in this direction.
I have no adequate background in this special computational area in order to express any appreciation or criticism of the mathematical algorithms. Only a restricted set of insiders can express a competent evaluation. I would not be honest to express any judgement on something that I cannot fully understand. My approach, as a geophysicists, is to accept the results and consider how they can fit into some general model on the origin of volcanism, etc. In this respect, I guess that the best judgment on the effectiveness of the method that is proposed by this paper will be possible when it will be eventually applied to several volcanoes and to repeated epochs on every volcanic area. I mean that all indeterminacies and arbitrariness that are implicit in every method can find support by how reasonable are the inferences derived in different case histories.
Reply
We thank you for this positive comment about the submitted paper and its significance in the framework of the modeling of volcanic deformation sources. We want only to specify that the methodology has been already applied to other simulated and real deformation patterns (Castaldo et al., 2018; Barone et al., 2019; Pepe et al., 2019; Barone et al., 2022) and that we are just working on the use of the integrated multiscale approach to evaluate the temporal evolution of the volcanic deformation sources as suggested by you.
Comment
Owing to these reasons, I cannot compare my evaluation with the review made by a specialist of the restricted set of insiders. To my understanding, the paper is well written, even though – according to my feeling – it is biased by the “fashion “ of journals that require short papers. In general, I prefer to read a smaller number of long papers than a set of short papers. The communication between interdisciplinary experts suffers by this “fashion”, because only insiders of selected ensembles of specialists can talk with each other. This is a bias for the development of understanding. As a practical personal suggestion, I like to see - at the end of every paper - a list of acronyms, as this may help the non-specialist reader the get a better understanding. However, this is only a personal feeling. As far as I can understand, the paper can be published as it is. It is obvious that everything can always be improved. However, the scientific progress occurs through an effective exchange of ideas. Communication is fundamental for the scientific debate, and discussion – and discussion and eventual controversies are the true seeds for the progress of science.
Reply
Thank you for this observation, we have extended some sections of the submitted paper in order to meet your point of view. In particular, we have mostly improved the Materials and Methods section by adding text and equations highlighted in yellow, Figure 1 and Table 1.
Round 2
Reviewer 1 Report
Dear authors.
The manuscript has been sufficiently improved and can be accepted n the present form.
