We would like to thank the reviewer for highly constructive comments on the article. The suggestions are highly appreciated. Our responses to the comments are provided below.

Reply to Comment 1

In previous events where earthquake DPMs were generated by the ARIA team, such as the 2015 Gorkha earthquake in Nepal and the 2016 Central Italy earthquakes, the DPMs were found to have good correlation with the actual damage mapped in field surveys [Yun et al. (2015), Sextos et al. (2018)]. However, landslides and rockfall can also lead to surface-level changes, and so can changes in vegetation and other phenomena such as building construction. Thus, while attempting to detect building damage, care needs to be exercised to limit the focus of the DPMs to locations where buildings are known to exist. The time-span between the acquisition of the pre-event and post-event images can also have a considerable impact on the potential false positives. The closer the 'before' and 'after' bracket the event, the fewer the false positives that are likely to be observed.



It is also certainly possible to have seismic building damage without observing significant change in the ground surface level. Damage to internal walls or columns that may have severely compromised the structural integrity of the building without causing externally visible damage or collapse may not be detectable through remote sensing. Storey drifts of 2% for braced steel structures or concrete shear wall structures may be technically classified as 'collapsed' (eg. FEMA 356), but such drift levels might be smaller than the level detectable with the 1–3 m spatial resolution offered by the current generation of SAR sensors. Dong and Shan (2013) provide a good review of previous studies that investigated the relationship between building appearance in remote sensing data and building damage grades. In general, they concluded that the higher damage states like complete collapse are more detectable through remote sensing data, but lower damage states are more challenging to detect. With the advent of commercial SAR satellite constellations like Capella Space and ICEYE, sub-meter SAR imagery is becoming available, and some of these deficiencies should be addressable.

In recognition of these limitations in the SAR and EO datasets, in our study we have also proposed to incorporate other variables (such as building attributes or the expected macroseismic intensity at the location of the building) to mitigate these issues. We propose to update this section of the manuscript to clarify these limitations, and how we propose to address them.

Reply to Comment 2

In a preliminary phase, we compared different algorithms that permit multiclass classification, including support vector machines, k-nearest neighbours, Naive Bayes, and Random Forest. Since the problem of damage classification typically involves highly imbalanced datasets, where the buildings in "no damage" state dominate the buildings in all other damage states, often by multiple orders of magnitude, all of the above classifier algorithms tended to overlearn the label with the higher number of training examples (i.e., "no damage"). The Random Forest algorithm was eventually selected for the study as it allows for the assignment of weights to the training examples. The training examples in each damage class were then weighted in inverse proportion to the class frequencies observed in the input data, in order to better handle the class imbalance in the input damage datasets. The Histogram-Based Gradient Boosting classifier was preferred in the cases where categorical features were present amongst the selected building attributes, in addition to purely numerical features. This was because the Histogram-Based Gradient Boosting classifier provides native categorical support, which helps avoid one-hot encoding to transform categorical features as numeric arrays. We propose to include this explanation in the revised version of the manuscript.

Reply to Comment 3

There is certainly a tradeoff between using more samples for training the algorithm versus reserving sufficient samples for the test set. Using a higher fraction of the available data for training can result in overfitting. Previous empirical studies have demonstrated that using 70-80% of the data for training and reserving 20-30% of the data for testing yields optimal results in terms of improving the accuracy of the model while minimizing the tendancy for overfitting [see Gholamy et al. (2018) for instance]. The decision to choose a 70%/30% split for the training and testing set (say, over an 80%/20% split) was ultimately driven by the paucity of 'collapse' labels in the damage datasets, particularly for the 2017 Puebla event where reserving only 20% of the dataset for testing would leave very few 'collapse' labels in the test set to evaluate the accuracy of the fitted model. We propose to add this explanation in this section, with references that justify this approach. 

The comments made by the reviewer are well taken. We would like to emphasize that the focus of the article is more about the integration of multiple input datasets including InSAR data for building damage detection, rather than on machine learning itself.

As far as we are aware, multi-class damage classification at the building level using SAR data has not been attempted before, so we are unfortunately unable to compare our results with any existing literature, and indeed this was precisely one of the reasons we pursued this study. It was also our intention to propose an open framework and data that other earthquake engineers and risk modellers could use for rapid loss assessment.

Deep learning techniques are more suited for structured data (images, audio, text) with large sample sizes, while the datasets used in this study are tabular (each row representing one building unit) and are small or medium sized (typically of the order of 1,000–10,000 samples). While it's true that for tabular data, both decision forest based approaches and deep neural networks could be used, as the reviewer acknowledges, deep learning techniques perform better with large sample sizes, which was unfortunately not the case for this study, given the limited availability of building-level damage datasets and the limited number of labelled damaged buildings within each dataset. Grinsztajn et al. (2022) conclude that for medium sized tabular data (~10,000 samples), tree-based models outperform deep learning methods, with much less computational cost. Similarly, Xu et al. (2021) also conclude that forests perform better than deep neural nets for tabular data with small sample sizes.

The reviewer's comment about the selection of appropriate building damage categories is apt. Dell'Acqua and Gamba (2012) highlight the need to develop damage scales specific to earth observation based damage assessments, possibly tied to existing damage scales that are widely used for field surveys of building damage (such as EMS 98). Cotrufo et al. (2018) propose a building damage assessment scale tailored for optical satellite imagery and aerial imagery. However, a similar damage scale tailored for InSAR based building damage assessment is still lacking. We propose to update the manuscript to list these limitations and potential areas for future research.

References cited in this response

Cotrufo, S., Sandu, C., Giulio Tonolo, F., & Boccardo, P. (2018). Building damage assessment scale tailored to remote sensing vertical imagery. European Journal of Remote Sensing, 51(1), 991–1005. https://doi.org/10.1080/22797254.2018.1527662

Dell’Acqua, F., & Gamba, P. (2012). Remote sensing and earthquake damage assessment: Experiences, limits, and perspectives. Proceedings of the IEEE, 100(10), 2876–2890. https://doi.org/10.1109/JPROC.2012.2196404

Grinsztajn, L., Oyallon, E., & Varoquaux, G. (2022). Why do tree-based models still outperform deep learning on tabular data? https://arxiv.org/abs/2207.08815

Xu, H., Kinfu, K. A., LeVine, W., Panda, S., Dey, J., Ainsworth, M., Peng, Y.-C., Kusmanov, M., Engert, F., White, C. M., Vogelstein, J. T., & Priebe, C. E. (2021). When are Deep Networks really better than Decision Forests at small sample sizes, and how? https://arxiv.org/abs/2108.13637v4