Gravitational Moon–Earth Forces Triggering Earthquakes in Subduction Zones

In this paper, we investigated the possible interactions of the moon and Earth, mainly in the period 1996-2015. Initially, we considered the gravitational force of Moon vs. Earth by Newton’s equation. The Moon has an elliptical orbit around the planet that reaches two points of maximum. One is the closest, the Perigee, and other the farthest is the Apogee. The Apogee and Perigee have distinct values monthly. In our study, the Perigee force was calculated during every month, year after year. This force creates an oscillation, which in, 13 – 14 months, completes a whole cycle. The wave period is 5400 hours as calculated. The energy generated by Moon on Earth from this closest position reaches a maximum during the Full or New Moon. We observed during these phases an enhancement of earthquakes near the shorelines of the Pacific. On the other hand, the wave minimum matches with the First or Third Quarter, but in this case, the effects of earthquakes are Data Article Hagen and Azevedo; JGEESI, 8(2): xxx-xxx, 2016; Article no.JGEESI.29227 2 smaller on the same regions observed for New or Full Moon. These results indicated that external forces created by MoonEarth system allied with internal ones are responsible for increase earthquakes in the pointed out areas. Also, the oscillating movement of Moon-Earth system provides a tool for predicting the next enhancement on earthquakes cycles.

This work was carried out in collaboration between both authors. Author MH designed the study, data catalogs and performed the statistical analysis. Author AA made the mathematical models and checked the analysis and the disposition of the sections. Both authors read and approved the final manuscript. (1) (2) (3) (4) Complete Peer review History:

INTRODUCTION
Relatively little research has been done so far about the connection between the gravitational interaction of moon-Earth system and earthquakes [1,2,3].
Investigators have doubts as to an accurate approximation of the problem. However, the evidence of an interaction between the moon and Earth are clear in studies of the ocean waves and tides, and it is well known and reviewed [4,5,6,7,8,9]. The Moon is the satellite orbiting around the Earth, in an elliptical trajectory. Its mass is eighty times less than Earth, has 27% of the earth's volume, and has no external magnetic field. The moon has a small paleomagnetic field with a magnitude of 2.5 nT. Moon's orbital movement around the Earth creates a gravitational force at the surface of the Earth, which varies every month in the extreme positions, as Perigee (closest) and Apogee (farthest). The satellite depending on its position around Sun-Earth system assumes different phases. If the moon is aligned with the Sun-Earth system, the phase is designated as the New or Full Moon. At the New Moon, it is facing the magnetic dayside of Earth, at the full Moon is on the night side of magnetosphere into the plasmasphere [10,11,12,13]. When the Moon position is 90 degrees in relation to the Sun-Earth, the phase is 1 st or 3 rd Quarter. These variants on the Moon position related to Earth mold different effects of the Earth as the spring and neap tides. Spring tides are the strongest tides of the moon cycle month, and the neap tides the weakest. The first step in this investigation was to calculate the variations in the gravity field of Moon-Earth system as per Newton's universal law as we see later. The result found is a gravity wave generated between the two bodies with specific values of oscillation, period, and wavelength. Then, we repeated this procedure for a complete Solar Cycle (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) to investigate how the force between Moon-Earth system varies. In this paper, we worked with two solar cycles, the Cycle 23 (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) and Cycle 24 (2008-2015) which is not complete. The reason this paper is from a series of solar variability possibly connections between the three-body system and earthquakes. The moon wave produced maximum peaks, which coincided with the Full or New Moon. The same was true for the minimum days were always, in the 1 st or 3 rd Quarter. After we had obtained the days for the maximum and minimum we search in the earthquakes catalog for the earthquakes location in those days, the magnitude of the earthquakes were M ≥4.0 Then, we examine the Megathrust earthquakes (1700-2015) and at last the large earthquakes in the interval 1996-2016. We created Tables for those two earthquakes occurrences and discussed the influence of the moon in both of the observed events. Those data were discussed as the result of our calculations.

THE PERIGEE FORCE VARIATION
The following picture Fig. 1 shows the position of the sun, Earth and the moon and the moon phases for spring tides. At the new moon and full moon, the sun, Earth, and moon arrange themselves more or less along a straight line in space. The pull on the Earth, consequently on the tides increases, since the gravity of the sun, reinforces the moon's gravity. Then, at these phases, the tide's range is at its maximum and is the definition of spring tide: the highest (and lowest) tide. The weaker forces happen at the 1 st or 3 rd Quarter named neap tides. It is when the sun and moon are at right angles as seen from Earth. Therefore the sun's gravity works against the moon's gravity. Therefore the moon's effect on the tides is smaller, defining a neap tide; the range of those tides is at its minimum.  As the Fig. 1 shows, at the "new moon," the moon is between the Earth and Sun, so that the side of the moon facing toward us receives no direct sunlight, and is lit only by dim sunlight reflected from the Earth. As it moves around the Earth, the side gradually becomes more illuminated by direct sunlight. At the "full moon," the moon is 180 degrees away from the sun, so that the Sun, Earth, and the Moon form a line. The moon is fully illuminated by the sun, so this is called "full moon". Full or New Moon have some unusual characteristics at the "new moon," the body receives radiation, ionized and energetic particles from the Sun, which intensifies, during solar storms. During the "full moon," earth's plasmasphere located at the magnetotail charges the satellite with electrons, therefore negatively.
Our first procedure in this study has been to calculate the change in gravitational force of the moon and the Earth, evident in the little difference in the perigee locations [16,17,18,19,20].
The calculations refer to the period 1996-2008, which is a complete Solar Cycle; the objective was to observe any alteration in the moon cycle connected to the maximum or minimum of Cycle 23, [21,22,23,24,25]. The period chosen is to detect in our calculations a possible change in the oscillatory behave of the Moon at the Perigee position. Also, we will observe any variation on earthquakes during the maxima of the solar cycles, which is connected, or not with the moon changes, [11]. The moon data positions for Perigee and Apogee during all years calculated are in the Tables in [18].
For example, on Jan15, 2016 the perigee was 369618 km. On Feb 11, 2016, it was 364357km, creating a gap between the two values of 5261 km. Therefore, an oscillation was apparent after ten months, set up by the small differences in the perigee values. Fig. 2 displays the maximum and minimum of the moon cycles against the days observed.
At the apogee locations, although the moon is further apart from earth, we followed the same method. Overall, the perigee position varied 3.5% during a year and the apogee position only 0.5% in the same period. The universal gravitational force is given by, In the equation (1), the moon mass (m), earth mass (M) and G= 6, 67 x10 -11 N.m 2 kg -2 are all constants; the only variable is being r, the distance between the moon and the Earth describing an elliptical path around the earth.
The Fig. 2 displays the results for the oscillating force during Cycle 23; the period 1996-2008 was a time scale to limit our lunar wave with known data. It is also an answer to the question what happen with the variation of gravitational Moon-Earth during a solar cycle. Moreover, established how many lunar cycles are in a solar cycle. We found that the there were 11 lunar cycles between the period 1996-2008 that comprehends the Solar cycle 23. The variation and the possible connections solar cycles and moon cycles demands more calculations that we did not develop in this paper.
For the moon we found a perigee force variation, with a maximum at F = 2.30 ×10 20 N and minimum at F= 2.14 ×10 20 N. Maximum values of F occurred at the Full or New moon and the Minimum; occurred at the First or Third Quarter. The period falls in the range of 52080 hours -5400 hours. The moon's speed around Earth is 3683 km/h generating a wavelength that is between 1, 94 ൈ 10 ݇݉ -2,05 ൈ 10 ݇݉ . The results in the Fig. 2 found a wave between the moon and the Earth, which depended on their distance variations when the satellite reaches the Perigee. The Cycle 23 took 11 moon cycles to accomplish; we took the Cycle 24 (2008-) and is in the eighth year for the possible total cycle. The Fig. 2 shows the wave with the Maximum and Minimum of the gravitational forces and the date corresponded at the horizontal axis. Fig. 3 shows the percentage of the moon phases during the maxima or minima of the gravitational force. The Full and New moon, reach the Maxima in equal percentages 25% and the minima of the force is 30 % during the First Quarter, and 20% at the Third Quarter. This result obtained between 1996-2008.

Fig. 3. The maximum or minimum perigee days distributed by moon phases
The next calculations were to consider the number of earthquakes occurred during each data of Maxima gravitational force. We took each day of the maximum force and search for the earthquakes happened at that data. The results found, corroborate the assumption that during the New or Full Moon enhancement of events.

maximum or minimum perigee days distributed by moon phases
The next calculations were to consider the number of earthquakes occurred during each data of Maxima gravitational force. We took and search for the earthquakes happened at that data. Fig. 4 showing the percentage of quakes number for or minima of the perigee with 4.0 on each data. The evaluation 37% of geohazard events befall at the Full Moon, 36% of the New Moon, 19% at the First Q and only 8% at Last pointed out that most 4.0 observed during those phases happened in their majority at 73% during , and others 19% at the First quarter with only 8% at the Last quarter.
The results found, corroborate the assumption during the New or Full Moon there is an The next steps are to find the link between the gravitational force variations and the events. It also tries to find out, the reason why the quakes happened more at the New or Full of the earthquakes occurred near the coast and subduction zones of the West Pacific area. During periods of spring tides, the gravitational pull from Sun and Moon acts jointly. Such ocean tides could create dramatic changes in the tectonic force balance in subduction zones located in the Pacific area. In an attempt to

maximum or minimum perigee days distributed by moon phases
The next steps are to find the link between the gravitational force variations and the events. It also tries to find out, the reason why the quakes happened more at the New or Full Moon. Most of the earthquakes occurred near the coast and subduction zones of the West Pacific area. During periods of spring tides, the gravitational pull from Sun and Moon acts jointly. Such ocean tides could create dramatic changes in the n subduction zones . In an attempt to examine the regions affected by the earthquakes during the days of Maximum or Minimum perigee compilations were carried out of the different phases of the moon based on the Fig. 2. Table 1 Tables 3  and 4).
During the moon's quarter phases the sun and moon at the right angles causing the bulges to cancel each other. Our results show evidence that the gravitational pull of the Moon and Earth enhanced earthquakes in areas near the coast. It supports the claim that the tides help to trigger earthquakes. In our calculations, we considered the magnitude of events M ≥4.0. The first part of this paper showed that the Moon at the Perigee created a variation in the gravitational force, which has a maximum at the Full or New Moon. The construction of this moon variation allowed to search the frequency of earthquakes during the days that the New or Full Moon reached the Maximum of the force. The events found were always near the coastlines with some few events inland. Earthquakes happen when a region under tension, pressure and, stress accumulate energy enough to a rupture point. When reaches this point it triggers an earthquake. For a quake to be correlated with external causes, we pointed some of them: flood, chemical explosion, ice quake, landslide, mine collapse, nuclear explosion, and quarry blast, among others. At this first step, we did not find an exact correlation between the Moon and earthquakes. We found during very special conditions that earthquakes would happen.

DISCUSSION OF RESULTS
The results at this point are: A variation on the Perigee position created a Moon-Earth wave varying in the interval 1996-2008. Peaks of maximum in the oscillation corresponded to the Full or New moon, peaks of minimum to the 1 st or 3 rd Quarter with correspondent date. The Moon can also be at the Full Moon at the apogee as well. We searched during the special days of the maximum and minimum points all the earthquakes and the regions they occurred. It coincided that the majority of earthquakes took place at the subduction or convergent zones at coastlines. The statistical calculation finds out that during the New or Full moon the higher tides doing more pressure accumulating energy at subduction regions. At the 1 st or 3 rd Quarter, the neap tides retract doing less tension. There is a lag time requested to trigger an earthquake not every Full or New Moon will create strain enough to trigger earthquakes. It happens when the rupture point is reached after a while the region deforming by the power of the ocean waves. If the tides are higher the deformation increase, if the tides are lower it decreases until the rupture break.
The dynamic of oceans allied to the gravitational push will trigger earthquakes. The Sun gravitational force adds the push when the moon aligned with the other two bodies. The range of time necessary to trigger large or megathrust earthquakes may be large, and we are going to see the next sections. In this paper, we are working with several data catalogs, earthquakes from Iris and USGS [29,30]. For Solar Cycles, NGDC/ NOAA [20,21,22,23,24,25], for moon data [10,17,18,19].

MEGATHRUST EARTHQUAKES EXTERNAL CONNECTIONS
The first part of this work demonstrated that the Moon-Earth gravitational connection is a force varying with the satellite position around the planet. This force, when located at the Perigee created a wave, which we calculated the period and the wavelength. The wave has maxima values coincident with the New or Full Moon, and the minima values with the First or Third Quarter. The Solar Cycle 23 accomplished eleven moon cycles as calculated in the Fig. 1. The Solar Cycle 24 started in 2008 and covered only eight Moon cycles so far. A possible interrelation between the lunar cycles, solar cycles, and earthquakes cycles is not feasible now. Our next step is to examine if the Moon gravitational force is linked to the Megathrust and giant earthquakes recorded.
The Table 5, displays some characteristics of those mega -events, occurrences between November-May, it also befell at the minimum of a solar cycle (we discuss this point in another paper). There was no event in the Third Quarter, which agrees with our Fig. 4 that only 8% of total events happened through this moon phase. Mega events occurred in shallow depths, near the coast, most of the Full or New Moon, with small delays in data [12].
In the examination of the events indicated there is a stress on deformed regions by the subduction stating that tides or the progression stress from gravitational forces Moon-Earth accumulates several years before the earthquake happening. The coincidence of a specific Moon phase and the event demonstrated the time when reaching the breakpoint triggers a Mega quake.
The next point it is to examine the larger earthquakes, which happens more often than the Megathrusts, in the period 1996-2016.

MOON PHASES CORRELATION TO LARGE EARTHQUAKES
This section amplifies the search to find possible connections between giant earthquakes and gravitational interactions between the moon and the Earth.  6 illustrates the giant quakes in the same period at the South America coast, mostly at New or Full Moon. The speed of the plate is now 79mm/ yr. In both pictures, there were no intraplate occurrences, and it was rare that giant earthquakes were happening inland. Table 7 shows the largest earthquakes M≥ 7.5, location, data, magnitude, Main Moon Phase, Tides, Days-Moon phase difference.
As observed for the earthquakes M≥8.0 in a small interval 1996-2008, we found that larger earthquakes are more likely to happen at New or Full Moon in the subduction margins. We marked in red the ones that are on time, delayed by one day before, or after the phase started. Our results indicated the majority of quakes happened on time, delayed, or advanced one day of the moon phase. Earthquakes most occurred at the subduction areas what indicated that the high tides are important for those interactions. Finally, we found out that few events Table 7 for M ≥7.5 and M≤8.0 happened intraplate. It indicates the largest magnitude earthquakes happened in their almost totality between 1996-2016 at the subduction locations. Connections gravitational variation, moon phase and tides increased for earthquakes with larger magnitudes most to subduction regions.    water and eventually disrupt these points triggering earthquakes. The external forces are the tides pressure around the shores or ocean lines that forcing cold water underneath the continental crust, which has a higher temperature, and in many cases, it breaks the lower plates and increases the tension. Generally, a straight correlation Full or New Moon and earthquakes is rare for earthquakes since it needs time to happen.

CONCLUSIONS
We defined external factors as the Moon-Earth gravitational variation, which can influence on the Tides especially during the New or Full Moon. Largest earthquakes and a discrete enhancement of events M ≥4 observed during those phases. The results found gravitational forces between Moon and Earth acting most at the oceans and affecting the coastlines. The energy from the higher tides is pushing on the subduction regions storing strain, stress enough to disrupt the region with asperities to trigger the largest earthquakes. However, it demands a time gap to happen.
Overall, the Moon and the Earth connection have interactions that require long time intervals to affect largest seismological events. The continuation of this research is to analyze the three -body system and the consequences of the interconnections among them on earthquakes.