The earthquake activities should be proportional to the harmonics’ amplitude. The bigger of the harmonics’ amplitude, the sooner the accumulated deformation exceed the critical thread, so that there should be more earthquake activities, and vice versa.

Tides are the rise and fall both of sea levels (ocean tide) and the solid earth’s surface (earth tide) caused by the combined effects of the gravitational forces exerted by the Moon and Sun. These two tides will affect the harmonics response and earthquake activities in turn.

Sun pass anywhere on earth in a 24 hours period, and the distance between Sun and earth changed year around, so it is easy to define earthquake activities related to Sun according above description.

If earthquakes are triggered by the harmonics, it is possible to find the harmonics triggered earthquake from earthquake time by Spectral Analysis.

The earthquake could be triggered at any time with unknown delay, it makes the Spectral Analysis more difficult. But as discussed above, the earthquake activities should be proportional to the harmonic amplitude, so that there should be a lower probability around harmonics zero amplitude to trigger earthquake, and increase along with the harmonics’ amplitude increase, there is still a chance to find the harmonics if there are enough earthquake data. If the harmonics could be found, it should be strongly confirmed that there is a correlation between earthquake and earth rotation harmonics.

The possible spectrum could include:

1) The harmonics triggered the earthquake.

2) Sun caused tide and its harmonics.

3) Moon caused tide and its harmonics.

4) Mixed frequency of 1) and 3) for the nonlinear response.

5) If the harmonics triggered the earthquake only in positive half cycle or negative half cycle, Spectral Analysis should find those spectrums.

6) If nth harmonic triggered the earthquake both in positive and negative half cycle (average) equally, only 2nth harmonic spectrum should be found instead of nth. Otherwise, both nth and 2nth harmonics should exist.

Longitude distribution is shown in Figure 5 Longitude distribution.

Most of the earthquake data shows a flat distribution except two peaks at northern hemisphere and two peaks at southern hemisphere as shown in Figure 6.

Two regions with more earthquakes at northern hemisphere located at Hawaii and Alaska, west coast of Canada and US. Two regions with more earthquakes at southern hemisphere located at New Zealand (Tonga Trench and Kermadec Trench), the coast of Peru and Chile (Peru–Chile Trench).

Latitude distribution of all earthquake data is shown in Figure 7 compared with cos function. It could be confirmed that earthquake activities decreasing toward to both northern and southern pole.

All of the above figures (Figures 8-11) could confirm the analysis in 2.1.2.

Vertical distribution is shown in Figure 12 Vertical distribution.

Earthquake started as deep as more than 700 km depth, and increase obviously from 20 km depth up. The earthquake reaches a maximum activity at depth of about 2.0 km, then decrease rapidly toward to earth surface as described in 2.1.3.

There is no any location with enough earthquakes to perform a meaningful daily sun tide effect on earthquake. But any earthquake with the same position to the Sun can be considered as the earthquake occurred at same time and same location, in this way, all earthquakes over the world can be mapped in one day to perform daily sun tide earthquake effect analysis. Consider that the Sun position relate to latitude will changing year around, use same related longitude between earthquake and sun instead. This can be done just by converting the UTC earthquake time to local geological time to map all of the earthquake into 24 hrs range.

Daily Sun tide effects for all earthquakes with 1 hour step are shown in Figure 13.

Figure 13 shows that more earthquakes occurred in the harmonics negative half cycle on southern hemisphere, and more earthquake occurred in the harmonics positive half cycle on northern hemisphere, both with ocean tide effect.

Figure 14 shows the distribution of magnitude <0.0 on northern hemisphere with only earth tide effect and more earthquakes occurred in the harmonics positive half cycle, there is no such data on southern hemisphere.

Figure 15 shows the distribution of magnitude 0.0 to 1.9, mainly with earth tide effect for magnitude 0.0 to 0.9 on northern hemisphere. For magnitude 1.0 to 1.9, there is only ocean tide effect on southern hemisphere, and there are more earthquakes in the harmonics positive half cycle on northern hemisphere with a strong ocean tide effect.

Figure 16 shows the distribution of magnitude 2.0 to 3.9. For magnitude 2.0 to 2.9, there are more earthquakes in the harmonics positive half cycle on both northern and southern hemisphere with both earth tide and ocean tide effects. For magnitude 3.0 to 3.9, there are more earthquakes in the harmonics positive half cycle on both northern and southern hemisphere with both earth tide and ocean tide effects.

Figure 17 shows the distribution of magnitude 4.0 and up. There are more earthquakes in the harmonics negative half cycle on both northern and southern hemisphere. For magnitude great than 5.0, there are no enough data to make a judgment.

Figure 18 shows that harmonics half cycle with more earthquakes changed from positive half cycle to the negative half cycle from magnitude 3.4 to 3.6.

Yearly earthquake distribution can be obtained by just simply putting the earthquake in the same date together, Figure 19 shows the yearly distribution with 1 day step. February 29th is a special day; it is only a quarter of other days. Earthquake are lower activities in January, and a little bit higher activities in July as described in 2.3.4.

The following function is used to calculate nth harmonics.

f(n) = 1/M∑e^{−j2πn(tm-t0)/24}

where M is total earthquake counts, tm is the mth earthquake time, t0 is selected reference origin and 2000-01-01 00:00:00 UTC is used in this Spectral Analysis. The Spectral Analysis is just intended to find out if the harmonic peaks exist. the order step of 0.25 is used for harmonics calculation, and a 0.25 day step is used for tide harmonics above 1day. Spectrum for all earthquake data is shown in Figure 20. Many peaks of earth rotation harmonics and tide caused harmonics can be seen in the figure.

Earthquake near earth’s surface could be considered less interference by other earthquake. Spectral Analysis for depth of 0.0 km is shown in Figure 21. Spectral Analysis for depth above 0.0 km is shown in Figure 22. Both figures show stronger earth rotation harmonics. Two stronger tides caused harmonics of 3.5 day and 7 day can be seen in Figure 22.

Figure 12 shows that there are more earthquakes at certain depths. More detailed data is shown in Figure 23. There is a pattern of 100.0 km major step and 50.0 km minor step below 100.0 km, and a pattern of 5.0 km major step and 1.0 km minor step above 100.0 km. Earthquake magnitude distribution at those depths is shown in Figure 24.

Figure 25 shows the magnitude distribution of all earthquake data. It shows that from magnitude 3.5, earthquake activities stop decreasing as normal, and start increasing until magnitude 4.4, then decreasing again until 5.0 to the normal level. From the harmonics point of view, the possibilities of more earthquake magnitude range from 3.5 to 5 should be:

1) sensitive to certain harmonics, and/or

2) sensitive to tides.

Spectrum for amplitude from 3.5 to less than 5.0 is shown in Figure 26. There is no any stronger earth rotation harmonics found, two strong tides related harmonics found—7 day and 31.5 day. This means that earthquake magnitude from 3.5 to 5.0 could be tides sensitive, it is suggested that this should be a kind of earthquake type—sliding between layers. This could be identified easily by earthquake monitoring system; the earthquake should be shaking mainly in west-east direction. And it is possible to identify which half cycle of earth rotation harmonics triggered the earthquake.

Figure 27 shows the spectrum below and above 100.0 km. Below 100.0 km, there is a more stronger 7 day peak and a very week 31.5 day peak. Above 100.0 km,

31.5 day peak is stronger. This is just implying there are some relations to the harmonics’ effects for these vertical distribution pattern, and will not be discussed in this paper.