the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
An Ensemble Random Forest Model for Seismic Energy Forecast
Abstract. Seismic energy forecasting is critical for hazard preparedness, but current models have limits in accurately predicting seismic energy changes. This paper fills that gap by introducing a new ensemble random forest model designed specifically for seismic energy forecasting. Building on an existing paradigm, provided by Raghukanth et al. (2017), the global energy time series is decomposed into intrinsic mode functions (IMFs) using ensemble empirical mode decomposition for better representation. Following this approach, we split the data into stationary (IMF1) and non-stationary (sum of IMF2-IMF6) components for modeling. We acknowledge the inadequacy of intrinsic mode functions (IMFs) in capturing seismic energy dynamics, notably in anticipating the final values of the time series. To address this restriction, the yearly seismic energy time series is also fed along with the stationary and non-stationary parts as inputs to the developed models. Here, we employed Support Vector Machine (SVM), Random Forest (RF), Instance-Bases learning (IBk), Linear Regression (LR), and MultiLayer Perceptron (MLP) algorithms for the modelling. Furthermore, the five models discussed above were suitably employed in a novel regression-based ensemble random forest algorithm to arrive at the final predictions. The root mean square error (RMSE) obtained in the training and testing phases of the final model were 0.127 and 0.134, respectively. It was observed that the performance of the developed ensemble model was superior to those existing in literature (Raghukanth et al., 2017). Further, the developed algorithm was employed for the seismic energy prediction in the active Western Himalayan region for a comprehensively compiled catalogue and the mean forecasted seismic energy for year 2024 is 7.21 × 1014 J. This work is a pilot project that aims to create a forecast model for the release of seismic energy globally and further application at a regional level. The findings of our investigation demonstrate the possibility of the established method in the accurate seismological energy forecast, which can help with appropriate hazard preparedness.
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RC1: 'Comment on nhess-2024-129', Anonymous Referee #1, 13 Nov 2024
The manuscript under consideration is focused on an open problem, the prediction of large earthquakes. This paper presents an interesting study based on Machine Learning, ML, to predict intense earthquakes in terms of the released energy.
In strictly sense, prediction is considered when the position of the epicenter, the time of occurrence and the magnitude are known with precision.
As it is well known, the underlying dynamics of tectonic plates is due to complex processes inside the Earth such as convection. Those involved processes give rise to the interaction between tectonic plates, being stick-slip the main mechanism for the earthquakes occurrence. On the basis of these aspects, seismic dynamics is complex.
This paper shows a good prediction approximation produced by ML-based algorithms.
The work is very important and their results are very interesting, however, in my opinion, some important aspects have not been considered in this study:
a) The catalogue use for the study considers a period from 1900 to 2015. In the period from 1900 to 1920 very few earthquakes are observed while in recent years the density of events is much higher. Authors should explain these differences time periods.
b) Figure 1a shows the magnitude of completeness (M6.4) which is only part of the Gutenberg-Richter law. The authors should show the Gutenberg-Richter law taking lower magnitudes (for example, M < 3) and thus determine the correct magnitude of completeness. To do this they can use the ZMAP platform where they can estimate the b-value and completeness Mc of the GR law.
c) It is important that the authors justify the reason for considering only earthquakes with large magnitudes and avoid the other ones with low magnitudes.
d) To calculate the IMF functions authors used the algorithm proposed by Huang et al. (1998). In my opinion, the authors should explain how the complex dynamics of seismic activity is involved to obtain IMF to obtain the smooth curve (a) in Figure 2.
e) When applying the algorithm proposed by Huang et al. it is not clear the role seismic activity with magnitudes M < Mc could have.
Their results do not consider time and epicentral position.
I consider that these suggestions can improve the context of the study that the authors have developed and then could be published
Citation: https://doi.org/10.5194/nhess-2024-129-RC1 -
RC2: 'Reply on RC1', Anonymous Referee #1, 21 Nov 2024
I have read the author's reply. Their comments are very interesting and improve widely their paper. I don't have any other comment and, for me the new version of their manuscript can be published in the currently version.
I appreciate the answers to my suggestions from the authors.
Citation: https://doi.org/10.5194/nhess-2024-129-RC2 -
AC2: 'Reply on RC2', Sukh Sagar Shukla, 27 Nov 2024
Dear Anonymous Referee #1,
Thank you very much for considering this manuscript for publication, and many thanks for the positive comments and reviews.
Citation: https://doi.org/10.5194/nhess-2024-129-AC2 -
RC3: 'Reply on AC2', Anonymous Referee #1, 27 Nov 2024
I hope your interesting article is published soon.
Citation: https://doi.org/10.5194/nhess-2024-129-RC3
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RC3: 'Reply on AC2', Anonymous Referee #1, 27 Nov 2024
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AC2: 'Reply on RC2', Sukh Sagar Shukla, 27 Nov 2024
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RC2: 'Reply on RC1', Anonymous Referee #1, 21 Nov 2024
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AC1: 'Reply on RC1', Sukh Sagar Shukla, 20 Nov 2024
Dear Anonymous Referee #1,
The authors would like to thank the reviewer for recognising the relevance of the present work, and finding the results interesting. We highly appreciate the insightful comments, and we are committed to making significant revisions. We have carefully considered all the suggestions and made substantial revisions to the manuscript accordingly. Please find the attached PDF file containing a documented list of changes we have made to the manuscript (marked as reply). We have considered a more comprehensive and updated global catalog for analysis and trained the models on updated dataset. We have refined the discussion on considering large magnitude events and physical interpretation of IMFs. We hope these clarifications will improve the readers understanding of our work.
Kind Regards,
Sukh Sagar Shukla
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RC4: 'Comment on nhess-2024-129', Anonymous Referee #2, 19 May 2025
The manuscript considers the problem of seismic energy forecasting.
The method proposed builds on previously published research while improving the results.
Overall, the manuscript is well structured, although some improvements are needed to improve the readability and reproducibility of the results.
Section 1 (Introduction) and Section 2 (Background) cover, for the most part, the same topics: why are they divided?
Furthermore, while these sections may provide a partial overview of previous studies using ML for seismic energy forecasting, these may be presented in a more coherent form.
In Section 1, the concept of "ensemble" is introduced in a way such that it seems like a modern concept, despite being used in many fields for many decades.
At line 158, the authors mention the inclusion of expert opinions in the random forest (RF): the authors should specify if this is a general comment on the RF approach or for this study. If the latter is true, how has the expert opinion been included?
In section 3, do the authors consider the uncertainties due to poor station coverage, empirical relationships, etc.?
The authors should discuss how completely removing the events with magnitudes below the magnitude of completeness could improve the results: having information about lower magnitude earthquakes, even though it is partial, should still be better than not having any information at all. Also, this could improve the temporal distribution of the events, possibly allowing for monthly basis analysis.
In Table 3, how is the %(variance) being computed?
In Section 4, the authors should describe in further detail the inputs and outputs of the different models. As an example, the authors should explain in greater detail the role of the lag and how the inputs are computed, especially at the beginning of the timeseries. Furthermore, the authors should better explain what the inputs and outputs are during the testing phase.
In the MLP section, considering the few data points in the training dataset, doesn't a batch of 100 samples consist of the whole dataset (especially for the Western Himalaya case)?
In the Linear Regression section, the authors should add a reference to the M5 method. Furthermore, the ridge hyperparameter seems to be specific to the authors' implementation, rather than a general parameter of LR.
The parameters S, Z, and Y should be properly introduced at the beginning of the section for improved readability.
What does a_r represent in equation 5? Is it the feature vector?
Check the formatting of equation 6: there's a missing parenthesis.
In Section 5, the use of the training dataset to choose the best model should be carefully motivated. This practice can produce biased models as they are selected on the same data they are trained on, hence favouring overfitting models. A better solution would be to use a third independent dataset (i.e. the validation dataset).
Section 8 (Discussion) could be extended, considering how the proposed method could be further improved in light of its current limitations.
Citation: https://doi.org/10.5194/nhess-2024-129-RC4
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