Informational analysis of Langevin equation of friction in earthquake rupture processes

Wu, Tsung-Hsi; Chen, C. C.; Lovallo, Michele; Telesca, Luciano

doi:10.1063/1.5092552

Cited by 7 publications

(5 citation statements)

References 60 publications

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“…By the combination of FIM and Shannon entropy power ( N X ), being defined through an exponential transformation of SE, the Fisher–Shannon (FS) information plane can be derived, where the discrimination of different dynamics governing the same time series could be carried out. The FS information plane was applied, for instance, to investigate the physical quantities of Langevin equation of friction in earthquake rupture processes [ 29 ] and the seismic waves of strong earthquakes [ 30 ]. In this paper, the satellite NDVI time series of Suomi-NPP VIIRS that were extracted from four different study sites were analyzed using the MFDFA and FS to investigate the changes of vegetation dynamics that are induced by the Camp Fire (California, USA, 2018).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Multifractal and Organization/Order Structure in Suomi-NPP VIIRS Normalized Difference Vegetation Index Series of Wildfire Affected and Unaffected Sites by Using the Multifractal Detrended Fluctuation Analysis and the Fisher–Shannon Analysis

Song

Lovallo

et al. 2020

Entropy

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The analysis of vegetation dynamics affected by wildfires contributes to the understanding of ecological changes under disturbances. The use of the Normalized Difference Vegetation Index (NDVI) of satellite time series can effectively contribute to this investigation. In this paper, we employed the methods of multifractal detrended fluctuation analysis (MFDFA) and Fisher-Shannon (FS) analysis to investigate the NDVI series acquired from the Visible Infrared Imaging Radiometer Suite (VIIRS) of the Suomi National Polar-Orbiting Partnership (Suomi-NPP). Four study sites that were covered by two different types of vegetation were analyzed, among them two sites were affected by a wildfire (the Camp Fire, 2018). Our findings reveal that the wildfire increases the heterogeneity of the NDVI time series along with their organization structure. Furthermore, the fire-affected and fire-unaffected pixels are quite well separated through the range of the generalized Hurst exponents and the FS information plane. The analysis could provide deeper insights on the temporal dynamics of vegetation that are induced by wildfire. Entropy 2020, 22, 415 2 of 16Under the influence of wildfires, the vegetation dynamics can be more complicated because of their interactions with biomass, soil, atmosphere, climate, and so on [8]. Deeper investigations need to be conducted at different spatial-temporal scales in conjunction with the local, regional, and global levels in order to assess the impact of fires on the vegetation communities [9]. Fortunately, the development of satellite remote sensing provides an excellent means of the continuous observation for the natural biomass [10,11]. Massive long-term data records are captured via multiple satellite sensors, of which the Suomi National Polar-Orbiting Partnership (Suomi-NPP) satellites were launched on October 28, 2011 as the new generation system to undertake the mission of the previous Moderate Resolution Imaging Spectroradiometer (MODIS) of Earth Observing System (EOS) satellites, which can further provide continuous data records and observations. For the Suomi-NPP sensors, the sensor of Visible Infrared Imaging Radiometer Suite (VIIRS) is designed to collect the measurements of spectral domain from 0.3µm to 14µm for the Earth, which advances its increasing applications in wildfires [12,13].Various vegetation indices (VI) have been developed to characterize the status of surface biomass, among which the Normalized Difference Vegetation Index (NDVI) [14] is generally used to quantify the status of vegetation. It is defined as the ratio between the reflectance in the spectral domain of visible red and near-infrared; this definition minimizes the noise that is related to different bands and diminishes the effects induced by clouds, shadows, sun, atmospheric attenuation, etc. [15]. The primary land product of VIIRS, the VNP13A1, records the NDVI series since 2012 all over the world, providing abundant data of the long-term satellite time series of the vegetation in the region of interest (ROI)....

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Section: Introductionmentioning

confidence: 99%

Analysis of Multifractal and Organization/Order Structure in Suomi-NPP VIIRS Normalized Difference Vegetation Index Series of Wildfire Affected and Unaffected Sites by Using the Multifractal Detrended Fluctuation Analysis and the Fisher–Shannon Analysis

Song

Lovallo

et al. 2020

Entropy

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“…Other major types of SDE, including the Wiener process, Ornstein-Uhlenbeck process, and Cox-Ingersoll-Ross process, do not show the properties because they do not have any termination mechanism therein. Therefore, a model with other types of SDE 22 is inherantly unable to explain EL1 and EL4, and the Bessel process is a prime candidate for our purpose. The squared Bessel process is another candidate, but it is essentially the same as the Bessel process because its square root is a solution of Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Stochastic differential equation (SDE)-based models have been employed in the field of earthquake source physics 20 – 22 . Matthews et al 20 and Ide 21 modeled recurrent and slow earthquakes, respectively, as Brownian motion.…”

Section: Introductionmentioning

confidence: 99%

“…On recurrent regular earthquakes 20 , they modeled a seismic cycle with a time scale longer than the characteristic time scales of each event, and the properties of STFs were not considered. Wu et al 22 assumed that the generalized Langevin equation can model the equation of motion for the fault slip rate. Although their model was based on some physical properties of dynamic friction, their solution was Brownian motion, which cannot satisfy the non-negativeness (EL1) or the -like spectrum (EL3).…”

Section: Introductionmentioning

confidence: 99%

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Source time functions of earthquakes based on a stochastic differential equation

Hirano

2022

Sci Rep

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Source time functions are essential observable quantities in seismology; they have been investigated via kinematic inversion analyses and compiled into databases. Given the numerous available results, some empirical laws on source time functions have been established, even though they are complicated and fluctuated time series. Theoretically, stochastic differential equations, including a random variable and white noise, are suitable for modeling complicated phenomena. In this study, we model source time functions as the convolution of two stochastic processes (known as Bessel processes). We mathematically and numerically demonstrate that this convolution satisfies some of the empirical laws of source time functions, including non-negativity, finite duration, unimodality, a growth rate proportional to $$t^3$$ t 3 , $$\omega ^{-2}$$ ω - 2 -type spectra, and frequency distribution (i.e., the Gutenberg–Richter law). We interpret this convolution and speculate that the stress drop rate and fault impedance follow the same Bessel process.

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“…The Fisher-Shannon method applied to the geoelectrical data enabled the identification of long-term deformation processes in the Taiwan orogeny [23]. Moreover, they were utilized to elucidate laboratory and theoretical earthquake rupture models [24].…”

Section: Introductionmentioning

confidence: 99%

Fisher–Shannon Investigation of the Effect of Nonlinearity of Discrete Langevin Model on Behavior of Extremes in Generated Time Series

Telesca,

Czechowski

2023

Entropy

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Diverse forms of nonlinearity within stochastic equations give rise to varying dynamics in processes, which may influence the behavior of extreme values. This study focuses on two nonlinear models of the discrete Langevin equation: one with a fixed diffusion function (M1) and the other with a fixed marginal distribution (M2), both characterized by a nonlinearity parameter. Extremes are defined according to the run theory with thresholds based on percentiles. The behavior of inter-extreme times and run lengths is examined by employing Fisher’s Information Measure and the Shannon Entropy. Our findings reveal a clear relationship between the entropic and informational measures and the nonlinearity of model M1—these measures decrease as the nonlinearity parameter increases. Similar relationships are evident for the M2 model, albeit to a lesser extent, even though the background data’s marginal distribution remains unaffected by this parameter. As thresholds increase, both the values of Fisher’s Information Measure and the Shannon Entropy also increase.

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Informational analysis of Langevin equation of friction in earthquake rupture processes

Cited by 7 publications

References 60 publications

Analysis of Multifractal and Organization/Order Structure in Suomi-NPP VIIRS Normalized Difference Vegetation Index Series of Wildfire Affected and Unaffected Sites by Using the Multifractal Detrended Fluctuation Analysis and the Fisher–Shannon Analysis

Analysis of Multifractal and Organization/Order Structure in Suomi-NPP VIIRS Normalized Difference Vegetation Index Series of Wildfire Affected and Unaffected Sites by Using the Multifractal Detrended Fluctuation Analysis and the Fisher–Shannon Analysis

Source time functions of earthquakes based on a stochastic differential equation

Fisher–Shannon Investigation of the Effect of Nonlinearity of Discrete Langevin Model on Behavior of Extremes in Generated Time Series

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