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Through the analysis of different seismic sequence, it is possible to observe that, before a strong earthquake, the values of longitude and latitude of the shocks begin to fluctuate in an abnormal way. The amplitude increases beyond the normal level just before the earthquake occurs, forming an easily identifiable pattern. The purpose of this study is to analyze the anomalous fluctuations of values the longitude and/or latitude during seismic activity and to carry out some simple procedures, reliable enough for the search of attention signals that precede a strong earthquake and in some cases its epicenter. The retrospective analyses carried out on many sequences of earthquake data occurred in different tectonic environments, have shown how all earthquakes were preceded by abnormal fluctuations in the values of longitude and/or latitude. This study describes the graphic and calculation procedures with the aim of obtaining information on the occurrence of the large earthquakes studied. In particular, we have noticed that the earthquake occurs after extreme levels of fluctuation are reached in the series of values analyzed. Through this model, it is possible to recognize elements discriminated during the evolution of the seismic sequence and using them as possible precursors of short-term, strong earthquakes.

Although earthquake forecasting is a highly controversial issue, scientists are continuing to find valuable precursors of earthquakes. Among various precursors, seismicity changes play an important role in intermediate-term forecast study and have been tested for a long period [

By analysing a seismic sequence, it is possible to observe significant fluctuations in the seismological parameters [

In the general scheme, we can see that, before a strong earthquake, the amplitude of fluctuation of the values of longitude and/or latitude tends to increase and then decrease, showing how earthquakes tend to group according to clusters [

The following analysis procedures have been elaborated after analysing the seismic sequences of 120 earthquakes of M ≥ 7 and 27 of M = 5.8 - 7.0 occurred in various parts of the world and using the earthquake catalogues of the United States (USGS) [

In this study, we have analysed the sequences of major earthquakes, classifying the anomalies of the fluctuation of the values of longitude and latitude. We also propose some graphic and calculation procedures to analyse the values of longitude, latitude and magnitude in the different states in which they can move through time, in order to identify the signals of possible precursors that precede strong earthquakes.

Through the proposed model described this paper, it is possible to study the seismicity of an area and obtain information during the evolution of the seismic sequence. This information can be used as possible short-term precursors of strong earthquakes.

Analysis of the longitude and latitude value series shows abnormal fluctuations before major earthquakes, highlighting the shift from a tendency to disperse values to its clustering or vice versa.

The process of seismicity clustering, and therefore its spatial-time distribution, can be interpreted as a preparatory process for the nucleation of a strong earthquake, in relation to the secondary structures and the main seismic source [

The analysis of seismic sequences shows an evident situation of dispersion of longitude and latitude data, which over time, evolve towards an increasingly structured configuration just before the main event and very structured after the seismic event (aftershock phase).

Moreover, after the formation of the absolute minimum and maximum (or vice versa) of each fluctuation cycle, it is possible to obtain information on the future evolution of the values, apparently random, but which could be the result of the interaction of several close seismogenic sources, and therefore of the earthquakes associated with them [

The first operation consists in identifying, in the series of values, the absolute maximum and minimum of the fluctuation cycle, which represent the points of maximum dispersion. The second operation to be performed is to identify on the graph of the values of longitude (

The areas where the blue and red circles tend to approach can be considered as a point of attention (AP) from which the amplitude of the fluctuations tends to increase. The succession of AP and abnormal fluctuations show how energy earthquakes are partially activated by previous events.

In general, it can be assumed that for large earthquakes (M > 6) the process essentially consists of a repeated and progressive rupture along the same fault, rather than the creation of a new fault segment [

The detailed analysis of the seismic sequences has highlighted the formation of some patterns of fluctuation of the values of longitude and/or latitude that can be grouped into the following categories:

1) CATEGORY A

In this category, it can be noticed how after the abrupt variation of the longitude values, the series develops along an orderly and regular sequence of values.

In

In the 2011 earthquake in Japan, the sequence of values covering the time span between the maximum value and the AP, would have led to the initial breakage point with the earthquake of magnitude 7.3 Mw (foreshock) on March 9, 2011.

The second sequence, which developed in a small area, would have contributed to reach a level of tension such as to trigger the main earthquake that occurred two days later.

A second AP (

The point of attention is formed when the magnitude values of the following earthquakes, are positioned above the trendline, and comparing them with the maximum value of the previous earthquake, allows you to know the phase of accumulation or energy release in place. In fact, if the magnitude values are below the trendline, we are in an energy storage phase, while if they are above, we are in an energy release phase where some earthquakes represent foreshocks.

A similar fluctuation in the values of longitude and latitude occurred in Italy, during the earthquakes of Perugia in 1997 and L’Aquila in 2009.

2) CATEGORY B

In this category, founded in 10% of the analyzed sequences, there is a sharp change in the values of longitude and/or latitude that remains for a given period and a subsequent change in the level of fluctuation after the occurrence of the foreshock.

3) CATEGORY C

This category includes most of the earthquakes analyzed. Longitude and latitude values are placed on different fluctuation levels, where before a strong earthquake there is a sharp fluctuation that causes a change in the longitude value.

An aspect of great importance in the analysis of the historical series of values of magnitude, longitude and latitude consists in the identification of anomalies that anticipate a cycle of energy release or a strong earthquake and therefore, allow to report critical phases.

Oscillators are essential tools for the analysis of seismic sequences capable of providing useful information to examine and interpret the sequences, in order to forecast short-term changes based on space-time of smaller events.

The oscillators are represented by curves, obtained from partially complex formulas, which oscillate around a central value or between a maximum value (top) and a minimum value (bottom) that highlight the different phases of the seismic sequence that develop over time.

The LLMO oscillator provides information on when an earthquake can occur, using the time series of latitude or longitude or magnitude values.

This type of trend has a great importance because the observation of several sections and their comparison allows to define an informative signal.

In fact, this feature allows us to understand that, when the values seem to no longer respect the trendlines within which they move, we can expect the occurrence of a more or less strong earthquake.

Sometimes the earthquake is preceded by trendlines with a smaller slope during the formation of a cluster and the values are more structured and close to that one of the main shock.

In particular, in the final part, when the system enters a critical phase, the values tend to get very close.

In some sequences, the values in the period before the mainshock, are taken out of the trendlines or their convergence.

The point where the oscillator deviates from the current trend and the values emerge from the trendlines is selected as a warning signal.

In

In Figures 15-18, the overlap of the LLMO oscillator on the series of longitude values, highlights the periods, where there are anomalous fluctuations of the values and/or approaching that can be assumed as attention signals.

The formula for calculating the LLMO oscillator is as follows:

where:

A = ln ( M n − LLMO n − 1 ) (1)

B = ∑ 1 n A (2)

LLMO = B n (3)

LLMO = ∑ 1 n ln ( M − n LLMO n − 1 ) n (4)

M = magnitude, longitude or latitude;

n = number of data;

for n = 1 LLMO_{(n-1)} = 0

The first five LLOM values are assumed to be equal to the sixth value, in order to make the graph easier to read trends:

LLMO ( 1 - 5 ) = LLMO ( 6 ) (5)

The MMA is a variant of Guppy’s Multiple Moving Average (GMMA) [

The moving averages used for the MMA are:

- Short-term: the first series of moving averages has a relatively short period of time. The period of events or days or months (N) used in these moving averages is 3, 5, 7, 10, 12 or 15.

n | M | A | B | LLMO | LLMO_{(1-10)} |
---|---|---|---|---|---|

1 | 4.9 | 1.5892 | 1.5882 | 1.2606 | 1.1710 |

2 | 5 | 1.3189 | 2.9081 | 1.2058 | 1.1710 |

3 | 5.1 | 1.3594 | 4.2676 | 1.1927 | 1.1710 |

4 | 4.6 | 1.2259 | 5.4935 | 1.1719 | 1.1710 |

5 | 4.9 | 1.3158 | 6.8094 | 1.1669 | 1.1710 |

6 | 5.3 | 1.4190 | 8.2284 | 1.1710 | 1.1710 |

7 | 5.1 | 1.3683 | 9.5968 | 1.1708 | 1.1708 |

8 | 4.6 | 1.2323 | 10.8291 | 1.1634 | 1.1634 |

9 | 4.6 | 1.2344 | 12.0635 | 1.1577 | 1.1577 |

10 | 4.8 | 1.2926 | 13.3561 | 1.1556 | 1.1556 |

- Long-term: the second series of moving averages uses longer time periods. The period of events or days or months (N) used in these moving averages is 30, 35, 40, 45, 50 or 60.

- Short-term: is the average of the short-term moving averages 3, 5, 7, 10, 12 (beginning of 15 periods).

- Long-term: is the average of the long-term moving averages 30, 35, 40, 45, 50 (beginning of 50 periods).

The following formula is used to calculate the MMA is:

M M A = M M A ( n − 1 ) + S F ⋅ [ V ( n ) − M M A ( n − 1 ) ] (6)

where:

V_{(}_{n)} = refers to the value of magnitude, longitude, latitude or LLMO;

SF refers to a smoothing factor, which is calculated as follows:

S F = 2 N + 1 (7)

where N represents the period used to calculate by the MMA.

The first MMA_{(}_{N)} value of each period is equal to the value of V_{(N)}.

MMA are applied as an overlap in the LLMO oscillator graph, preferably obtained from the set of magnitude values.

The use of several moving averages at the same time, allows to obtain attention signals and avoid some false signals that the single averages create.

The areas during which the different moving averages overlap, move away or approach, represent signals of attention. The information and attention signals provided by the Multiple Moving Averages (MMA) are as follows:

n | V_{(n) } | MMA_{(3-10)} |
---|---|---|

1 | 2.3 | --- |

2 | 2.2 | --- |

3 | 2.7 | 2.7 |

4 | 2.1 | 2.4 |

5 | 2.0 | 2.2 |

6 | 2.6 | 2.4 |

7 | 2.2 | 2.3 |

8 | 2.1 | 2.2 |

9 | 2.2 | 2.2 |

10 | 2.0 | 2.1 |

n | V_{(n) } | MMA_{(5-10)} |
---|---|---|

1 | 2.3 | --- |

2 | 2.2 | --- |

3 | 2.7 | --- |

4 | 2.1 | --- |

5 | 2.0 | 2.0 |

6 | 2.6 | 2.2 |

7 | 2.2 | 2.2 |

8 | 2.1 | 2.166 |

9 | 2.2 | 2.177 |

10 | 2.0 | 2.118 |

- The areas where the short-term averaging group moves above the long-term averaging group indicate that there is a phase of energy release that could end in a major earthquake.

- The areas where the short-term group falls below the long-term group indicate a phase of energy accumulation that could end with a strong earthquake.

- The areas where there is much separation between the averages, indicate that in the area analyzed is underway a phase of release or accumulation of significant energy, with a development of a significant seismicity.

- The areas in which the groups compress each other or cross, indicate that it is possible to invert the phase in progress. In particular, after a period of energy storage, when the lines start to separate it means that the energy storage phase is over and a phase of energy release could begin.

- The areas in which the short term bands approach those of the long term moving averages and become a thread (they stretch out like lines and almost never come back on themselves), indicate the disappearance of the trend and a standby phase in progress. This circumstance is what indicates that an energy event is possible.

- The areas in which there is a strong upward trend and the group of short term averages is carried over the long term ones (but do not cross) and begin to rise quickly, provide a strong signal of the phase in progress (of energy release). The same concept applies to downward trends (energy storage phase).

Modified Stochastic Oscillator [

This type of oscillator indicates the relative position assumed by the last value of the series analyzed within a given period between 5 and 10 periods that can represent earthquakes, days or months and it is based on the principle that in the phases of rising trend (phase of energy release), the values tend to be stabilized in the upper area of the range and vice versa in the case of falling trend (phase of energy accumulation).

The graph of the OSM is therefore represented by two curves that oscillate in the range 0% - 100%.

The thinner green curve (Figures 21-24) is defined as fast stochastic or 5-period % K-line. It is the most sensitive line to the trend of values, therefore it is the fastest and the most reactive.

The thinnest red curve is called slow stochastic or 10-period D-line %. It is the slowest and represents the simple moving average of the %K-line.

It aims to filter out the erratic movements of the fast stochastic and to generate a crossover effect with the %K line.

In predictive practice, a first signal of attention is given in cases where the medium-term mean is descending and/or when the %K-line crosses the %D-line and vice versa.

In particular, there is a warning signal, when the %D-line is increasing, it is in an area greater than 80% and the K-line is crossed downwards, which simultaneously passes below the value of 80%.

Usually, when the OSM value is less than 20%, it shows an energy storage phase in progress, i.e. a situation that could soon result in the activation of an energy release phase;

when the value of the OSM is higher than 80% it shows an energy release phase in progress, that is a situation that soon could give rise to the activation of an energy storage phase.

The first step in calculating the OSM is to determine the maximum and minimum values for the period considered.

Then we move on to the calculation of %K-line and %D-line with 5 and 10 periods with the following formulas:

% K = C − L m H m − L m ⋅ 100 (8)

( % K − line ) = ∑ 1 N % K N (9)

where

C = last value of the period;

L_{m} = minimum value of the period N;

H_{m} = maximum value of period N;

N = 5

Once the %K-line value is obtained, the %D-line value is calculated, which is a simple moving average a 10 period.

In

The attention signal was generated by crossing the fast and slow stochastic lines (red triangles) and by the magnitude values that were placed above the downward trendline.

In

In

The study of seismic clusters can represent a useful approach for understanding the nucleation phenomenon of strong earthquakes. In fact, the retrospective analysis of the values of longitude, latitude and magnitude of several sequences showed the beginning of a critical state before a strong earthquake that can be exploited as a possible precursor.

Through the proposed model described this paper, it is possible to study the seismicity of an area and obtain information during the evolution of the seismic sequence. This information can be used as possible short-term precursors of strong earthquakes.

In particular, we have noticed that strong earthquakes are preceded by smaller events than in the series of latitude and longitude values generate irregular fluctuations, in which their amplitude increases progressively to a maximum value that depends on the size of the area analysed and the distribution of seismogenic structures.

Usually the strong earthquake occurs after the maximum fluctuation value has been reached, followed by a rapid reduction during which earthquakes tend to group together, forming clusters.

The organization in space and time of the values of longitude and latitude before a strong earthquake can be used, in some cases, to identify the most likely area where the strong earthquake will occur.

To identify significant changes in the values of longitude, latitude and magnitude and establish valid attention signals to be used for the study of earthquake forecasting, simple calculation procedures and graphics have been developed to identify the periods where most likely earthquakes will occur stronger.

Through this model of seismic sequence analysis it has been possible to obtain information that can be exploited as possible precursors of strong earthquakes. In effect the analyses have shown that the procedures developed provide fairly reliable information on the period of occurrence of the large earthquakes studied.

The authors declare no conflicts of interest regarding the publication of this paper.

Riga, G. and Balocchi, P. (2019) Information and Predictive Oscillators of Energy Earthquakes. Open Journal of Earthquake Research, 8, 201-222. https://doi.org/10.4236/ojer.2019.83012