Improved IDW Interpolation Application Using 3D Search Neighborhoods: Borehole Data-Based Seismic Liquefaction Hazard Assessment and Mapping

Round 1

Reviewer 1 Report

The study is very meaningful that it extends IDW interpolation method for 2D to 3D Space.

It is very remarkable the study suggests new method to 3D neighbor searching technique and develop algorithm for it so I would recommend to making up for the below for it be more clarify the study.

 

For section 2.3.1,

It should be more specifically explained the relation between 9IM and 3D search neighborhoods technique.

The study presents clear reasons why it applies B-rep and 9IM whereas it insufficiently explains the relation between 9IM and 3D search neighborhoods. Especially, It should be explained more about “within3D” relationship.

 

For section 3.3.1,

More detailed explanation has to be added for it is why proposed approach to IDW divides to 'Fixed distance' and 'Number of points' and feature of each method when it applied to. It will be easier to understand all concepts if additional explanations why it has to be divided into two approaches.

Author Response

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Reviewer 2 Report

The study proposed an interpolation method for observation data collected in 3D, such as altitude, depth, or water level, and as an example, it showed the results of the seismic liquefaction hazard assessment and mapping using the borehole data. As a result, the study showed that the interpolation of 3D observation data was possible through the integration of IDW, the most widely used interpolation method, and the B-rep-based topological relationship in 3D GIS. Such an approach is advantageous in the interpolation and visualization of various data observed in the real world and can contribute to the expansion of 3D GIS applications.

In the reviewer's opinion, the article is interesting and the manuscript is worthy of publication.

Here are some minor suggestions for the author to modify：

1.Figure 2 pictures are not high quality, (a) (b) and other subheadings are blurred.

2.There are two Figure 3 in the manuscript, please revise.

3.Figure 5 font is too small, need to adjust the font size before publication.

4.The format of the references is not correct, and the format and order of the references need to be adjusted according to the requirements of the journal.

5. The following literature is suggested to be added to section 1.2.1 of the manuscript

Li Q., Jia H. T., Qiu Q., Lu Y. Z., Zhang J., Mao J.H., Fan W. J., Huang M. F. Typhoon-induced fragility analysis of transmission towers in Ningbo area considering the effects of long-term corrosion. Applied Sciences, 2022, 12, 9, 4774.

 

Author Response

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Reviewer 3 Report

The paper presents an improved IDW interpolation workflow by combining GIS software to implement 3D search neighborhoods, and applies the workflow to hazard assessment in civil engineering. The approach and application are clearly presented, and it is a pleasure to read the manuscript.

 

Though IDW has been a traditional and well-studied approach for spatial interpolation, it’s still worth it to discuss how it can be improved for various applications and contexts. However, a more thorough literature review is needed, and the proposed approach/workflow should be improved further to be applicable and should be compared with a base method to be more convincing. Therefore, I recommend publication if the followings are addressed:

 

1.     Section 1.2 (literature review) should be extended. 3D IDW and 3D search neighborhoods aren’t new. Though for many geographical applications, 2D interpolation is the most popular, 3D interpolation has been widely studied and applied in fields such as geology (mining, petroleum), civil engineering, medical imaging, and computer graphics. These are the most active fields that study and use 3D interpolation. 3D search neighborhood (or 3D search ellipsoid) has also been studied extensively in geostatistics. I recommend acknowledging their efforts for a comprehensive introduction (see literature recommendations below). The authors should also properly address the difference between IDW and Kriging. In Section 1.2.1, the authors mention that “The biggest difference between IDW and Kriging …Kriging is an extrapolation method..”, with which I disagree. It’s true that Kriging considers spatial correlation, but Kriging is not an “extrapolation” approach. The biggest difference between IDW and Kriging is that Kriging is a geostatistical approach and provides an estimation of uncertainty with the Kriging variance, while IDW is a deterministic approach. 

 

Here are a few relevant references: 

 

Here is another recent study on improving IDW for 3D interpolation:

 

Liu, Z., Zhang, Z., Zhou, C., Ming, W. and Du, Z., 2021. An adaptive inverse-distance weighting interpolation method considering spatial differentiation in 3D geological modeling. Geosciences, 11(2), p.51.

 

Here is a paper that utilizes 3D IDW as part of its 3D geological modeling workflow with borehole data:

 

Yang, L., Achtziger-Zupančič, P. & Caers, J. 3D Modeling of Large-Scale Geological Structures by Linear Combinations of Implicit Functions: Application to a Large Banded Iron Formation. Nat Resour Res 30, 3139–3163 (2021).

 

Here are two book references from geostatistics for 3D search neighborhoods, and 3D (co-)Kriging methods:

 

Chiles, J.P. and Delfiner, P., 2009. Geostatistics: modeling spatial uncertainty (Vol. 497). John Wiley & Sons.

 

Remy, N., Boucher, A. and Wu, J., 2009. Applied geostatistics with SGeMS: A user's guide. Cambridge University Press.

 

This paper is from medical imaging and used 3D kriging:

 

Aissiou, M., Périé, D., Gervais, J. and Trochu, F., 2013. Development of a progressive dual kriging technique for 2D and 3D multi-parametric MRI data interpolation. Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 1(2), pp.69-78.

 

This paper uses radial basis functions (similar to Kriging) for point-based 3D interpolation, from the field of computer graphics:

 

Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C. and Evans, T.R., 2001, August. Reconstruction and representation of 3D objects with radial basis functions. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (pp. 67-76).

 

 

2.     The method should be improved a bit more to address the “NoData” issue. The purpose of interpolation is to fill in values at locations where observations are not available, so if an interpolation algorithm frequently returns “NoData” at locations where we want to have data, then the algorithm is not useful for most applications. Kriging, radial basis interpolation, and even the nearest neighbor (NN) method would be preferable in that case. Though the authors claim in Section 3.3.1 that the frequency of “NoData” shouldn’t be considered a criterion for evaluating interpolation performance, I would have to disagree with that. Figure 9 shows many “NoData” occurrences. One quick solution to this is to take an iterative process and use previously interpolated values as inputs to interpolate at the “NoData” locations.

 

 

3.     The proposed workflow/approach should be compared with a baseline. Figure 9 shows the results of using the “improved 3D IDW”, but readers would be curious about what ordinar (or traditional) 3D IDW could do. As mentioned, IDW can be applied to 3D contexts directly (Yang et al., 2021). For example, authors can compare the proposed workflow with a “vanilla” 3D IDW, which simply interpolates all data available in the ROI without the use of a search neighborhood. The workflow can also be compared with 3D IDW which uses a spherical search neighborhood, which doesn’t account for the vertical and horizontal anisotropy. Or, the method can be compared with Sun et al. (2019), which authors have already cited. Either a qualitative comparison (e.g., visually more realistic results with some explanations) or a quantitative comparison (e.g., an improvement in accuracy by using a few boreholes for testing) with any base method would convince readers that the approach has indeed improved something.

 

Two additional minor comments regarding the format and writing style:

 

1.     There are two Figure 3s, one in Section 1.2.2 and one in Section 2.3.1. Figure numbering should be double-checked and corrected. There is no Figure 3(a) from the sentence “… it is limited in searching neighborhoods located diagonally (Figure 3(a))”.

 

2.     Section 2.3.1 is unnecessarily lengthy. The use of B-rep and topology is just one way of implementing 3D search neighborhoods based on GIS software. Without these concepts, one can still directly check if a point is within an ellipsoid (source: Remy et al. (2009)). This section can be shortened, and authors only need to concisely mention what methods they used and properly cite the sources. Figure 3 (in Section 2.3.1) and Table 1 are not necessary since they are not the key innovation of the paper.

Author Response

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Round 2

Reviewer 2 Report

Revised manuscripts can be published

Reviewer 3 Report

The manuscript has improved significantly and I recommend publication.