Information and Predictive Oscillators of Energy Earthquakes

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.


Introduction
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 By analysing a seismic sequence, it is possible to observe significant fluctuations in the seismological parameters [1] [2] [3], as longitude and/or latitude values recorded shortly before major earthquakes ( Figure 1). These fluctuations generally occur in a disorderly manner, but through analysis with appropriate calculation procedures and graphics it is possible to identify patterns that allow you to understand the processes that precede major earthquakes.
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 [1] [2], whose seismogenic source may be also different from the one that generates the mainshock [2] [3]. This study describes, as usually, a strong earthquake occurs after the amplitude of the fluctuation reaches the maximum value that depends on the size of the area analyzed and the geometry of seismogenic structures.
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) [4], Italy (INGV) [5], and Japan (NIED) [6].
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.

Trendlines Model
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 [7] [8] [9]. Some authors point out that earthquakes belonging to different clusters are representative of main and secondary seismic sources [10] [11].
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 [12] [13] [14]. 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 ( Figure 2) and/or latitude, the relative maxima and minima (blue and red circles). The third operation consists in joining the maximum and minimum values with segments (blue and red lines, respectively).   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 [13] [14].
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: 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 Figure 3, we can see how in general, before a strong earthquake (main-   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 ( Figure 4) can be envied by tracing the line joining an energy event (mainshock, foreshock or afteshock) and the subsequent earthquake of greater magnitude that must be preceded and/or followed by a lower maximum magnitude (green circles). The three earthquakes form a small scale Foreshocks-Mainshock-Aftershocks (FMA) pattern [15] [16] [17].

Oscillators
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.

Latitude Longitude Magnitude Oscillator (LLMO)
The LLMO oscillator provides information on when an earthquake can occur, using the time series of latitude or longitude or magnitude values. Figure 13 shows how, during a short-term phase, values move within channels usually marked by parallel or otherwise inclined trendlines, whose slope reflects the speed of the values compared to time.
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 Figure 14 Table 1 shows a brief example of the calculation of the LLMO oscillator.

Multiple Moving Averages (MMA)
The MMA is a variant of Guppy's Multiple Moving Average (GMMA) [20] which identifies significant trend changes and their strengths on the base of two sets of moving averages of different time amplitudes. 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.
where: V (n) = refers to the value of magnitude, longitude, latitude or LLMO; SF refers to a smoothing factor, which is calculated as follows: 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) . Table 2 and Table 3 show a brief example of the calculation of the MMA. 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. Figure 19 shows the twelve moving averages plotted on a graph of the LLMO oscillator, where the green moving averages represent the short-term trend and the red moving averages the long-term trend, while Figure 20 shows the average of the short-term moving averages in relation to the LLMO oscillator and the magnitude values of the seismic sequence.
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: Open Journal of Earthquake Research   Figure 19. Armenia Earthquake of 07/12/1988. The green and red lines indicate respectively the short and long term multiple moving averages.  -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).      Progressive number of events 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.

Modified Stochastic Oscillator (OSM)
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. Once the %K-line value is obtained, the %D-line value is calculated, which is a simple moving average a 10 period. Figure 21 shows the attention signals that were activated when the average of short term descends below that of long term. (green triangles). Other attention signals were generated by crossing the fast and slow stochastic lines (red triangles) and by the magnitude values that were positioned above the downward trendline (red dotted line).
In Figure 22, we can see how the short term bands approach those of the long term moving averages and become a thread. This circumstance is the one that indicates a possible occurrence of an energy event.
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 Figure 23 we can observe how the group of short-term moving averages fell below the long-term one, during the phase of energy accumulation that ended with the occurrence of the foreshock of magnitude 6.1 Mw on 28/09/18.
After the foreshock, the group of short term moving averages was brought over Open Journal of Earthquake Research the long term one, generating a signal of attention. Another attention signal was activated when the magnitude values were above the downward trendline.
In Figure 24, the group of short-term moving averages moved over the group in the long run, indicating a phase of energy release. The attention signal was generated by crossing the fast and slow stochastic lines (red triangles) and by the magnitude values that are positioned above the downward trendline.

Conclusions
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.