the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Jun 2024
2021 Alaska Earthquake: entropy approach to its precursors and aftershock regimes
Abstract. For the first time, an entropy analysis has been made in Alaska, a seismic-rich region located in a subduction zone that shows a nontrivial behavior: the subduction arc changes the seismic activity from the eastern zone to the western zone, showing a decrease in this activity along the subduction. We analyze this zone through the Tsallis entropy and the mutability (or dynamic entropy). The data set used for this analysis was measured between 2000 and 2023, considering 19549 seismic events. We have found an agreement between the results for the two entropies. We have followed the value of the q parameter of the Tsallis entropy, finding values between 1.70 and 1.85, in concordance with values previously found in other seismic regions of the planet. Also, the values of the q-parameter tend to decrease over time but show an increase before the main earthquakes. Mutability also shows a tendency to decrease over time and an increase previous to the main earthquakes. To deeply analyze this zone, we divided the region into four sub-zones. The results show how mutability can identify the seismic activity in each zone. This study shows how an entropy approach can shed light on understanding the seismicity in subduction zones.
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RC1: 'Comment on nhess-2024-106', Anonymous Referee #1, 03 Jul 2024
I read careful the manuscript titled “2021 Alaska Earthquake: entropy approach to its precursors and aftershock regimes.”
This work is very interesting for the scientific community because the study is focused to know more about the subduction zone in Alaska which has not been studied in the context of seismic activity.
However, in my opinion, the authors left important conceptual issues without consider deeply. In particular the physical interpretation about the mutability which is a concept not well known for everyone.
On the other hand, regarding with the format, there are many problems, un particular some figures aren´t set in the correct paragraphs and the captions do not explain correctly the important points in the graphs.
I think the manuscript requires a major revision in order to improve it.
I consider that the following issues must be taking into account by the authors.
Suggestions
- Section 2. In figure 2 the authors do no report the b-value and a-value estimated from the Gutenberg-Richter law. I suggest determine these values calculated yearly in order to search some pattern between the b-value and the largest magnitudes.
- In line 72, authors cited first the Figure 4 but Figure 3 is not cited previously.
- Relocate figures 3 and 4 close the paragraphs where they are cited.
- In line 77, at the end, the authors cite an “Appendix” which does not appears in the manuscript.
- Figure 3 does not correspond with the description, in the text, lines 78-79.
- In section 2.2 the authors describe the method used where they describe the Tsallis’s entropy in Equation 4. However, to calculate the q-index the procedure is based on the fitting of Equation 10 (generalized Gutenberg-Richter) in the paper: “Flores-Márquez, E.L et al. Non-extensive statistical analysis of seismicity on the western coast of Mexico. Fractal fractal. 2024, 8, 306. https://doi.org/10.3390/fractalfract8060306.” (This paper should be cited). The authors should explain the procedure they used to determine the q-index as well as present the fitting in Figure 2.
- Authors have to describe with more detail mutability concept (for example, as was described in: Eugenio E. Vogel et al., NHESS (2019) https://doi.org/10.5194/nhess-2019-309) as well as their physical interpretation.
- In section 3.3. Caption of Figure 6 is not clear: it is written as “Left) Mutability on magnitude for the seismic sequence”, but the y-label in Figure 6 Left appears “Sq” and, in Figure 6 Right, y-label indicate Mutability. Actually, the caption does not coincide with the Figure.
- Figure 8 is offside; it must be relocated within the section 3.4.
- The authors could design the Figure 8 as a panel with the four catalogues independently and indicating the EQ considered.
- Results of Mutability reported in Figures 9 to 11 require a better explanation as well as their captions.
- Finally, and according with the title, the authors must explain what about the precursors associated with the four earthquakes studied.
Citation: https://doi.org/10.5194/nhess-2024-106-RC1 - AC1: 'Reply on RC1', DENISSE PASTEN, 26 Jul 2024
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RC2: 'Comment on nhess-2024-106', Anonymous Referee #2, 10 Jul 2024
Although the subject of the study is interesting, there are many points that need to be adequately addressed
1) The English in the text is not fluent, resulting in misunderstandings in several sections. It requires thorough proofreading by a native English speaker.
2) Throughout the text, the authors appear to use the term "seismic risk" to refer to the "precursor" of large events. It is important to note that seismic risk is defined as the product of seismic hazard and vulnerability. Seismic hazard refers to the natural phenomena generated by an earthquake, while seismic risk is the probability of human loss or damage to the built environment when exposed to a seismic hazard.
3) In the Introduction, the authors state: “The aim of the present analysis is to find patterns in the data sequence that could lead to understanding the following aspects of the process: a) entropic activity of the zone or sub-zone that can be an indicator of seismic risk; b) parameters serving as indicators of seismic risk; c) behavior of the data sequence during the earthquake and immediate aftershocks; d) recovery to the ‘normal’ or previous seismic activity following the aftershock period.” However, these patterns or analyses seem poorly discussed in the text.
4) The description of data selection in Section 2.1 appears to be quite complicated. Initially, the authors extract earthquakes with a maximum depth of 100 km, then they re-select those with a maximum depth of 70 km. Why not select events with a maximum depth of 70 km from the beginning? Furthermore, there is another potentially more critical issue: the authors first apply the GR law to select all events (among those with a maximum depth of 100 km) with a magnitude larger than the completeness magnitude, then from this subset, they extract events with a maximum depth of 70 km. I believe the selection process should be different: first, they should select events with a maximum depth of 70 km, then apply the GR law to this dataset and consider only the events with a magnitude larger than the completeness magnitude.
5) The estimation of b-value is missing.
6) Lines 72-73 “To the left, we appreciate how the activity of this region continuously increased irregularly since the beginning of the century”: this is not “activity” (generally indicated by the number of events in a specified timescale), but the magnitude or the “energy”.
7) Lines 75-77: “At this point, we can follow two complementary ways to analyze these data through entropy: a) magnitude sequence, and b) sequence of intervals between consecutive seisms. We have chosen the former since entropy is more easily associated with energy, even since the early thermodynamics courses. However, we will include some results using the latter in the Appendix”. Actually, this is quite a peculiar way to indicate their preference for analyzing magnitude instead of interevent times. Moreover, they mention that interevent times will be analyzed in the Appendix, which is missing!
8) Line 78: “In Fig. 3, the depiction presents the magnitude of each of the 15 011 seisms at the time of their production.” Fig. 3 should be Fig. 4. And, please, rephrase: “Fig. 3 shows the time distribution of the analysed magnitudes”.
9) Lines 82-84: The sentence is really complicated. The authors can simply write “We calculated the Tsallis entropy and mutability in a moving window of size W, shifting by one event through the entire catalog and associate the calculated values to the time of the last event in the window”.
10) Line 90: “states” are simply “magnitudes”.
11) Line 94-98: why so complicated way to calculate the average magnitude? Just simply say that within each window you calculate the average magnitude.
12) I don’t understand why the authors mention Shannon entropy (eq. 4) if it is never used in the study! While I understand the desire to shorten the theoretical treatment, the way the authors have done it makes the text very difficult to comprehend. It would be better to include all the details that allow the reader to understand how to calculate q.
13) The same issue applies to the description of mutability. Mathematical details are required. Simply writing “the weight in bytes of the map created by wlzip of the time window at position 𝑛 n” leaves the reader unsure about what "weight," "wlzip," and "map" refer to.
14) Lines 119-123 are repeated in lines 131- 134.
15) Line 152: “Fig. 5 reports the Tsallis’ entropy calculated for windows W = 512 and W = 1024”, Line 155: “Fig. 5 presents the average value of the Tsallis entropy over windows with W=512 and W=1024”: is it the average value of Tsallis entropy or not??
16) Lines 153-154: “The left-hand side presents the variations along the 24 years of this study, while the right-hand side zooms on the last 4 years, where most of the important activity shows up.” This is repeated few lines below.
17) Line 158: “it can be noticed that at the precise moment the large earthquakes are produced, the Tsallis entropy suddenly decreases”: better to write “The Tsallis entropy is characterized by a decrease before the occurrence of a large shock”
18) Line 161: “to detect risk in advance” please see my comment in the point2)
19) Line 161: “poor statistics”??
20) Line 162: “The average magnitude tends to be minimized before a large earthquake”. Where is the figure showing this behavior of mean magnitude?
21) Lines 165-175: the authors try to explain on a physical basis the behavior of Tsallis entropy, but honestly, I cannot follow their argument. They talk about 4 degrees latitude, 6 degrees longitude, stalagmites, stalactites, compressible gas…I would suggest to delete all this explanation, which, furthermore, lacks of adequate literature to be based on.
22) In Line 158 “at the precise moment the large earthquakes are produced, the Tsallis entropy suddenly decreases.”; in line 179 “Mutability decreases previous to a large earthquake because small seisms of restricted magnitude dominate the sequence”, but in line 188 for W=256 “simultaneous increases of Tsallis entropy and decreases of mutability as the large earthquake approaches” the behavior of the two quantities is opposing. So, I should argue that the Tsallis and mutability have a correlated behavior for W=512 and 1024 and anticorrelated for W=256??? A DEEP explanation is NECESSARY.
23) Line 205: “We choose to present the time in number of days “ but Figs. 8-12 shows years.
24) Line 217: “Then, near day 7500,” so, when?
25) Section 3.5 shows results only for W=256. At least for sub-zoness A and D, the results should also be presented for W=512 (due to what observed in my previous point 22).
26) Fig. 13 should present also the results for W=1024.
27) A further figure is necessary showing the time variation of the Tsallis entropy Sq for the interevent times.Citation: https://doi.org/10.5194/nhess-2024-106-RC2 - AC2: 'Reply on RC2', DENISSE PASTEN, 26 Jul 2024
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RC3: 'Comment on nhess-2024-106', Anonymous Referee #3, 16 Jul 2024
The comment was uploaded in the form of a supplement: https://nhess.copernicus.org/preprints/nhess-2024-106/nhess-2024-106-RC3-supplement.pdf
- AC3: 'Reply on RC3', DENISSE PASTEN, 26 Jul 2024
Status: closed
-
RC1: 'Comment on nhess-2024-106', Anonymous Referee #1, 03 Jul 2024
I read careful the manuscript titled “2021 Alaska Earthquake: entropy approach to its precursors and aftershock regimes.”
This work is very interesting for the scientific community because the study is focused to know more about the subduction zone in Alaska which has not been studied in the context of seismic activity.
However, in my opinion, the authors left important conceptual issues without consider deeply. In particular the physical interpretation about the mutability which is a concept not well known for everyone.
On the other hand, regarding with the format, there are many problems, un particular some figures aren´t set in the correct paragraphs and the captions do not explain correctly the important points in the graphs.
I think the manuscript requires a major revision in order to improve it.
I consider that the following issues must be taking into account by the authors.
Suggestions
- Section 2. In figure 2 the authors do no report the b-value and a-value estimated from the Gutenberg-Richter law. I suggest determine these values calculated yearly in order to search some pattern between the b-value and the largest magnitudes.
- In line 72, authors cited first the Figure 4 but Figure 3 is not cited previously.
- Relocate figures 3 and 4 close the paragraphs where they are cited.
- In line 77, at the end, the authors cite an “Appendix” which does not appears in the manuscript.
- Figure 3 does not correspond with the description, in the text, lines 78-79.
- In section 2.2 the authors describe the method used where they describe the Tsallis’s entropy in Equation 4. However, to calculate the q-index the procedure is based on the fitting of Equation 10 (generalized Gutenberg-Richter) in the paper: “Flores-Márquez, E.L et al. Non-extensive statistical analysis of seismicity on the western coast of Mexico. Fractal fractal. 2024, 8, 306. https://doi.org/10.3390/fractalfract8060306.” (This paper should be cited). The authors should explain the procedure they used to determine the q-index as well as present the fitting in Figure 2.
- Authors have to describe with more detail mutability concept (for example, as was described in: Eugenio E. Vogel et al., NHESS (2019) https://doi.org/10.5194/nhess-2019-309) as well as their physical interpretation.
- In section 3.3. Caption of Figure 6 is not clear: it is written as “Left) Mutability on magnitude for the seismic sequence”, but the y-label in Figure 6 Left appears “Sq” and, in Figure 6 Right, y-label indicate Mutability. Actually, the caption does not coincide with the Figure.
- Figure 8 is offside; it must be relocated within the section 3.4.
- The authors could design the Figure 8 as a panel with the four catalogues independently and indicating the EQ considered.
- Results of Mutability reported in Figures 9 to 11 require a better explanation as well as their captions.
- Finally, and according with the title, the authors must explain what about the precursors associated with the four earthquakes studied.
Citation: https://doi.org/10.5194/nhess-2024-106-RC1 - AC1: 'Reply on RC1', DENISSE PASTEN, 26 Jul 2024
-
RC2: 'Comment on nhess-2024-106', Anonymous Referee #2, 10 Jul 2024
Although the subject of the study is interesting, there are many points that need to be adequately addressed
1) The English in the text is not fluent, resulting in misunderstandings in several sections. It requires thorough proofreading by a native English speaker.
2) Throughout the text, the authors appear to use the term "seismic risk" to refer to the "precursor" of large events. It is important to note that seismic risk is defined as the product of seismic hazard and vulnerability. Seismic hazard refers to the natural phenomena generated by an earthquake, while seismic risk is the probability of human loss or damage to the built environment when exposed to a seismic hazard.
3) In the Introduction, the authors state: “The aim of the present analysis is to find patterns in the data sequence that could lead to understanding the following aspects of the process: a) entropic activity of the zone or sub-zone that can be an indicator of seismic risk; b) parameters serving as indicators of seismic risk; c) behavior of the data sequence during the earthquake and immediate aftershocks; d) recovery to the ‘normal’ or previous seismic activity following the aftershock period.” However, these patterns or analyses seem poorly discussed in the text.
4) The description of data selection in Section 2.1 appears to be quite complicated. Initially, the authors extract earthquakes with a maximum depth of 100 km, then they re-select those with a maximum depth of 70 km. Why not select events with a maximum depth of 70 km from the beginning? Furthermore, there is another potentially more critical issue: the authors first apply the GR law to select all events (among those with a maximum depth of 100 km) with a magnitude larger than the completeness magnitude, then from this subset, they extract events with a maximum depth of 70 km. I believe the selection process should be different: first, they should select events with a maximum depth of 70 km, then apply the GR law to this dataset and consider only the events with a magnitude larger than the completeness magnitude.
5) The estimation of b-value is missing.
6) Lines 72-73 “To the left, we appreciate how the activity of this region continuously increased irregularly since the beginning of the century”: this is not “activity” (generally indicated by the number of events in a specified timescale), but the magnitude or the “energy”.
7) Lines 75-77: “At this point, we can follow two complementary ways to analyze these data through entropy: a) magnitude sequence, and b) sequence of intervals between consecutive seisms. We have chosen the former since entropy is more easily associated with energy, even since the early thermodynamics courses. However, we will include some results using the latter in the Appendix”. Actually, this is quite a peculiar way to indicate their preference for analyzing magnitude instead of interevent times. Moreover, they mention that interevent times will be analyzed in the Appendix, which is missing!
8) Line 78: “In Fig. 3, the depiction presents the magnitude of each of the 15 011 seisms at the time of their production.” Fig. 3 should be Fig. 4. And, please, rephrase: “Fig. 3 shows the time distribution of the analysed magnitudes”.
9) Lines 82-84: The sentence is really complicated. The authors can simply write “We calculated the Tsallis entropy and mutability in a moving window of size W, shifting by one event through the entire catalog and associate the calculated values to the time of the last event in the window”.
10) Line 90: “states” are simply “magnitudes”.
11) Line 94-98: why so complicated way to calculate the average magnitude? Just simply say that within each window you calculate the average magnitude.
12) I don’t understand why the authors mention Shannon entropy (eq. 4) if it is never used in the study! While I understand the desire to shorten the theoretical treatment, the way the authors have done it makes the text very difficult to comprehend. It would be better to include all the details that allow the reader to understand how to calculate q.
13) The same issue applies to the description of mutability. Mathematical details are required. Simply writing “the weight in bytes of the map created by wlzip of the time window at position 𝑛 n” leaves the reader unsure about what "weight," "wlzip," and "map" refer to.
14) Lines 119-123 are repeated in lines 131- 134.
15) Line 152: “Fig. 5 reports the Tsallis’ entropy calculated for windows W = 512 and W = 1024”, Line 155: “Fig. 5 presents the average value of the Tsallis entropy over windows with W=512 and W=1024”: is it the average value of Tsallis entropy or not??
16) Lines 153-154: “The left-hand side presents the variations along the 24 years of this study, while the right-hand side zooms on the last 4 years, where most of the important activity shows up.” This is repeated few lines below.
17) Line 158: “it can be noticed that at the precise moment the large earthquakes are produced, the Tsallis entropy suddenly decreases”: better to write “The Tsallis entropy is characterized by a decrease before the occurrence of a large shock”
18) Line 161: “to detect risk in advance” please see my comment in the point2)
19) Line 161: “poor statistics”??
20) Line 162: “The average magnitude tends to be minimized before a large earthquake”. Where is the figure showing this behavior of mean magnitude?
21) Lines 165-175: the authors try to explain on a physical basis the behavior of Tsallis entropy, but honestly, I cannot follow their argument. They talk about 4 degrees latitude, 6 degrees longitude, stalagmites, stalactites, compressible gas…I would suggest to delete all this explanation, which, furthermore, lacks of adequate literature to be based on.
22) In Line 158 “at the precise moment the large earthquakes are produced, the Tsallis entropy suddenly decreases.”; in line 179 “Mutability decreases previous to a large earthquake because small seisms of restricted magnitude dominate the sequence”, but in line 188 for W=256 “simultaneous increases of Tsallis entropy and decreases of mutability as the large earthquake approaches” the behavior of the two quantities is opposing. So, I should argue that the Tsallis and mutability have a correlated behavior for W=512 and 1024 and anticorrelated for W=256??? A DEEP explanation is NECESSARY.
23) Line 205: “We choose to present the time in number of days “ but Figs. 8-12 shows years.
24) Line 217: “Then, near day 7500,” so, when?
25) Section 3.5 shows results only for W=256. At least for sub-zoness A and D, the results should also be presented for W=512 (due to what observed in my previous point 22).
26) Fig. 13 should present also the results for W=1024.
27) A further figure is necessary showing the time variation of the Tsallis entropy Sq for the interevent times.Citation: https://doi.org/10.5194/nhess-2024-106-RC2 - AC2: 'Reply on RC2', DENISSE PASTEN, 26 Jul 2024
-
RC3: 'Comment on nhess-2024-106', Anonymous Referee #3, 16 Jul 2024
The comment was uploaded in the form of a supplement: https://nhess.copernicus.org/preprints/nhess-2024-106/nhess-2024-106-RC3-supplement.pdf
- AC3: 'Reply on RC3', DENISSE PASTEN, 26 Jul 2024
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