A High-Resolution Global Moho Model from Combining Gravimetric and Seismic Data by Using Spectral Combination Methods

Round 1

Reviewer 1 Report

I miss some references when describing  the models (page 2 end first paraghaph. 

The same with regard to the description of methods for combining seismic data and gravities to assess the improvements of the methods exposed by the authors (filter Butt. and spectral combination).

Mistake describing XGM2019 (pg.3) "Moho"

Distorsion in greek letters and sme formulae. ie 5.b

page 8, textcolor 

page 11 cur figures. Bad resolution in one of them 

 

Author Response

Dear Reviewer 

Please see attached word file.

Best regards

Author Response File: Author Response.docx

Reviewer 2 Report

Review for manuscript “A high-resolution global Moho model from combining gravimetric and seismic data using spectral combination methods” by Arash Dashtbazi, Behzad Voosoghi, Mohammad Bagherbandi*, and Robert Tenzer for publication in Remote Sensing (Manuscript ID: remotesensing-2094439)


The manuscript describes and applies methods for combining gravity data with seismic data to improve resolution of global Moho discontinuity maps caused by often sparse seismic data coverage. Gravity data have an inherent non-uniqueness to address this question and the authors perform a correction to the gravity data prior to merging the datasets. Two methods to accomplish merging - butterworth filtering and spectral combination - are presented, which yield highly similar results. The manuscript is well-written, the topic is interesting, and the results presented are promising.


1. However, as a non-expert in this field, I am wondering what is really new in this manuscript compared to other publications. The author group has an extensive record on this type of work and spectral merging methods have been presented several years ago, for example Eshagh et al. 2011 and Bagherbandi 2012. It is not clear from the manuscript what is new and what the improvements are. It seems the input data are ‘new’ in the sense that different gravity (harmonic expansions) and an older version of CRUST were used earlier compared to the current version. Is that really all that is different? Please make a clear case about what is new in manuscript compared to earlier papers; please do so early on (Introduction or similar).

2. The authors present two methods and the results look pretty much the same. No attempt is made to explore whether one approach is superior to the other (or whether that is depending on the dataset(s) used or region investigated). The summary contains a sentence that the spectral combination approach performs better that the Butterworth filtering but that seems to be based on a single, average number from one comparison. I understand that it is not easy to know what works better as the true Moho depth is not known. (I don’t know if one could device synthetic examples with known answers and then try to apply the methods?).

Considering that the two methods perform similarly, why keep showing both of them - without ever talking about their differences. I would thus show both maps in Figure 3 but then show results only for one in the subsequent figures (5, 6, 7, 8, A3 - but leave both in A2) after explaining either why one method is better or that both methods perform equally well.

3. A discussion of the performance is lacking. The authors compare merged HRMC models with regional Moho maps from seismic datasets with higher spatial resolution than CRUST1.0. The two HRMC models are graphically compared with the regional models showing relatively small amounts of differences; overall performance is provided as a table for each region that is compared. What is lacking, for example, is to show that the HRMC models perform better than CRUST1.0 alone (or better than other existing global Moho models - the author group has already older models that performed well, are current models better?). The comparison also completely ignores uncertainties in the regional models. This could be addressed (at least at surficial level) by comparing regional seismic models (such as the two models that contain Northern Europe used in the manuscript — Perhaps comparing [6] and [29] with each other - where they overlap - could be insightful to show variability of seismic models relative to each other.). This could also be addressed by comparing more seismic models relative to each other, a prime example could be the US with the USArray data and several competing Moho maps. The Makran region model used for comparison is perhaps not that well suited as the surfaces waves have only limited vertical sensitivity and combining surface wave data and gravity data may not necessarily result in the best Moho model. Perhaps comparing to models that use receiver functions (Mothagi et al., 2020; Penney et al., 2017) or active source seismics offshore (Kopp et al., 2000) could be useful? Though more models may just show lack of agreement? All of the comparisons are simply showing depths relative to (yet another) Moho model. What do we learn from this?

Without a discussion, what has been found? Merging the two datasets alone is an insufficient reason for a publication as merging had already been introduced. Are the new HRMC models better than CRUST1.0? If not generally, are there regions where this is the case? What are realistic examples where the new model may be useful for other research; text very vaguely describes how a high res Moho may be useful but nothing specific.

The main advantage of the propose merging is to improve the resolution relative to CRUST1.0. But there are no comparisons showing CRUST1.0 performance except for Figure 7. I would expect that a merged model may perform better in regions where CRUST1.0 is largely based on interpolation but performance may be similar where CRUST1.0 is based on relatively dense data. I don’t know if this is available, but the authors should compare CRUST1.0 vs. HRMC model performance for both cases (region with good and with sparse cover for CRUST1.0). That could show that the HRMC models represent an improvement. The comparisons chosen seem somewhat arbitrary but perhaps already follow my suggestion (but not explained). A targeted comparison would also help shape the discussion.

4. Appendix, Figure A2. Perhaps one of the most interesting figures shows that most systematic differences are essentially restricted to the boundaries of continents. Everything else, on the scale shown in the figure, looks close to random. Are these systematic differences real, and if so, what do they mean? Where do they come from (sediments? Inadequate CRUST1.0? Something else?). Why is, usually, west negative and east positive (like along Africa, blue on west, orange on right side)? Please explain. Also, are there other, smaller regions (in oceans or on continents) where differences are systematic (and not random blue-orange-blue-etc)? I would try concentrating on these in a discussion. Like are they real Moho differences or are there other things at play?

Another unexplained issue is the average crustal depth of the HRMC model which are more than twice the thickness of normal oceanic crust. What causes the difference (is it real)? Sediment cover may account for a small part but not for all of the difference. Is this a problem of using the seismic data to calibrate the gravity data but calibration is skewed (because of different composition/density of oceanic lithospheric material compared to continental crust/upper mantle?). The oceanic regions would be one region where seismic data are lacking and other data would perhaps be most useful to increase resolution. Though the results shown here suggest that the approach and/or gravity data cannot accomplish this; please explain.


The manuscript is in no way “worse” than many papers that have been published. What I find lacking is clarity about purpose and lack of a discussion (a method is applied and results are presented).

These are my main concern. I have a long list of other issues that the authors should consider.

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List of other issues:

1. For all tables, please reduce number of (in-)significant digits.

2. For all differences, please say relative to what (A-B or B-A, define A and B). Maps (and captions) mention differences, but be explicit which model is subtracted from which.

3. For all color palettes, use the same palettes when you show both Butterworth and spectral combination models. Otherwise it is impossible to compare results visually.

4. More than 1/5 of references are self-references. That is excessive.

5. Philosophically, why “waste time” with gravity on land for Moho depth (there are many other sources for anomalies and requires proper, unknown choice of spatial filtering, etc.)? On the other hand increased resolution could be relevant for oceanic crust where global seismic data coverage is much worse and concentrated on a small number of places with active source studies or similar - usually at mid ocean ridges and other plate boundaries with few other Moho estimates. The oceanic regions would thus be a natural place to argue for need for improved resolution. However, it seems from Figure 3, that both HRMC models return oceanic Moho depths way in excess of the common ~7 km thick crust. Why are the mean oceanic Moho depths 16 km and 19 km, respectively? Are the larger HRMC values real or within uncertainty or a result of the merging procedure?

6. The abstract reads more like a statement of the problem or an introduction - this is fine for first third of abstract - The results of the study and context, such as whether they agree with other models, should be expanded and the introduction-like part shortened. The abstract as is, is not informative.

7. Filtering and spectral merging depend on the order to which CRUST1.0 is used. In sections 3.2 and 3.3 “M” is given in the equations but the value chosen is not. Neither in 3.2 nor in 3.3.
3.2: choice of M is not given and not explained
3.3: How do you determine where to cut off the seismic model (n = 0, …, M — M selection?)
Perhaps as a test of performance, one could use different values of M to illustrate its effect and to show that the preferred value chosen results in “good results” (define “good”).

8. Validation section, Line A1-A2 in Figure 7: Line A1-A2: What is the purpose of that line considering the blue dots are the data points in [30] and most of A1-A2 is relatively far from the blue dots? If you want to make a line, then follow the blue dots (for example along E coast of Sweden that continues N close to, let’s say, Hammerfest/Norway, perhaps start at blue dot near Bornholm so you have a sea-land transition)! Please do remove current A1-A2! The current comparison in the paragraph “We further compared …” is not really fair.


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Small issues (mainly editorial or minor questions/comments):

Abstract …

- “In regions where low seismic data coverage is irregular, …” — Sounds like “no problem if low coverage as long as it is regular,” you probably don’t mean that? “… where seismic data coverage is low and irregular, …”?
- What do you mean by “relatively reproduce …”?
- What do you mean by “such methods …”? Using gravity to estimate Moho depth?
- What do you mean by “theoretical deficiencies”? [better to say directly what that is “non-uniqueness of gravity inversion” as explained in section 3.2 on page 5.]

1. Introduction …

- remove “the” in front of “geodynamic modelling”
- remove “density” at “detect the Moho density interface”? - while density changes, the seismic data are sensitive to impedance though intrinsically density plays a large role.
- Should “[1]” be removed in line “static model. [14] modified …”?
- Seems references are not called in order: Paragraph starting with “[26]” while [21-25] have not yet been called.
- “[24] applied a similar approach …” The next sentence cannot be understood without already knowing [24]. If important, describe what method they used to assign weights and what you mean by “found a set of flaws …”? This is not clear.
- “… we examines a possibility of combining …”, why “possibility”; the preceding paragraph says this has already been done several times?

2. Materials and Methods …
2.1 Seismic models …

- Is attribution “[31]” correct at end of section 2.1? Should it be “[32]” or cut entirely as the sentence starts with “[32]”?

2.2 XGM2019a …

- Typo; change “Mogo” to “Moho” in third line.
- “negligible” instead of “ignorable”?

2.3 Earth2014 global topography …

- not that crucial but 1 arcmin is ~1.8 km in latitude but not in longitude (except at equator).

3. Methods …

[I am not an expert on gravity and the spectral merging method described here and have very limited insight in the derivations and the validity of the proposed approach]

3.1 VMM method …
3.2 Butterworth filter …

- Correct me if I’m wrong. It seems the purpose of the logarithmic line fitting is to find delta-a and delta-b (equation 9) to correct the VMM harmonic coefficients? This is not immediately clear (to me, at least). For a general readership it would help to explain, in words, what is done and why. Equation is ‘simply’ a way of mixing the two but apparently a correction is needed first, correct?
- Choice of M is not given not explained.

3.3 Spectral combination …

- Question arises why combined model should be better when the gravity model overall has serious differences relative to the seismic model; it adds ‘high frequency’ to the Moho map but there is no way of checking the accuracy/reliability of that?
- How do you determine where to cut off the seismic model (n = 0, …, M — M selection?)

4. Results …
4.1 Global combined high-res Moho depth model …

- First paragraph. VMM model. Why are depth values different here compared to, e.g., Table 1 in Bagherbandi 2012? Mentioning standard deviation for VMM and CRUST1.0 is okay but it has no meaning In terms of ‘accuracy’, it simply shows depth spread in dataset.

- Second paragraph mentions selection of nb and tests of filter order k. What about M (equation 11 and, e.g., 22)? — Also, why 5x5 grid when, nominally, CRUST1.0 is already at 1x1?

- Table 1, RMS of Moho depth differences. Calculated every 5x5 degrees or how? Not clear. Any idea why fit for Fennoscandia and Makran is ’worse’ than for other regions?

- Paragraph 4+5 “The HRCM model …”. (a) A steep line means smoother model, correct? (b) The choice of starting the fit at degree 25 seems arbitrary. (c) The curve, even in log-space is not linear (Figure 1), so why apply a linear fit? What Figure 1 shows, perhaps, is that the 2 curves are offset and a ‘simple shift’ (delta-a) and that is all that is needed to ‘correct’ the VMM harmonic coefficients? Does delta-b even affect results as it is very small? I don’t understand.

- Paragraph 6 “To model a HRCM by using the spectral combination method, …” How would different choices of uncertainties affect your results; both for seismic (10% used) and VMM (are standard errors a good way or do they underestimate true uncertainty?) This could be part of a discussion.

- Paragraph 7 “The HRCM Moho depth …” Why are the mean oceanic Moho depths 16 km and 19 km, respectively? That seems much too large (~7 km is normal?). Is this due to mixing various types of oceanic crust? Still, most of the oceanic crust is considered ‘normal’ and other provinces - flood basalts, extended crust, or similar - are more the exceptions. Very little ‘blue’ in oceans for models b and c in Figure 3, seems implausible? Please explain. All validation models are for continental regions, which means no control for oceanic models. How did you decide what is continental, what is oceanic? Averages are based on what sampling (1x1 degree)? Please add info.

- Figure 3. (a) All figures seem to be of low resolution; I assume this is due to the pdf provided for review and not due to the figures themselves. Perhaps same issue: text for Moho color bar is chopped off (at least for part (a)). (b) Please use same color scheme for all Moho depth maps (a, b, and c), otherwise one cannot compare them visually. Please use same range (min and max values) for display, otherwise one cannot compare visually. (c) The resolution is 1x1 for CRUST1.0, which is based on sparse data (many gaps and model is interpolated heavily), while combined HRCM models have a 5x5 resolution after including the spatially higher-resolution gravity data. That makes little sense to me; the combined models should have higher resolution rather than lower resolution; why is the HRCM model supposedly better? Please explain. (d) Please consider making color palettes that are sensitive to thickness variations, right now Fig 3 a is blue or green and b and c are greenish and orange without much variation within each group. It is okay to hand edit the palette to highlight the variations as the Moho depth distribution is essentially bi-modal while the current color scheme is continuous; please consider this suggestion.

- Paragraph 8. (a) Oceanic crust is thinner along ridges than in basins. Fine, but overall likely too thick? See comment above about oceanic crust thickness. Why does the oceanic crust become thicker in the HRMC models away from the ridge? Clear why lithosphere thickness grows with age, but why should crust; is all of this due to sedimentation? (b) From Figure 3 I cannot see the maxima as everything is orange. Since the HRCM model is a mix, it is not surprising that it matches the (longer wavelength) CRUST1.0 thicknesses. (See earlier comment about color palette and its importance to make a visual point).

- Figure 4. The lithospheric age map is ‘nice’ but what is the purpose? Perhaps you could show a correlation of oceanic lithosphere age and thickness of the crust? As is, little information that is not, more or less, generally known.

4.2 Validation …

- Paragraph 1. Here you mention how the HRCM model was resampled. Please do this the first time you show the HRMC models or results if the same resampling was used everywhere (when making comparisons).

- Paragraph 2. Perhaps comparing [6] and [29] with each other - where they overlap - could be insightful to show variability of seismic models relative to each other. This could be compared to the differences between the HRCM model and the seismic models from different regions (Table 2), like are RMS values similar? I suspect they are.

- Table 2. (a) All “Min” values should be negative, please correct “23.15” to “-23.15” (b) While such comparisons are ‘good’, I wonder whether Max and Min are very useful if they are localized outliers. Probably too much, but for one comparison, you could show the depth difference distribution?

- “In the Supplementary Materials …” (a) “HRMD models”? Do you mean “HRCM”? (b) Figure A2 shows that differences are large at the transition from continental to oceanic, which is perhaps a problem due to 1x1 degree gridding? See below “As seen …”

- Table 3. (a) The %-differences could be given as integers (86% instead of 85.86%). No need for more, I think. (b) Interesting comparison, seems the HRCM spectral model has more ‘problems’ with the US than the Butterworth HRCM model (86% vs. 98% within 5 km). Why is that?

- “As seen in Figs. 5 and 6, large Moho depth differences …’ - margins and polar areas … okay … so which one is ‘better’ CRUST1.0 or one of the HRCM models? And why? Otherwise this is just some sophisticated math exercise. — Caption: Either “Moho depth of the HRCM model … with respect to …” or “Moho depth differences between the HRCM model … and the Eurasian Moho model”; please say how difference is calculated, like HRCM-Eurasian_model or Eurasian_model-HRCM … to see what the positive and negative differences mean. — Again, I’m not sure about the choice of the color palette for Figures 5 and 6 (and they differ in each case between a and b - please use one palette for Fig. 5 and one for Fig. 6 but not 4 different ones). For example, a 5 km difference is red, so is a 35 km difference; please use a palette where differences are easy to spot [for example, if there are only a few large outliers, you could make a palette from -15 to +15 km and make all >15 white and all <-15 gray] — Why is there a stripe at 0 longitude?

- “We validate our HRCM models …” (a) The sentence “We also identified …” is redundant and should be cut. (b) What do you mean by “Our results indicate that the Moho is deeper under the Gulf of Bothnia”? Deeper than what? If relative to reference [30], then you would need to show a comparison for that area (which you are not doing).

- (A) Figure 7, per figure legend (c) and (e) are for Butterworth, (d) and (f) are for Spectral Combination. Please change caption accordingly. (B) X axis in (c) and (d) is Latitude (not Long) (C) Why do the point wise depths scatter that much, are there some data points (green) for the same latitude (D) In (a) and (b), the blue dots simply show the points with Moho depth from reference [30]? I don’t understand the point of (a) and (b), both methods provide essentially the same results.

- “We further compared … Makran …” (a) as said above, the Makran seismic model is perhaps not that well constrained. I am sure the seismic model does not really have good cover over the region shown in Figure 8. This comparison is pretty much meaningless. What is the point of this figure?

- “Finally, …” Same as for Makran: What is the point of the comparison and what are the results, what model is better, where and why? As is, simply compares two models without evaluation or interpretation. AS said above, there are many high resolution studies available in the US for Moho depth but their results are not 100% in sync, which one to use?
 
5. Summary and concluding remarks …

- (a) “CRUST1.0 … limited resolution … in large parts of the world …. Global gravitational models … homogeneous information … spatial resolution … high”. To make that point, you have to compare the HRMC model(s) and CRUST1.0 with a few regions where high-resolution Moho information exists. Then you would formally compare how well HRMC and how well CRUST1.0 predict the high-res Moho. Crucial would be - and that may be difficult - to find a region where a high-res Moho exists but CRUST1.0 is based on (different) sparse data or no data; these are the regions where the HRMC model(s) might be better than CRUST 1.0. For other regions, HRMC may have shorter wavelengths included but may not necessarily be better (You have to show that they are better at short wavelengths, otherwise what is the point of the manuscript?!]

- Paragraphs 1 and 2 of summary section are general summaries of what has already been said but does not add anything. A repeat of earlier statements/assertions. What is missing are pointers to results from this study that substantiate these claims.

- “The gravimetric … not unique …” Because it is a potential field. It is always non-unique unless additional constraints are applied or assumptions are made.

- Two methods presented. Yes, but what have we learned? Are both equally good or is one better than the other? Would that depend on something (what would that be)? The models have simply been derived (and that had been done previously) but we don’t know anything more than before? “The combination … further reduced additional errors in the long-wavelength Moho geometry …”: Where do you show this? This is not shown, but is asserted.

- Okay, here is a statement about performance of the two methods relative to each other - preference for spectral combination over Butterworth. For each validation test, would be nice to also compare with CRUST1.0 to show/see whether the HRMC models are actually better than CRUST1.0. Otherwise no point in doing the HRMC models.

- “The absence of low and irregular seismic data …” (a) but one of the main advantages supposedly is that gravity data can fill the gaps and provide high-resolution when seismic data are missing? If you need seismic data to make a better model, why not directly use the seismic model? Or else, what is the advantage of the joint gravity and seismic data? This is a bit contradictory?

- “Such large errors …” — This is the last paragraph of the manuscript. Everything in these last sentences should be adequately introduced and discussed. For example, point to the sediment deposits and explain what the problem is and which model does a better job (or what is needed to improve a model). For example, explain what you mean by rigidity variations and where does that show up? What do you mean by “substantial improvements of the results …”, how do you know they are improvements, how have you shown this, what is the evidence?


Data availability statement: At least the models should be made public (could be as an electronic supplement or a link to a web page like zenodo where model(s) could be stored). The authors argue about potential uses for the combined model. The model can only be used if being made available. It therefore seems logical to make it openly and easily available. - Perhaps too much, but data and codes could also be deposited at zenodo for general, open access.


Appendix.

Figure A1. The differences are mainly on continents [but not in Australia, Russia and Europe, and northern America]. Why is that? They look like random + and - differences. Agreed though that the differences overall are small.

Figure A2. Perhaps one of the most interesting figures showing that the systematic differences are essentially restricted to the boundaries of continents. Everything else, on that scale, looks close to random. Are these systematic differences real, and if so, what do they mean? Where do the come from (sediments? Inadequate CRUST1.0, …). Why, usually, west negative and east positive (like along Africa, blue on west, orange on right side). Please explain. — Are there other regions where differences are systematic (and not random blue-orange-blue-etc)? I would try concentrating on these in a discussion. Like are they real Moho differences or are there other things at play?.

Figure A3. The differences in the central US are pretty large. Why is that? The region shown goes from  California in the SW corner to Michigan in the NE corner, I don’t think that region is eastern U.S.

Author Response

Dear Reviewer 

Please see attached word file.

Best regards

Author Response File: Author Response.docx