Percolation framework of the Earth's topography

Scaling and Clustering in Southern California Earthquake Sequences: Insights from Percolation Theory

Earthquake activity poses significant risks to both human survival and economic development. However, earthquake forecasting remains a challenge due to the complex, poorly understood interactions that drive seismic events. In this study, we construct an earthquake percolation model to examine the relationships between earthquakes and the underlying patterns and processes in Southern California. Our results demonstrate that the model can capture the spatiotemporal and magnitude characteristics of seismic activity. Through clustering analysis, we identify two distinct regimes: a continuous increase driven by earthquake clustering, and a discontinuous increase resulting from the merging of clusters dominated by large, distinct mega-earthquakes. Notably, in the continuous increase regime, we observe that clusters exhibit a broader spatiotemporal distribution, suggesting long-range and long-term correlations. Additionally, by varying the magnitude threshold, we explore the scaling behavior of earthquake percolation. The robustness of our findings is confirmed through comparison with multiple shuffling tests.

Percolation analysis of spatiotemporal distribution of population in Seoul and Helsinki

Spatiotemporal distribution of urban population is crucial to understand the structure and dynamics of cities. Most studies, however, have focused on the microscopic structure of cities such as their few most crowded areas. In this work, we investigate the macroscopic structure of cities such as their clusters of highly populated areas. To do this, we analyze the spatial distribution of urban population and its intraday dynamics in Seoul and Helsinki with a percolation framework. We observe that the growth patterns of the largest clusters in the real and randomly shuffled population data are significantly different, and highly populated areas during the daytime are denser and form larger clusters than highly populated areas during the nighttime. An analysis of the cluster-size distributions at percolation criticality shows that their power-law exponents during the daytime are lower than those during the nighttime, indicating that the spatial distributions of urban population during daytime and nighttime fall into different universality classes. Finally measuring the area-perimeter fractal dimension of the collection of clusters demonstrates that the fractal dimensions during the daytime are higher than those during the nighttime, indicating that the perimeters of clusters during the daytime are rougher than those during the nighttime. Our findings suggest that even the same city can have qualitatively different spatial distributions of population over time, and propose a way to quantitatively compare the macrostructure of cities based on population distribution data.

Percolation analysis of the atmospheric structure

The atmosphere is a thermo-hydrodynamical complex system and provides oxygen to most animal life at the Earth's surface. However, the detection of complexity for the atmosphere remains elusive and debated. Here we develop a percolation-based framework to explore its structure by using the global air temperature field. We find that the percolation threshold is much delayed compared with the prototypical percolation model and the giant cluster eventually emerges explosively. A finite-size-scaling analysis reveals that the observed transition in each atmosphere layer is genuine discontinuous. Furthermore, at the percolation threshold, we uncover that the boundary of the giant cluster is self-affine, with fractal dimension d_{f}, and can be utilized to quantify the atmospheric complexity. Specifically, our results indicate that the complexity of the atmosphere decreases superlinearly with height, i.e., the complexity is higher at the surface than at the top layer and vice versa, due to the atmospheric boundary forcings. The proposed methodology may evaluate and improve our understanding regarding the critical phenomena of the complex Earth system and can be used as a benchmark tool to test the performance of Earth system models.

Universality class of epidemic percolation transitions driven by random walks

Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a precritical to the postcritical phase is modeled by a percolation problem driven by random walks on a two-dimensional lattice with an extra average number ρ of nonlocal links per site. Using finite-size scaling analysis, we find that the effective exponents of the percolation transitions as well as the corresponding time thresholds, extrapolated to the infinite system size, are ρ dependent. We argue that the ρ dependence of our estimated exponents represents a crossover-type behavior caused by the finite-size effects between the two limiting regimes of the system. We also find that the universal scaling functions governing the critical behavior in every single realization of the model can be well described by the theory of extreme values for the maximum jumps in the order parameter and by the central limit theorem for the transition threshold.

Statistical physics approaches to the complex Earth system

Global warming, extreme climate events, earthquakes and their accompanying socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, multiple interactions and complex structures of the Earth system, the understanding and, in particular, the prediction of such disruptive events represent formidable challenges to both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge of the Earth system, including climate extreme events, earthquakes and geological relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as critical phenomena, network theory, percolation, tipping points analysis, and entropy can be applied to complex Earth systems. Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics concepts and theories can be useful in the field of Earth system science.