# Variability in the Statistical Properties of Continuous Seismic Records on a Network of Stations and Strong Earthquakes: A Case Study from the Kamchatka Peninsula, 2011–2021

^{1}

^{2}

^{*}

## Abstract

**:**

_{w}= 7.5–8.3 over months to about one year according to observations from the entire network of stations, as well as according to data obtained at groups of continental and non-volcanic stations. A less-pronounced manifestation of coherence effects diagrams plotted from data obtained at coastal and volcanic groups of stations and is apparently associated with the noisiness in seismic records caused by coastal waves and signals of modern volcanic activity. The considered synchronization effects correspond to the author’s conceptual model of seismic noise behavior in preparation of strong earthquakes and data from other regions and can also be useful for medium-term estimates of the place and time of seismic events with M

_{w}≥ 7.5 in the Kamchatka.

## 1. Introduction

_{w}= 8.3 and 9.0 were found according to data of the Japanese F-net network. Such changes showed the evolution of the statistical structure of microseismic oscillations to white noise [8].

## 2. Region, Data, Method

#### 2.1. Network of Stations

#### 2.2. Stations Identification

#### 2.2.1. Northern, Central and Southern Groups of Station

#### 2.2.2. Volcanic Stations

#### 2.2.3. Coastal and Continental Stations

_{2}(period 12.42 h) and O

_{1}(period 25.82 h), are clearly distinguished in the spectra of records from coastal stations [35,36]. Such features of seismic noise records showed a high degree of signal noisiness at coastal stations due to sea tidal waves.

#### 2.3. Strong Earthquakes

_{w}− 1.289 [37] and the calculated radii of level deformations 10

^{−8}(R, km) at preparation of earthquakes with M

_{w}: R = 10

^{0.43⋅Mw}[38], makes it possible to roughly estimate the network sensitivity to the preparation of earthquakes with magnitudes of at least 7–9. For such earthquakes, the maximum sizes of sources are about 60–450 km according to [37]. The radii of deformation sensitivity of 10

^{−8}, equivalent to the areas of earthquake preparation with magnitudes 7–9 by [38], are 1–7 thousand km. Therefore, we believe that the configuration of the operating network (Figure 1) can cover completely or partially the areas of earthquake preparation in magnitude range 7–9. However, a more reasonable estimate of the network sensitivity for earthquake magnitudes can be obtained from experimental data. As will be shown in this study, the method used, based on the existing network of stations, may be sensitive to the preparation for earthquakes with a magnitude of at least 7.5.

#### 2.4. Seismic Noise Parameters

^{h}

^{(t)}: μ(t, δ)~δ

^{h}

^{(t)}, or if there is a limit $h\left(t\right)=\underset{\delta \to 0}{\mathit{lim}}\frac{\mathit{log}\left(\mu \left(t,\delta \right)\right)}{\mathit{log}\left(\delta \right)}$, then the h(t) is called the Hölder-Lipschitz exponent.

_{min}and maximum α

_{max}, such that only for α

_{min}< α < α

_{max}does the set C(α) contain some elements.

_{max}− α

_{min}, called the singularity spectrum support width, is an important multi-fractal characteristic. In addition, of considerable interest is the argument α* that provides the maximum of the singularity spectrum: F(α*) = max F(α),when α

_{max}≥ α ≥ α

_{min}, called the generalized Hurst exponent. To get the estimates of the multi-fractal characteristics of signals, we used a method based on the analysis of fluctuations after the removal of scale-dependent trends [41] by polynomials of the 8th order.

#### 2.4.1. Minimum Normalized Entropy of Squared Orthogonal Wavelet Coefficients En

_{j}

^{(k)}are the wavelet coefficients of the analyzed signal x(t), t = 1, ..., L are a discrete indexes numbering successive values of the time series.

_{k}is the number of wavelet coefficients at the level of detail with number k.

^{n}, then m = n, M

_{k}= 2

^{(n−k)}. If the length L is not equal to a power of two, then the signal x(t) is padded with zeros to the minimum length N, which is greater than or equal to L: N = 2

^{n}≥ L.

^{(n−k)}of all wavelet coefficients at level k, only L·2

^{−k}coefficients correspond to the decomposition of the real signal, while the remaining coefficients are equal to zero due to the addition of zeros to the signal x(t).

_{k}= L·2

^{−k}, and only “real” coefficients are used to calculate the entropy. The number N

_{r}is equal to the number of “real” coefficients, that is, ${N}_{r}={\displaystyle \sum}_{k=1}^{m}{M}_{k}$. By construction, 0 ≤ En ≤ 1.

#### 2.4.2. Visualization of the Seismic Noise Parameters Distribution

**Table 3.**Earthquakes with M

_{w}= 7.2–8.3 (http://earthquake.usgs.gov/earthquakes (accessed on 31 December 2021)).

No | Date dd.mm.yyyy Name | Time hh:mm:ss | Coordinates, deg. N° E° | H, km | M_{w} | M_{0}, N∙m∙10 ^{20} |
---|---|---|---|---|---|---|

1 | 24 May 2013 Sea of Okhotsk | 05:44:48 | 54.89 153.22 | 598 | 8.3 | 38.4 |

2 | 30 January 2016 Zhupanovskoe | 03:25:12 | 53.98 158.55 | 177 | 7.2 | 0.8 |

3 | 17 July 2017 Near Islands Aleutian | 23:34:13 | 54.44 168.86 | 10 | 7.7 | 5.2 |

4 | 20 December 2018 Uglovoye Podnyatiye | 17:01:55 | 55.10 164.70 | 17 | 7.3 | 1.0 |

5 | 25 March 2020 North Kuril | 02:49:21 | 48.96 158.70 | 58 | 7.5 | 2.0 |

#### 2.5. Spectral Measure of Coherent Behavior of Seismic Noise Parameters

^{−1}; τ is the time coordinate of the right end of the sliding time window, consisting of a given number of samples of the time series; μ

_{j}(τ, ω) is the canonical coherence of the j-th scalar time series, which characterizes the degree of connection of this series with all other series that make up the multidimensional series.

_{j}(τ, ω)|

^{2}is a generalization of the quadratic coherence spectrum between two signals, where the first signal represents the j-th scalar time series, and the second signal is a vector that reflects the overall changes of the remaining three series.

_{j}(τ, ω) satisfies the inequalities 0 ≤ |μ

_{j}(τ, ω)| ≤ 1, from which it follows that the closer the value |μ

_{j}(τ, ω)| to unity, the more linearly related are the variations at the frequency ω in the time window with the coordinate τ of the j-th time series, with similar variations in the other three time series.

^{4}samples. For this multidimensional series, a time-frequency diagram of the evolution of the spectral measure of coherence was constructed in successive non-overlapping time windows 365 samples long, which provides 10,000 independent estimates of ν(τ, ω). The resulting time-frequency diagram was a chaotic pattern, for which the average value of random bursts of the coherence measure is 0.008, the median is 0.006, and the maximum value is 0.15. The length of the time window corresponded to the same length of 365 samples as in construction of the diagrams in Figure 5 and Figure 6.

#### 2.6. Conceptual Model Used in Data Interpretation

^{∗}and the β value, as well as the low values of the minimum normalized entropy of the squared orthogonal wavelet coefficients En, are due to an increase in the number of outliers in the original seismic records. For example, an increase in the number of outliers in the time series of a continuous seismic signal can occur when seismicity is activated during the aftershock stages of strong earthquakes. On the other hand, the consolidation of individual elements of the geological environment and the weakening of near-surface movements may manifest itself in a decrease in the number of high-amplitude outliers in seismic records and will be reflected in high values of entropy En and low values of Δα, α

^{∗}, and β.

_{w}= 8.3 and 9.0 in Japan [8].

## 3. Data Analysis

#### 3.1. Variability of Seismic Noise Parameters’ Spatiotemporal Distribution

_{w}= 7.2–8.3 occurred in the latitude range 54–58° N (Table 3), identified in previous authors’ publications [35,36] as “dangerous” for the emergence of strong earthquakes with M

_{w}≥ 7.5. In this case, the magnitudes of two events out of four, the Sea of Okhotsk (No. 1 in Table 3) and Near Islands Aleutian (No. 3 in Table 3), corresponded to the magnitude range of expected events. The Sea of Okhotsk deep-focus earthquake on 24 May 2013, with M

_{w}= 8.3 was the strongest seismic event in the region of the Kamchatka Peninsula during detailed seismological observations since 1961 [20]. Its seismic moment exceeded by 7–48 times the seismic moments of all other considered earthquakes (Table 3)

**.**

_{w}= 7.5 (No. 5 in Table 3) occurred to the south of the indicated area.

#### 3.2. Synchronization Signals in Noise Parameter Changes

_{w}≥ 7.5 (No. 1, 3, 5 in Table 3). The maximum amplitudes, ν(τ, ω) ≥ 0.45, were recorded before the strongest Sea of Okhotsk earthquake (No. 1 in Table 3, M

_{w}= 8.3) for half a year. Before the two considered earthquakes with M

_{w}< 7.5, similar signals of spectral coherence growth either did not appear (Zhupanovskoe, No. 2 in Table 3, M

_{w}= 7.2), or were much less pronounced (Uglovoye Podnyatiye, No. 4 in Table 3, M

_{w}= 7.3).

_{w}≥ 7.5 (No. 1, 5 in Table 3) is very weak. This may be due to the fact that 67% of the stations in the southern group (six stations out of nine, Table 2) are coastal, and seismic records from them are noisy due to sea waves. In addition, the Ebeko volcano, located 6 km from the SKR station, has been erupting since 2019, and volcanic microseisms could mask the North Kuril earthquake preparation. However, it should be noted that Figure 5f shows an increase in the synchronization of seismic noise parameters during all 11 years of observations. The most pronounced increase in synchronization has manifested itself over the past year and a half, from mid-2020 to the end of 2021. This may indicate an increased danger of strong earthquakes in the southern part of the region under consideration. This assumption is consistent with the spatial distribution of noise parameters on maps for 2019–2021 (Figure 4, maps on the right), showing the increased danger of strong earthquakes in the southern part of the region.

_{w}≥ 7.5 on the diagrams based on data from all network stations, as well as data from non-volcanic and continental stations (Figure 5a–c), are quite pronounced in the frequency range 0.15–0.35 day

^{−1}(periods 3–7 days).

## 4. Discussion and Conclusions

_{w}= 7.2–8.3.

_{w}= 7.5 occurred on 25 March 2020, near this area.

_{w}= 7.7.

_{w}≥ 7.5 (Table 3), a noise parameter synchronization effect was found by increased values of the spectral measure of coherent behavior of noise parameters’ time series constructed from the data from the entire network and for groups of stations least affected by volcanic activity and sea waves. A property of this type of synchronization is an increase in the measure of spectral coherence ν(τ, ω) ≥ 0.3 during the time period from several months to a few years before seismic events.

_{w}≥ 7.5 manifests itself on the time-frequency diagrams of the evolution of spectral coherence as a time-compact increase in the spectral coherence at frequencies of 0.15–0.35 day

^{−1}. Meanwhile, bursts of increase of spectral coherence of presumably volcanic and marine genesis can manifest in a wider frequency range.

_{w}≥ 7.5 in the region of the Kamchatka Peninsula.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Map of the Kamchatka Peninsula showing the location of seismic stations (Table 1), earthquake epicenters with M

_{w}= 7.2–8.3, and tectonic plate boundaries: 1—seismic stations with codes indicated: blue designates coastal stations, and white designates continental stations; 2—earthquake epicenters; 3—areas of earthquake sources according to [20,21,22,23,24]; 4—boundaries of the northern, central, and southern groups of stations (from top to bottom); 5—northwestern and northeastern boundaries of the considered area of the Pacific Oceanic Plate (PA); 6—boundary of the North American continental plate (NA) with PA and small lithospheric plates Beringia (BE) and Okhotsk (OK) [25,26]. White arrows indicate the direction of PA movement; numbers—the speed of TO movement [27].

**Figure 2.**Location map of seismic stations and active volcanoes: 1—non-volcanic station, 2—volcanic station, 3—active volcano near which a seismic station is located, 4—active volcano at rest or near which there is no seismic station, 2011–2021.

**Figure 3.**Determination of the coloring area on maps showing the distribution of noise parameters. (

**a**) circular areas with a radius of 120 km around seismic stations; (

**b**) corresponding colored area (see text for explanation).

**Figure 4.**Maps of seismic noise parameters’ distribution for 2011–2018 (left) and for 2019–2021 (right). (

**a**) Generalized Hurst exponent α*; (

**b**) singularity spectrum support width ∆α; (

**c**) wavelet-based spectral exponent β; and (

**d**) normalized entropy of the squared orthogonal wavelet coefficients En. The white circles show the earthquake epicenters (Table 3) that occurred over the corresponding time periods. Rectangles with a coordinate grid show the area of noise parameters’ calculation. The coloring corresponding to the color scales was carried out for the area at a distance of no more than 120 km from the edge stations of the network (Figure 3).

**Figure 5.**Time-frequency diagrams of the spectral measure of coherence of 4-dimensional time series of seismic noise parameters ν(τ, ω) in comparison with earthquakes (Table 3) according to data from (

**a**) the entire network of stations, (

**b**) non-volcanic, and (

**c**) continental stations, as well as for the (

**d**) northern, (

**e**) central, and (

**f**) southern groups of stations, 2011–2021. Synchronization effects of seismic noise parameters are distinguished by the values ν(τ, ω) ≥ 0.3.

**Figure 6.**Time-frequency diagrams of the spectral measure of coherence of 4-dimensional time series of seismic noise parameters ν(τ, ω) in comparison with occurred earthquakes (Table 3) constructed from (

**a**) the group of volcanic stations and (

**b**) the group of coastal stations, 2011–2021.

**Table 1.**Seismic stations, their equipment [28], and the belonging of stations to selected groups.

Seismic Station | Station Code | Coordinates | Equipment | Frequency Range/ Registration Frequency, Hz | Belonging to Dedicated Groups of Stations | ||||
---|---|---|---|---|---|---|---|---|---|

N ° | E ° | h asl, m | |||||||

Avacha | AVH | 53.264 | 158.740 | 942 | CMG-6TD | 0.033–40/100 | southern | continental | volcanic |

Bering | BKI | 55.194 | 165.984 | 12 | CMG-3TB | 0.0083–40/100 | central | coastal | non-volcanic |

Dal’niy | DAL | 53.031 | 158.754 | 57 | CMG-6TD | 0.033–40/100 | southern | coastal | non-volcanic |

Institut | IVS | 53.066 | 158.608 | 160 | CMG-3TB | 0.0083–40/100 | southern | coastal | non-volcanic |

Kamenskaya | KMSK | 62.467 | 166.206 | 40 | CMG-6TD | 0.033–40/100 | northern | continental | non-volcanic |

Karymshina | KRM | 52.828 | 158.131 | 100 | CMG-3TB | 0.033–40/100 | southern | continental | non-volcanic |

Kirisheva | KIR | 55.953 | 160.342 | 1470 | CMG-6TD | 0.033–40/100 | central | continental | volcanic |

Klyuchi | KLY | 56.317 | 160.857 | 35 | KS2000 | 0.01–40/100 | central | continental | volcanic |

Kozyrevsk | KOZ | 56.058 | 159.872 | 60 | CMG-6TD | 0.033–40/100 | central | continental | volcanic |

Krutoberegovo | KBG | 56.258 | 162.713 | 30 | CMG-3TB | 0.0083–40/100 | central | coastal | non-volcanic |

Ossora | OSS | 59.262 | 163.072 | 35 | CMG-6TD | 0.033–40/100 | northern | coastal | non-volcanic |

Palana | PAL | 59.094 | 159.968 | 70 | STS-2 | 0.0083–40/100 | northern | coastal | non-volcanic |

Pauzhetka | PAU | 51.468 | 156.815 | 130 | CMG-6TD | 0.033–40/100 | southern | continental | non-volcanic |

Petropavlovsk | PET | 53.023 | 158.650 | 100 | STS-1 | 0.0027–10/20 | southern | coastal | non-volcanic |

Severo-Kuril’sk | SKR | 50.670 | 156.116 | 30 | CMG-3TB | 0.0083–40/100 | southern | coastal | volcanic |

Tigil | TIGL | 57.765 | 158.671 | 115 | CMG-6TD | 0.033–40/100 | northern | continental | non-volcanic |

Tilichiki | TL1 | 60.446 | 166.145 | 25 | CMG-3TB | 0.0083–40/100 | northern | coastal | non-volcanic |

Tumrok | TUMD | 55.203 | 160.399 | 478 | CMG-6TD | 0.033–40/100 | central | continental | volcanic |

Khodutka | KDT | 51.809 | 158.077 | 22 | CMG-6TD | 0.033–40/100 | southern | coastal | non-volcanic |

Shipunskiy | SPN | 55.106 | 160.011 | 95 | CMG-6TD | 0.033–40/100 | southern | coastal | non-volcanic |

Esso | ESO | 55.932 | 158.695 | 490 | CMG-6TD | 0.033–40/100 | central | continental | non-volcanic |

**Table 2.**Distribution of stations into groups, taking into account the number of stations affected by sea waves (coastal stations) and volcanic activity (volcanic stations).

Station Groups Influence Factors * | All Stations, N= 21 (100%) | Northern, N = 5 (100%) | Central, N = 7 (100%) | Southern, N = 9 (100%) | Non-Volcanic, N = 15 (100%) |
---|---|---|---|---|---|

coastal, n (%) | 11 (52%) | 3 (60%) | 2 (29%) | 6 (67%) | 10 (67%) |

volcanic, n (%) | 6 (29%) | – | 4 (57%) | 2 (22%) | – |

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Kopylova, G.; Kasimova, V.; Lyubushin, A.; Boldina, S. Variability in the Statistical Properties of Continuous Seismic Records on a Network of Stations and Strong Earthquakes: A Case Study from the Kamchatka Peninsula, 2011–2021. *Appl. Sci.* **2022**, *12*, 8658.
https://doi.org/10.3390/app12178658

**AMA Style**

Kopylova G, Kasimova V, Lyubushin A, Boldina S. Variability in the Statistical Properties of Continuous Seismic Records on a Network of Stations and Strong Earthquakes: A Case Study from the Kamchatka Peninsula, 2011–2021. *Applied Sciences*. 2022; 12(17):8658.
https://doi.org/10.3390/app12178658

**Chicago/Turabian Style**

Kopylova, Galina, Victoriya Kasimova, Alexey Lyubushin, and Svetlana Boldina. 2022. "Variability in the Statistical Properties of Continuous Seismic Records on a Network of Stations and Strong Earthquakes: A Case Study from the Kamchatka Peninsula, 2011–2021" *Applied Sciences* 12, no. 17: 8658.
https://doi.org/10.3390/app12178658