# Unveiling Informational Properties of the Chen-Ouillon-Sornette Seismo-Electrical Model

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## Abstract

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## 1. Introduction

## 2. COS Seismo-Electrical Model

## 3. FS Method

## 4. Results

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the Chen–Ouillon–Sornette (COS) seismo-electrical model (originated from Chen et al. [46]. For the spring-block system, ${v}_{L}$ is the velocity of the loading plate; ${K}_{C}$ and ${K}_{L}$ are the spring stiffness. For the RLC-type circuit, r and c are the block resistance and capacitance, respectively; R and L are the earth resistance and inductance surrounding the blocks, respectively; q is the stored electrical charge in one block; ${i}_{r}$, ${i}_{c}$, and I are the currents; ${V}_{in}$ is the stress-induced voltage. Subscript k means the index of the blocks. ${V}_{g}$ is the grounding voltage and set to be 0 V by convention.

**Figure 3.**(

**a**) Time series of the voltages simulated under the electrical parameters of $\widehat{r}=5$, $\widehat{L}=5$, and $\widehat{c}=0.001$. (

**b**) Power spectral density (PSD) of the time series in (

**a**). The red line represents the fitting of the $1/{f}^{-\beta}$ noise with the scaling of $\beta =1.95$ and the R-squared ${R}^{2}$ of 0.93.

**Figure 4.**Fisher–Shannon (FS) information plane of the simulated voltages: (

**a**) the voltages simulated through the COS model for $\widehat{r}=5$ and $\widehat{L}=5$, while increasing $\widehat{c}$ from 0.001 to 1000. Each case has 10 simulations with different initial block positions; (

**b**) the voltages with the fixed parameters $\widehat{r}=5$ and $\widehat{c}=5$ and the increase of $\widehat{L}$ from 0.001 to 1000; (

**c**) the voltages with the fixed parameters $\widehat{c}=5$ and $\widehat{L}=5$ and the increase of $\widehat{r}$ from 0.001 to 100; (

**d**) FS information plane for all cases from (

**a**) to (

**c**). Red circles represent the simulations of changing $\widehat{c}$, blue triangles changing $\widehat{L}$, and black squares changing $\widehat{r}$.

**Figure 5.**Complexity (${I}_{x}{N}_{x}$) for the simulations of changing $\widehat{c}$ (

**a**), changing $\widehat{L}$ (

**b**), and changing $\widehat{r}$ (

**c**). Each vertical line represents the mean value within one standard error.

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**MDPI and ACS Style**

Chen, H.-J.; Telesca, L.; Lovallo, M.; Chen, C.-C.
Unveiling Informational Properties of the Chen-Ouillon-Sornette Seismo-Electrical Model. *Entropy* **2021**, *23*, 337.
https://doi.org/10.3390/e23030337

**AMA Style**

Chen H-J, Telesca L, Lovallo M, Chen C-C.
Unveiling Informational Properties of the Chen-Ouillon-Sornette Seismo-Electrical Model. *Entropy*. 2021; 23(3):337.
https://doi.org/10.3390/e23030337

**Chicago/Turabian Style**

Chen, Hong-Jia, Luciano Telesca, Michele Lovallo, and Chien-Chih Chen.
2021. "Unveiling Informational Properties of the Chen-Ouillon-Sornette Seismo-Electrical Model" *Entropy* 23, no. 3: 337.
https://doi.org/10.3390/e23030337