Guest Editorial: Special Issue on “Lithosphere Dynamics and Earthquake Hazard Forecasting”

Brilliant scientific ideas coupled with quantitative modelling and laboratory experiments have determined progress in seismology and geodynamics for the last several decades. Methods of nonlinear geophysics, inverse problems, mathematical statistics, extreme theory and data analysis have improved knowledge of the structure of the Earth’s lithosphere, earthquake generation, predictability, and seismic hazards. This Special Issue of Surveys in Geophysics “Lithosphere Dynamics and Earthquake Hazard Forecasting” is dedicated to the 100th anniversary of the birth of Professor Vladimir (Volodya) Keilis-Borok (1921–2013), a distinguished mathematical geophysicist. For more than 60 years, the topics of seismology, nonlinear dynamics of the lithosphere, and earthquake prediction were central in Keilis-Borok's research.Open Access funding enabled and organized by Projekt DEAL.https://www.springer.com/journal/10712hj2022Geolog

The Horizontal Tunnelability Graph is Dual to Level Set Trees

Time series data, reflecting phenomena like climate patterns and stock prices, offer key insights for prediction and trend analysis. Contemporary research has independently developed disparate geometric approaches to time series analysis. These include tree methods, visibility algorithms, as well as persistence-based barcodes common to topological data analysis. This thesis enhances time series analysis by innovatively combining these perspectives through our concept of horizontal tunnelability. We prove that the level set tree gotten from its Harris Path (a time series), is dual to the time series' horizontal tunnelability graph, itself a subgraph of the more common horizontal visibility graph. This technique extends previous work by relating Merge, Chiral Merge, and Level Set Trees together along with visibility and persistence methodologies. Our method promises significant computational advantages and illuminates the tying threads between previously unconnected work. To facilitate its implementation, we provide accompanying empirical code and discuss its advantages

Guest editorial : Special issue on lithosphere dynamics and earthquake hazard forecasting

Brilliant scientific ideas coupled with quantitative modelling and laboratory experiments have determined progress in seismology and geodynamics for the last several decades. Methods of nonlinear geophysics, inverse problems, mathematical statistics, extreme theory and data analysis have improved knowledge of the structure of the Earth’s lithosphere, earthquake generation, predictability, and seismic hazards. This Special Issue of Surveys in Geophysics “Lithosphere Dynamics and Earthquake Hazard Forecasting” is dedicated to the 100th anniversary of the birth of Professor Vladimir (Volodya) Keilis-Borok (1921–2013), a distinguished mathematical geophysicist. For more than 60 years, the topics of seismology, nonlinear dynamics of the lithosphere, and earthquake prediction were central in Keilis-Borok's research.Open Access funding enabled and organized by Projekt DEAL.https://www.springer.com/journal/10712hj2022Geolog

Dynamics of drainage under stochastic rainfall in river networks

We consider a linearized dynamical system modelling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes and streams as well as their spatial variation. The resulting stochastic process is a piece-wise deterministic Markov process of the Orstein-Uhlembeck type. We provide an explicit formula for the Laplace transform of the invariant density of streamflow in terms of the geophysical parameters of the river network and the statistical properties of the precipitation field. As an application, we include novel formulas for the invariant moments of the streamflow at the watershed's outlet, as well as the asymptotic behavior of extreme discharge events