2.1 Case studies: EQ occurrence over a high seismic intensity zone V (North-East India) and relative solar status:
To initiate our analysis, a few strong EQ (M ≥ 6) cases that occurred over a high seismic intensity belt, Zone V, of North-East India (Latitudinal and longitudinal coverage: 21⁰50' N − 29⁰34'N and 85⁰34'E- 97⁰50'E. along Sub Himalayan terrain), are examined for possible relation of their occurrences in terms of high/low solar cycle status. The events highlighted here are EQ of M = 7.4 that occurred at solar maximum (1947), the EQ of M = 7.7, 1954 that happened at the solar declining phase, and one of the strongest EQs of magnitude M = 8.6, as well as another moderate event with M = 6.0, occurred at the declining solar phase of the years 1950 and 1984 respectively (Fig. 1). This observation though for limited cases, offers a background that the peak phase of a cycle is not an environment for the growth of a seismic event. However, the phase of a cycle will not necessarily reflect a comparative solar state as the peak strength varies drastically from one cycle to another (Fig. 1). It is worthwhile thus, to evaluate a relationship factor between global EQ events in terms of a solar index, Rz.
2.2 EQ and the yearly variation within cycles No 18 to 24
Before proceeding with the EQ event and Rz relation analysis, the trend pattern on the growth of events during the years covered under the study is essential to view, and presented in Fig. 2 by plotting total global EQ cases with magnitude M ≥ 4.5 to the recorded highest as event-inputs against the years from 1950 onwards. The presence of a reasonably positive relationship between the number of EQ events and years is clear i.e EQ cases increase as the year moves on, especially from the year 1970. This increase in EQ cases is not apparently influenced by solar status because, over the years, the Rz (Fig. 1) offers a declining trend, thereby a negative association between EQ–event and solar strength seems to exist. However, the direct relationship between the two is necessary especially to identify the sources either the solar or the availability of more EQ data pools as the year advances ( bias effect), in contributing to the year-wise increasing trend of EQ events.
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Figure 2 Year-wise variations of the total number of EQ cases of M ≥ 4.5. Note the increase in the event number with special reference from 1970 onwards.
2.3 Correlation between Rz and global earthquakes events of magnitudes (a) M ≥ 6.0 and(b) M ≥ 4.5 covering the studied cycles
Following the above background, the EQ event & Rz relation is formulated but separately for M ≥ 4.5 and strong cases M ≥ 5.5/6.0. This filtering of EQ event in these two classes is considered necessary when the preparatory area increases exponentially with EQ magnitude (Dobrovolsky et al. 1979) along with the amount of energy released in the process and thereby enhancing complex dynamical inter-mode relation between solar energy and lithosphere and thereby on the EQ growth. Therefore we present separately the relation- profiles between (i) EQ ≥ 4.5-event number & Rz (ii) EQ ≥ 5.5/6.0–event number & Rz, in Fig. 3 along with correlation magnitude in respective cases. The values of R=-0.31 for M ≥ 6.0 & R=-0.34 for M.≥4.5 so obtained, offer the conclusion that the EQ events decrease in number (for both the classes of EQ magnitudes) with the increase in solar strength, and thus support the existence of a negative correlation between the two.
However, the scattered modulation along the trend line (Fig. 3), on the contrary, suggests that their relationship is perhaps affected by bias in the event records as the cycle advances. In an attempt to reduce the bias effect, each cycle is now considered as an individual case, and the contribution of Rz to the occurrence of an EQ is evaluated by comparing the event numbers between the Low Solar Active year (LSA) and High Solar active Year (HSA ) of each cycle, the analyses and results are presented in the next article.
2.4 Global earthquake events of magnitude M ≥ 4.5 and Rz relation within an individual cycle
The approach now is to evaluate “the number of EQ events that exceeds/lags in the LSA or in HSA year of the same cycle” and finally compare this difference in the number of events with the “difference between Rz values of the respective years”, i.e., to find out the ratio of the events between LSA year and those of an HSA year (i.e., ðEQ = EQ LSA / EQ HSA) and also the Rz ratio of these years (ðRz = Rz HSA/RZ LSA). Let us first brief our first case of cycle 18. Here, as dictated by the Rz value, 1947 is selected as the HSA year and 1954 as the LSA one, where the EQ events show a 5.6-time increase in event number in contrast to cases in the HSA year, as displayed along with the event profiles of Fig. 4a. Similar results also come up for other cycles but the event ratio ðEQ (Fig. 4b-d) gets changed, nonetheless higher events always occur in the LSA period, except for a deviation in the year 2014 (HSA) when event numbers are marginally lower in the solar minimum year 2019 (Fig. 4e). Also, we note that the EQ of maximum strength always occurred during the LSA period except for the year 2014.
The conclusions that come up from the analyses are:
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The number of EQ events of M ≥ 4.5 is more in the LSA period compared to the HSA year of a cycle, the negative relationship thus obtained between EQ events and Rz, is in corroboration with our earlier conclusion.
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The events’ ratio EQLSA/EQHSA is variable with Rz-cycles an issue we will pursue in the next article by filtering out strong EQ events i.e. of M ≥ 5.5/6.0, as a further input to the observation.
2.5 Global earthquake events of M ≥ 5.5/ 6.0 and Rz in an individual cycle
The procedure here is the same as that of the above, except for the EQ events considered are of M ≥ 5.5/6.0. The respective ratio of EQLSA and EQHSA for this class of EQ events of individual cycles presented in Fig. 5, also shows a 4-fold increase in the LSA year 1954 compared to that of the HSA year 1947 (Fig. 5a), supporting the observation of the article 2.4. This “event ratio” for this class of EQ events also changed in magnitude (Fig. 5b, c) in different cycles, and with more number of cases always in LSA years except for the 2014 & 2019 years (Fig. 5d), similar to the results that came out for the M ≥ 4.5 EQ cases.
The prime factor leading to the variation in this “event ratio” is likely to be associated with the intensity of the sun when Rz magnitudes change in the HSA and LSA years of each cycle. So, finally, to complete our approach we draw the relationship, between ðEQ=“ðy” and ðRz= “ðx” of the respective cycle, as displayed in Fig. 6, where we see an increase in event ratio with an increase in the sunspot ratio following Eq. (1), i.e., it suggests that the number of EQ events increases in LSA year when the difference in Rz values between HSA and LSA years gets larger. But also to note that on attaining a particular Rzmax (i.e. strong solar ambiances), the profile (ðEQ - ðRz) breaks the liner trend and slowed down its value (Fig. 6), which might be the result either of the decrease in overall EQ events or increase of events in HSA period in strong solar background.
ðy = 0.115 ðx+ (0.302) (1)
The overall results of the observations are:
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The EQ events of all magnitudes are more in the LSA period compared to the HSA period by following the Rz HSA/RZLSA ratio, of Eq. (1), which further supports our earlier conclusion of the existence of a negative relationship between EQ growth and Rz.
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The above aspect may serve as a prelude that high solar status is not a favorable environment for the growth of a seismic event and at the same time, Rz, depending on its strength has a role in modulating the number of events as well as in magnitudes of the EQ (Eq. 1 and Fig. 6).
With conclusions (ii) and Figs. (4, 5, and 6), we take up the issue further by segregating EQ event magnitude-wise in steps of unity for EQ \(\ge\)M.5.5, and plot these events with corresponding Rz value.; a few cases are displayed in the next article covering low/mid and high solar status.
2.6 The relation between Rz and EQ events of different magnitudes of M ≥ 5.5: role of Rzmax to the growth of strong EQ
The analysis now consists of filtering out different magnitudes of EQ at a step of unity for a selected period of a year /month and distribution plots are made with the total events against each magnitude of EQ and respective Rz, a few cases are presented now .
Case I: The first case here is of an LSA year 1954, (Fig. 7a) with Rz varying from 0 to 16. Even in this low solar background, Rz shows an overall negative trend as the events decrease as Rz reaches the peak, but with a complex polynomial relation in Rz –EQ distribution when, EQ events of almost all magnitudes from M = 5.5 to M = 8, occur (except one of M > 7.5) in the lowest range of solar activity, and also below 60–70% of the peak value of Rz but not at the Rz max. The distribution is well fitted specially for the M = 5.5 to 6.5 range as displayed in Table 1, when the number of events is relatively large. But as the EQ strength increases, the events go fewer, one can't have a clear distribution profile between the two.
Table 1
EQ strength and relation profile with Rz: for the period 1954
EQ strength | Relation: EQ events-Rz | Correlation factor |
M = 5.5-6 | y = 0.074x2 + 1.168x + 7.115 | R2 = 0.367 |
M = 6-6.5 | y = 0.026x2 + 0.318x + 2.322 | R2 = 0.186 |
M = 6.5-7 | y = 0.007x2 + 0.144x + 0.789 | R2 = 0.224 |
M > 7 | As the event number decreases, the distribution plot cannot be well defined, but more are the events of all magnitudes below 60–70% Rz max. Two strong events did appear at the maximum Rz, but the solar background seems still low to inhibit the strong events. | |
Case II: This presented case falls on high solar periods of November-December 2000 with Rz varying from 60 to 240. The Rz - EQ event relation profiles also show that EQ of all magnitude from M = 5.5 to M = 8, occurred at 60–70% below the peak Rz and the EQ of only M = 5.5 did occur at Rz maximum and that with low event numbers (Fig. 7b). But unlike the case I above, the polynomial distribution is fitted mainly for the M = 5.5 to 6.0 magnitude of EQs (Table 2), because the number of EQ events of strong magnitudes reduces significantly (even for M = 6.5) in high solar ambiances prevailing during this periodand the distribution plot cannot be defined for strong EQ events and no strong event occurred at peak Rz.
Table 2
EQ strength and relation profile with Rz: period November –December 2000
EQ strength | Relation EQ events-Rz, Nov-Dec 2000 | Correlation factor |
M = 5.5-6 | y=-0.003x2 + 0.958x-55.41 | R2 = 0.303 |
M = 6-6.5 | y=-0.0001x2 + 0.154x-8.571 | R2 = 0.341 |
M > 6.5 | As the strong magnitude-EQ events decrease significantly at the prevailing high solar ambiances, the distribution plot cannot be defined for such EQ cases, but more are the events of all magnitudes below 60–70% of Rz max and no strong event occurred at the peak Rz. | |
Case III: 1965 is a year with a low-moderate solar active period when Rz varies between 10 to 35. In this case, too, the polynomial relation fits in the EQ and Rz distribution relations, especially in M = 5.5 to 6.5 magnitude range of EQs (Table 3), and events of all magnitude did occur more at 70% below the peak Rz value with the number started declining as Rz goes to the maximum (Fig. 7c) but unlike the year 2000, strong events did occur though fewer in number at the peak Rz, as expected in the moderate solar background.
Table 3
EQ strength and relation profile with Rz: for the period 1965
EQ strength | Relation EQ events-Rz, Year: 1965 | Correlation Factor |
M = 5.5-6 | y = 0.06x2 + 2.698x-8.840 | R2 = 0.217 |
M = 6-6.5 | y=-0.014x2 + 0.49x + 2.163 | R2 = 0.277 |
M > 6.5 | As strong-event numbers decrease, the distribution plot is not well defined but most of the cases occur within 60–70% below Rz peak and as expected in the background of moderate solar activity two strong events did occur at the maximum Rzmax. | |
Figure 7 Rz-EQ event relation for different strengths of EQ from M ≥ 5.5 to maximum: (a) 1954 low solar period, (b) November-December 2000 high solar status, and (c) a low - moderate solar active year 1965. Note polynomial distribution is well-fitted in most cases except for very strong events.
The conclusions that come up are that over and above the negative relation between EQ events (M ≥ 5.5) and Rz, a relatively complex polynomial distribution exists in most cases except for very strong events (because of fewer numbers). And that EQ of all magnitudes occur preferably at 60–70% below the Rz peak but are dictated by its strength which is variable based on the period covered, but strong solar ambiances inhibit the growth of strong EQ events.
2.7 Special cases: Historic Chile EQ of May 22, 1960, and a few deadly events
In continuation of EQ –Rz association analysis, the solar status during the historic Chile EQ of May 22, 1960, with magnitude M = 9.5 is considered worthwhile to examine as it provides a rare occasion to understand the mode of relation between EQ and Rz. To make this analysis comprehensive, the diurnal Rz value of each day of 1960 is plotted along with the respective EQ cases of M ≥ 6.0 and presented in Fig. 8, displaying how the historic EQ of May 22, 1960, with magnitude M = 9.5 (marked by a star) did not occur at the solar maximum and also that not a single major EQ of M > 7.0 appeared at the peak of solar activity. This result thus corroborates our earlier conclusion that the peak solar activity is not a factor associated with the occurrence of an earthquake, now with special reference to the strongest event too. Also, it is necessary to focus on the point that more events occurred within Rz values ranging from 125 to 175 (around 70% below the Rz peak value).
In this case, too, the polynomial response (significantly for M = 6-6.5 events)) is maintained between the number of EQ events of different magnitudes and respective Rz (Fig. 9,) with more EQ cases around 60–70% below Rz max, and even the Chile EQ occurred not at the peak solar status. As expected in this strong solar background, there are no EQ events of M > 6.5 at Rz max. This observation is supported by a few more deadly events as presented in Fig. 10.
Here, the 1920 China EQ of M = 8.5 (Fig. 10a), 1923 Japan EQ of M = 7.9 (Fig. 10b), and EQs of 1964 Alaska M = 9.2 (Fig. 10c), 2004 Sumatra of M = 9.1 (Fig. 10d), 2001 Bhuj of M = 8.1 (Fig. 10e) and 2010 Chile of M = 8.8 (Fig. 10f), all occurred at solar minimum or 60–70% below peak Rz (increasing/declining) in the monthly sunspot trend, irrespective of whether the period is in high-active (1920,2001) or low-mid (1923, 1964, 204, 2010) solar status.
The conclusions of this analysis are:
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The deadly EQ event, also presents a relatively complex relationship between EQ events & Rz, with the polynomial response (significantly for M = 6-6.5 events) between the number of EQ events of different magnitudes and respective Rz (Fig. 9,) with more EQ cases around 60–70% below Rz max
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No strong EQ of M > 6.5 occurred at the Rz peak, as expected at strong solar ambiances,
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The historic Chile EQ did occur at 70% below the Rz peak.
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Deadly global EQ events occurred at the solar minimum or its declining phase of the respective month.
Regarding conclusion (ii) there may be a few instances like in1947 when strong EQ events did occur almost at the peak Rz. These are exceptional cases and will be dealt with in the future. In the next exercise, the contribution of the geomagnetic factor to the growth of an EQ is examined in brief, as an additional factor to the above results.