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Multifractal Characterization of Seismic Activity in the Provinces of Esmeraldas and Manabí, Ecuador^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Art State: Fractals

## 3. Data Source

## 4. Methodology

#### Multifractal Detrended Fluctuation Analysis (MF-DFA)

_{k}with a length = N, which is a set of k indexes with x

_{k}non-zero values. The series is compact if the values x

_{k}= 0; that is, it is a negligible fraction compared to the total length of the series. For the null components of the series, values are not assigned to the index k.

## 5. Results and Discussion

## 6. Conclusions

- -
- Due to its enormous importance and the need to expand knowledge, multifractal analysis of the seismic activity of the provinces of Esmeraldas and Manabí in Ecuador was carried out by obtaining their multifractal spectra.
- -
- The studied seismic phenomena displayed a dynamic change of heterogeneity towards homogeneity, and from variance to becoming constant during the activation of the replica. This was revealed by a loss of multifractality after a main event.
- -
- The results of this study revealed a persistent behavior of the magnitude and inter-distance series, while the interevent series showed a behavior of fluctuating noise.
- -
- When determining a relationship between the resulting curves, all series appeared biased to the right, which was consistent with r > 1. This indicates that small variations in the series are more dominant than large fluctuations. It seems, also, that such dominance is more intense for the interevent series than the other two, due to the resulting values for each of the series and their respective exponents of Hurst.

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Magnitude | ||||

Width | Asymmetry r | Average h(q) | St. Dev. h(q) | Max. Delta. |

0.55 | 1.23 | 0.8283 | 0.1106 | 0.2396 |

Inter-distance Km | ||||

Width | Asymmetry r | Average h(q) | St. Dev. h(q) | Max. Delta. |

0.56 | 1.94 | 0.7649 | 0.1464 | 0.3579 |

Interevent (min) | ||||

Width | Asymmetry r | Average h(q) | St. Dev. h(q) | Max. Delta. |

1.44 | 2.04 | 1.5562 | 0.5527 | 0.4584 |

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**MDPI and ACS Style**

Cuenca, D.I.; Estévez, J.; García-Marín, A.P.
Multifractal Characterization of Seismic Activity in the Provinces of Esmeraldas and Manabí, Ecuador. *Proceedings* **2019**, *24*, 27.
https://doi.org/10.3390/IECG2019-06196

**AMA Style**

Cuenca DI, Estévez J, García-Marín AP.
Multifractal Characterization of Seismic Activity in the Provinces of Esmeraldas and Manabí, Ecuador. *Proceedings*. 2019; 24(1):27.
https://doi.org/10.3390/IECG2019-06196

**Chicago/Turabian Style**

Cuenca, David I., Javier Estévez, and Amanda P. García-Marín.
2019. "Multifractal Characterization of Seismic Activity in the Provinces of Esmeraldas and Manabí, Ecuador" *Proceedings* 24, no. 1: 27.
https://doi.org/10.3390/IECG2019-06196