# Modeling Locations with Enhanced Earth’s Crust Deformation during Earthquake Preparation near the Kamchatka Peninsula

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## Abstract

**:**

## 1. Introduction

## 2. Research Significance

## 3. Research Methods

## 4. Simulation of Stress and Strain Fields

## 5. The Results of Computational Experiment

#### 5.1. Earthquake No. 1

#### 5.2. Earthquake No. 2

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic description of the earthquake source model. In the figure: $\alpha $ is the dip angle, $\beta $ is the strike angle, $\delta $ is the angle of displacement direction, C is the hypocenter depth, L is the plane length, W is its width, N is the North direction (the axis is aligned with $OY$), and $\Sigma $ is the fault plane with an equivalent distributed system of double forces with a moment.

**Figure 2.**Schematic representation of an additional coordinate system centered at the earthquake epicenter (asterisk). The dotted line is the projection of the fault plane onto the Earth’s surface ($z=0$).

**Figure 3.**Map of Kamchatka peninsula with location of earthquake epicenters presented in the CMT catalog and occurred during the period from 1 January 1976 to 30 June 2022 (black circles) in the area under the study and location of simulated earthquake epicenters (red squares). Location of earthquake epicenters are shown in scaled part of map. The black triangle on the map indicates the location of the Karymshina observation site.

**Figure 4.**An example of a simultaneous acoustic-deformation anomaly before earthquake No. 1. (

**a**) Variations of rock relative deformation $\epsilon $, (

**b**) variations of deformation rate $\dot{\epsilon}$, (

**c**) variations of acoustic pressure ${P}_{s}$, accumulated over 4 s in the frequency range of 2.0–6.5 kHz.

**Figure 5.**Zones of relative shear deformations on the Earth’s surface $z=0$ simulated for earthquake No. 1. The triangle on the map indicates the location of the Karymshina observation site.

**Figure 6.**Record fragment of acoustic emission in different ranges and rock deformations from 00:00 on 6 October 2009, to 10:00 on 8 October 2009. (

**a**) Variations of acoustic pressure ${P}_{s}$, accumulated over 4 s in the frequency range 2.0–6.5 kHz, (

**b**) change in the strainmeter base $\Delta L$. The red arrow shows the earthquake moment. At the bottom (

**c**–

**e**), enlarged fragments of the rock relative deformation $\epsilon $, the deformation rate $\dot{\epsilon}$, and sound pressure ${P}_{s}$, accumulated over 4 s in the frequency range of 2.0–6.5 kHz, are presented.

**Figure 7.**Zones of relative shear deformations on the Earth’s surface $z=0$ simulated for earthquake No. 2. The triangle on the map indicates the location of the Karymshina observation site.

**Table 1.**Data on nine small-focus earthquakes that occurred during the period from 1 January 1976 to 30 June 2022 in the area under the study (latitude interval: [52${}^{\circ}$, 53${}^{\circ}$], longitude interval: [160${}^{\circ}$, 161${}^{\circ}$]).

No | Date, Time | Coordinates of the Epicenter | Depth, km | ${\mathit{M}}_{\mathit{W}}$ | Strike Angle ^{1}, $\mathit{\beta}$ | Dip Angle ^{1}, $\mathit{\alpha}$ | Angle of Displacement ^{1}, $\mathit{\delta}$ | Focal Mechanism |
---|---|---|---|---|---|---|---|---|

1 | 1977/12/2, 12:57:22.6 | 52.32${}^{\circ}$ N, 160.48${}^{\circ}$ E | 40.0 | 5.6 | 217 | 35 | 96 | |

2 | 1977/12/21, 16:39:40.9 | 52.60${}^{\circ}$ N, 160.52${}^{\circ}$ E | 55.6 | 5.6 | 218 | 38 | 93 | |

3 | 1979/6/25, 18:45:57.2 | 52.68${}^{\circ}$ N, 160.06${}^{\circ}$ E | 57.3 | 5.0 | 210 | 19 | 76 | |

4 | 1979/9/1, 17:54:59.9 | 52.86${}^{\circ}$ N, 160.66${}^{\circ}$ E | 15.0 | 5.5 | 309 | 25 | −150 | |

5 | 1980/1/23, 1:51:49.8 | 52.22${}^{\circ}$ N, 160.69${}^{\circ}$ E | 20.3 | 5.8 | 213 | 26 | 86 | |

6 | 1980/1/23, 2:34:17.6 | 52.25${}^{\circ}$ N, 160.79${}^{\circ}$ E | 15.0 | 5.7 | 192 | 21 | 57 | |

7 | 1980/1/23, 6:52:53.7 | 52.23${}^{\circ}$ N, 160.84${}^{\circ}$ E | 19.6 | 5.5 | 216 | 28 | 90 | |

8 | 1980/1/23, 8:12:31.6 | 52.23${}^{\circ}$ N, 160.65${}^{\circ}$ E | 15.0 | 5.6 | 219 | 21 | 92 | |

9 | 1980/1/23, 10:7:17.1 | 52.26${}^{\circ}$ N, 160.57${}^{\circ}$ E | 17.2 | 5.2 | 205 | 22 | 77 |

^{1}Degree measures of the angle are given.

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**MDPI and ACS Style**

Gapeev, M.; Marapulets, Y.
Modeling Locations with Enhanced Earth’s Crust Deformation during Earthquake Preparation near the Kamchatka Peninsula. *Appl. Sci.* **2023**, *13*, 290.
https://doi.org/10.3390/app13010290

**AMA Style**

Gapeev M, Marapulets Y.
Modeling Locations with Enhanced Earth’s Crust Deformation during Earthquake Preparation near the Kamchatka Peninsula. *Applied Sciences*. 2023; 13(1):290.
https://doi.org/10.3390/app13010290

**Chicago/Turabian Style**

Gapeev, Maksim, and Yuri Marapulets.
2023. "Modeling Locations with Enhanced Earth’s Crust Deformation during Earthquake Preparation near the Kamchatka Peninsula" *Applied Sciences* 13, no. 1: 290.
https://doi.org/10.3390/app13010290