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15 pages, 3219 KiB

Open AccessArticle

Earthquake Forecasting Based on b Value and Background Seismicity Rate in Yunnan Province, China

by Yuchen Zhang, Rui Wang, Haixia Shi, Miao Miao, Jiancang Zhuang, Ying Chang, Changsheng Jiang, Lingyuan Meng, Danning Li, Lifang Liu, Youjin Su, Zhenguo Zhang and Peng Han

Entropy 2025, 27(2), 205; https://doi.org/10.3390/e27020205 - 15 Feb 2025

Viewed by 834

Abstract

Characterized by frequent earthquakes and a dense population, Yunnan Province, China, faces significant seismic hazards and is a hot place for earthquake forecasting research. In a previous study, we evaluated the performance of the b value for 5-year seismic forecasting during 2000–2019 and [...] Read more.

Characterized by frequent earthquakes and a dense population, Yunnan Province, China, faces significant seismic hazards and is a hot place for earthquake forecasting research. In a previous study, we evaluated the performance of the b value for 5-year seismic forecasting during 2000–2019 and made a forward prediction of M ≥ 5.0 earthquakes in 2020–2024. In this study, with the forecast period having passed, we first revisit the results and assess the forward prediction performance. Then, the background seismicity rate, which may also offer valuable long-term forecasting information, is incorporated into earthquake prediction for Yunnan Province. To assess the effectiveness of the prediction, the Molchan Error Diagram (MED), Probability Gain (PG), and Probability Difference (PD) are employed. Using a 25-year catalog, the spatial b value and background seismicity rate across five temporal windows are calculated, and 86 M ≥ 5.0 earthquakes as prediction samples are examined. The predictive performance of the background seismicity rate and b value is comprehensively tested and shown to be useful for 5-year forecasting in Yunnan. The performance of the b value exhibits a positive correlation with the predicted earthquake magnitude. The synergistic effect of combining these two predictors is also revealed. Finally, using the threshold corresponding to the maximum PD, we integrate the forecast information of background seismicity rates and the b value. A forward prediction is derived for the period from January 2025 to December 2029. This study can be helpful for disaster preparedness and risk management in Yunnan Province, China. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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15 pages, 3622 KiB

Open AccessArticle

Analysis of Aftershocks from California and Synthetic Series by Using Visibility Graph Algorithm

by Alejandro Muñoz-Diosdado, Ana María Aguilar-Molina, Eric Eduardo Solis-Montufar and José Alberto Zamora-Justo

Entropy 2025, 27(2), 178; https://doi.org/10.3390/e27020178 - 8 Feb 2025

Viewed by 612

Abstract

The use of the Visibility Graph Algorithm (VGA) has proven to be a valuable tool for analyzing both real and synthetic seismicity series. Specifically, VGA transforms time series into a network representation in which structural properties such as node connectivity, clustering, and community [...] Read more.

The use of the Visibility Graph Algorithm (VGA) has proven to be a valuable tool for analyzing both real and synthetic seismicity series. Specifically, VGA transforms time series into a network representation in which structural properties such as node connectivity, clustering, and community structure can be quantitatively measured, thereby revealing underlying correlations and dynamics that may remain hidden in traditional linear or spectral analyses. The time series transformation into complex networks with VGA provides a new approach to analyze seismic dynamics, allowing scientists to extract trends and behaviors that may not be possible by classical time-series analysis. On the other hand, many studies attempt to find viable trends in order to identify preparation mechanisms prior to a strong earthquake or to analyze the aftershocks. In this work, the seismic activity of Southern California Earthquake was analyzed focusing only on the significant earthquakes. For this purpose, seismic series preceding and following each earthquake were constructed using a windowing method with different overlaps and the slope of the connectivity (k) versus magnitude (M) graph (k-M slope) and the average degree were computed from the mapped complex networks. The results revealed a significant decrease in these parameters after the earthquake, due to the contribution of the aftershocks from the main event. Interestingly, the study was extended to synthetic seismicity series and the same behavior was observed for both k-M slope and average degree. This finding suggests that the spring-block model reproduces a relaxation mechanism following a large-magnitude event like those of real seismic aftershocks. However, this conclusion contrasts with conclusions drawn by other researchers. These results highlight the utility of VGA in studying events that precede and follow major earthquakes. This technique may be used to extract some useful trends in seismicity, which could eventually be employed for a deeper understanding and possible forecasting of seismic behavior. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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20 pages, 7208 KiB

Open AccessArticle

Statistical Characteristics of Strong Earthquake Sequence in Northeastern Tibetan Plateau

by Ying Wang, Rui Wang, Peng Han, Tao Zhao, Miao Miao, Lina Su, Zhaodi Jin and Jiancang Zhuang

Entropy 2025, 27(2), 174; https://doi.org/10.3390/e27020174 - 6 Feb 2025

Viewed by 590

Abstract

As the forefront of inland extension on the Indian plate, the northeastern Tibetan Plateau, marked by low strain rates and high stress levels, is one of the regions with the highest seismic risk. Analyzing seismicity through statistical methods holds significant scientific value for [...] Read more.

As the forefront of inland extension on the Indian plate, the northeastern Tibetan Plateau, marked by low strain rates and high stress levels, is one of the regions with the highest seismic risk. Analyzing seismicity through statistical methods holds significant scientific value for understanding tectonic conditions and assessing earthquake risk. However, seismic monitoring capacity in this region remains limited, and earthquake frequency is low, complicating efforts to improve earthquake catalogs through enhanced identification and localization techniques. Bi-scale empirical probability integral transformation (BEPIT), a statistical method, can address these data gaps by supplementing missing events shortly after moderate to large earthquakes, resulting in a more reliable statistical data set. In this study, we analyzed six earthquake sequences with magnitudes of M_S ≥ 6.0 that occurred in northeastern Tibet since 2009, following the upgrade of the regional seismic network. Using BEPIT, we supplemented short-term missing aftershocks in these sequences, creating a more complete earthquake catalog. ETAS model parameters and b values for these sequences were then estimated using maximum likelihood methods to analyze parameter variability across sequences. The findings indicate that the b value is low, reflecting relatively high regional stress. The background seismicity rate is very low, with most mainshocks in these sequences being background events rather than foreshock-driven events. The p-parameter of the ETAS model is high, indicating that aftershocks decay relatively quickly, while the α-parameter is also elevated, suggesting that aftershocks are predominantly induced by the mainshock. These conditions suggest that earthquake prediction in this region is challenging through seismicity analysis alone, and alternative approaches integrating non-seismic data, such as electromagnetic and fluid monitoring, may offer more viable solutions. This study provides valuable insights into earthquake forecasting in the northeastern Tibetan Plateau. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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15 pages, 265 KiB

Open AccessArticle

Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg–Richter Law, Omori Law, Roll-Off Effect, and Negative Binomial Distribution

by Roumen Borisov and Nikolay K. Vitanov

Entropy 2025, 27(2), 130; https://doi.org/10.3390/e27020130 - 26 Jan 2025

Viewed by 3586

Abstract

We discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg–Richter relationship and the Omori law. These laws [...] Read more.

We discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg–Richter relationship and the Omori law. These laws are valid for earthquakes that happen in a single cluster of sources of seismic activity. Further, we discuss the distribution of earthquakes for several clusters containing sources of seismic activity. This distribution contains, as a specific case, a version of the negative binomial distribution. We show that at least a part of the roll-off effect connected to the parameter b of the Gutenberg– Richter law occurs because one records earthquakes that happen in more than one cluster of sources of seismic activity. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

15 pages, 5103 KiB

Open AccessArticle

Relationship Between the 2019 Ridgecrest, California, M_W7.1 Earthquake and Its M_W6.4 Foreshock Sequence

by Jianchang Zheng, Zhengshuai Zhang and Xiaohan Li

Entropy 2025, 27(1), 16; https://doi.org/10.3390/e27010016 - 28 Dec 2024

Viewed by 674

Abstract

The 2019 Ridgecrest M_W7.1 earthquake has received significant attention due to its complex fault activity. It is also noticeable for its M_W6.4 foreshock sequence. There are intricate dynamic relationships between earthquakes in such vigorous sequences. Based on the relocated [...] Read more.

The 2019 Ridgecrest M_W7.1 earthquake has received significant attention due to its complex fault activity. It is also noticeable for its M_W6.4 foreshock sequence. There are intricate dynamic relationships between earthquakes in such vigorous sequences. Based on the relocated catalogue, we adopt the nearest neighbour algorithm to analyze its foreshock and aftershock sequences. Detailed links and family structures of the sequence are obtained. The results show that a M_W5.0 event at 03:16 (UTC) on 6 July is a direct foreshock of the M_W7.1 mainshock. It is likely related to barriers on the northwest-striking fault. The M_W6.4 event on 4 July is characterized as a complex conjugate rupture. Notably, a magnitude 4.0 event occurred on the northwest-striking fault before the M_W6.4 event, establishing it as a direct foreshock. The Ridgecrest sequence is predominantly influenced by northwest fault activity. It first caused small fractures on the northwest-striking fault. Then, it triggered conjugate slips on the southwest-striking fault. Lastly, it led to larger ruptures on the northwest-striking fault. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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21 pages, 14807 KiB

Open AccessArticle

Multimodal Non-Extensive Frequency-Magnitude Distributions and Their Relationship to Multi-Source Seismicity

by Erick de la Barra, Pedro Vega-Jorquera and Sérgio Luiz E. F. da Silva

Entropy 2024, 26(12), 1040; https://doi.org/10.3390/e26121040 - 30 Nov 2024

Viewed by 803

Abstract

We investigate multimodal seismicity by analyzing it as the result of multiple seismic sources. We examine three case studies: the Redoubt and Spurr regions in Alaska, where volcanic and subduction-related seismicity occur, and the Kii Peninsula in Japan, where shallow and deep earthquakes [...] Read more.

We investigate multimodal seismicity by analyzing it as the result of multiple seismic sources. We examine three case studies: the Redoubt and Spurr regions in Alaska, where volcanic and subduction-related seismicity occur, and the Kii Peninsula in Japan, where shallow and deep earthquakes are clearly separated. To understand this phenomenon, we perform spatial, temporal, and magnitude analyses. Our application of non-extensive statistical mechanics shows that multimodal models provide a significantly better fit than unimodal ones. We identify patterns in the distributions of time between events and distances between events using multimodal Tsallis q-gamma distributions. In addition, we use the multimodal Sotolongo–Costa model to analyze the magnitude distribution, which effectively captures the complex interactions that may explain the observed lack of fractality in multimodal seismicity. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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16 pages, 2116 KiB

Open AccessArticle

Visibility Graph Investigation of the Shallow Seismicity of Lai Chau Area (Vietnam)

by Luciano Telesca, Anh Tuan Thai, Dinh Trong Cao and Thanh Hai Dang

Entropy 2024, 26(11), 932; https://doi.org/10.3390/e26110932 - 31 Oct 2024

Viewed by 930

Abstract

In this study, the topological properties of the shallow seismicity occurring in the area around the Lai Chau hydropower plant (Vietnam) are investigated by using visibility graph (VG) analysis, a well-known method to convert time series into networks or graphs. The relationship between [...] Read more.

In this study, the topological properties of the shallow seismicity occurring in the area around the Lai Chau hydropower plant (Vietnam) are investigated by using visibility graph (VG) analysis, a well-known method to convert time series into networks or graphs. The relationship between the seismicity and reservoir water level was analyzed using Interlayer Mutual Information (IMI) and the Frobenius norm, both applied to the corresponding VG networks. IMI was used to assess the correlation between the two variables, while the Frobenius norm was employed to estimate the time delay between them. The total seismicity, which resulted in an

M \geq 0.8

with a b-value of 0.86, is characterized by a

k - M

slope of ≈9.1. Analyzing the variation of the seismological and topological parameters of the seismicity relative to the distance from the center of the Lai Chau reservoir revealed the following features: (1) the b-value fluctuates around a mean value of 1.21 at distances of up to 10–11 km, while, for distances larger than 25–30 km, it tends to the value of 0.86; (2) the maximum IMI between the monthly number of earthquakes and the monthly mean water level occurs at a distance of 9–11 km, showing a distance evolution similar to that of the b-value; (3) at these distances from the center of the reservoir, the time lag between the earthquake monthly counts and the monthly water level mean is 9–10 months; (4) the relationship between the b-value and the

k - M

slope suggests that the

k - M

slope depends on the number of earthquakes within a 22 km radius from the center of the dam. Our study’s findings offer new insights into the complex dynamics of seismicity occurring around reservoirs. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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17 pages, 4318 KiB

Open AccessArticle

Prognostic Properties of Instantaneous Amplitudes Maxima of Earth Surface Tremor

by Alexey Lyubushin and Eugeny Rodionov

Entropy 2024, 26(8), 710; https://doi.org/10.3390/e26080710 - 21 Aug 2024

Cited by 1 | Viewed by 1459

Abstract

A method is proposed for analyzing the tremor of the earth’s surface, measured by GPS, in order to highlight prognostic effects. The method is applied to the analysis of daily time series of vertical displacements in Japan. The network of 1047 stations is [...] Read more.

A method is proposed for analyzing the tremor of the earth’s surface, measured by GPS, in order to highlight prognostic effects. The method is applied to the analysis of daily time series of vertical displacements in Japan. The network of 1047 stations is divided into 15 clusters. The Huang Empirical Mode Decomposition (EMD) is applied to the time series of the principal components from the clusters, with subsequent calculation of instantaneous amplitudes using the Hilbert transform. To ensure the stability of estimates of the waveforms of the EMD decomposition, 1000 independent additive realizations of white noise of limited amplitude were averaged before the Hilbert transform. Using a parametric model of the intensities of point processes, we analyze the connections between the instants of sequences of times of the largest local maxima of instantaneous amplitudes, averaged over the number of clusters and the times of earthquakes in the vicinity of Japan with minimum magnitude thresholds of 5.5 for the time interval 2012–2023. It is shown that the sequence of the largest local maxima of instantaneous amplitudes significantly more often precedes the moments of time of earthquakes (roughly speaking, has an “influence”) than the reverse “influence” of earthquakes on the maxima of amplitudes. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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