[Object]
Especially for the one of the 12 Singular Epicenter (#SP12-2), I tried the micro analysis in the narrow area around the #SP12-2. From all epicnters of the felt earthquake database of JMA (Japan Meteorological Agency) since 1919-Jan2026 , 18 epicenters are picked up as the common grids as the same grid latitude and longitude. By this analysis, the physical meaning will be lead from the geometric features.
[Conceptual framework]
In this analysis, we examine multiple earthquake source sequences distributed within a narrowly defined spatial region in the vicinity of a singular source.
Under such a constrained regional setting, it is mathematically inevitable that, for the set of regression lines approximating each source sequence, the correlations between their slopes and intercepts become unity.
What is essential, however, is not this constraint itself, but the mode of intersection exhibited by the ensemble of regression lines under this condition.
In practice, the regression lines do not intersect at a single exact point. Rather, a small number of representative lines intersect in the vicinity of a central region, while the remaining lines are distributed around this region in an envelope-like manner.
In this study, we define the reference point formed near this central region as a fixed point, and interpret it as a central structure by which the earthquake source distribution is geometrically constrained.
This fixed point does not appear as a strictly defined mathematical point, but instead as a stable region with a finite spatial width. Such a feature is interpreted as reflecting a state in which the transmission of stress and strain is not entirely free, but instead the system as a whole is undergoing partial synchronization while maintaining a preferred directional tendency.
[The list of the 18 epicenters neighborhood of #SP12-2 in Hyuga Nada(日向灘) ]
18 epicenters are picked up as the common grids as the same grid latitude and longitude with #SP12-2 ( 31.6° N, 131.9° E, 37km depth). See the list as below,
These 18 epicenters have the common grid of N Lat/E Lon as the rounded values. #SP12-2 data are showed as orange colored. #2-1 is the 1st stage of M of #SP12-2 as the initial occurence of the grid)(The number of the stage of M (段数) is "1"). #2-3 is the 2nd stage of M of #SP12-2 as the bigger than the 1st stage in the same grid(段数 is "2") . #2-10 is the same stage of M of #SP12-2 as the less than the initial value of the 2nd stage(M5.2 <M7) in the same grid(段数 is "2". But, not the initial value). Initial values of each stage of M as 段数 are with red bold font.
[Time-series plot of the 18 earthquake epicenters (N Lat, E Lon)]
Time-series plot of the 18 earthquake epicenters (N Lat, E Lon) is as below,
Each label value shows the Magnitude value. The start point was M5.2(#2-1) with orange colored scqure as the one of #SP12-2 in 1930. The route went with CCW until M3.9(#2-4). The route went straight back the same way on M3.9(#2-4), and extened until M5.1 (#2-5). The route continued to M5.2(#2-10) as the 2nd step of #SP12-2. Since M5.2(#2-10) until M5.3(#2-16), the route went CCW. Then, it changed to CW until the goal "M3.8(#2-18)" in 2024.
[Time-series plot of the 18 earthquake epicenters (N Lat, E Lon) "with correlation lines"]
Red correlation lines are added on the above graph as below,
There are 7 red lines as below,
3 red lines cross with #2-6（Ｍ３．９）<L1-L3>
ｌ１：#2-5（Ｍ４．３）・#2-6（Ｍ３．９）・#2-7（Ｍ５．１）
y = -0.2971x + 70.773 R² = 0.9999
ｌ２：#2-6（Ｍ３．９）・#2-11（Ｍ５．２）・#2-16（Ｍ５．３）
y = 0.2x + 5.2033 R² = 1
ｌ３：#2-6（Ｍ３．９）・#2-12（Ｍ４．５）・#2-13（Ｍ３．７）
y = 1.2342x - 131.21 R² = 0.9986
2 red lines cross #2-3（Ｍ７）<L4/L5>
ｌ４：#2-3（Ｍ７）・#2-5（Ｍ４．３）・#2-9（Ｍ４．６）
y = -1.5329x + 233.81 R² = 1
ｌ５：#2-3（Ｍ７）・#2-15（Ｍ３．５）・#2-18（Ｍ３．８）
y = 3.0822x - 374.86 R² = 0.9996
2 red lines cross #2-10（Ｍ５．２）<L6/L7>
ｌ６：#2-8（Ｍ５．１）・#2-10（Ｍ４．３）・#2-12（Ｍ４．５）・#2-18（Ｍ３．８）
y = 0.2765x - 4.9011 R² = 0.9995
ｌ７：#2-9（Ｍ４．６）・#2-10（Ｍ５．２）・#2-17（Ｍ４．５）
y = 31.5633333333333 R² = na
※This line isn't a correlation line because of horizontal one.
[Meta correlation between slopes and intercepts among L1-L6]
Meta correlation between slopes and intercepts among L1-L6 always has the correlation coefficient as the gragh below,
It's a truism for any lines in narrow area. Even though the natural resilt, we can find out the center of the epicenter from both the slope and intercept of meta correlation formula as the geometric center among them.(It's at 131.89E, 31.596N). In the time-series plot with correlation lines, the lines shows "the single geometric center" of them as the rotation cencer or convergence point of the lines. It suggests the center shouldn't only the result of the calculation, but the fixed point as "great tough and huge rock mass" (extra high intensity asperity) phisically. In fact, there has been no felt earthquake more than M4.2 within a radius of 4km since 1977.
[Location plots among 3 Singularity points/ "the single geometric center"]
Location plots among 3 Singularity points/ "the single geometric center" are shown as below,
The single geometric center among L1-L6 is located on 560m south of the midpoint between
#2-3(M7) and
#2-10(M5.2) . They are not located directly below the top of the triangle formed L4/L5. The structure doesn't consist of a single line, but also of some main lines and envelopes. This distance means the tilt between them in depth. #2-2(M4.7) is the geometric boundary condition of 0km, and controls the degree of freedom of this structure. The single geometric center acts not as "the Load oapplication point", but as the fixed point. It was led out as the center of correlationship of the structure. It doesn't suggest the instant break of the structure, but the metastable statement of it as the being fixed the transmission path of the stress.
[L7 (Lat N = const.) treatment]
Because of enable of the difinition as a correlation for contant lines of Lat, there should be no discussion of the intrerpretation about L7 in this blog.
[Time-series plot of the epicenters except ones with high correlations on L1-L7 ]
There are only 4 epicenters with no colored in the 18 epicenter's list. These epicenters, #2-1 (M5.2)/ #2-2(M4.7) /#2-4(M5.3)/#2-14 (M4.6), are located as below,
There are two pairs of the silmilar M on the diagonal epicenters, and one line segment between M4.7/M4.6 goes through the midpont between M5.2/M5.3. The other one goes through near the midpoint of the other one.
It suggest the bipolar destructions between each diagonal epicenter as the sililar magnitudes. It also suggest that the center of them should not be the destruction point, but the pivot point of the stess point.
It is interpreted that the appromaxinate location of midpoint of these diagonal lines should show the ballanced system spatially. It shows the stress transmission should be not random ones. It is interpreted phisically that the center should not accuate as the maximum destructive point, but also the "pivot" of the applied torques.
[Conclusion]
There have been some M7+ earthquakes in Hyuga Nada area (日向灘). The fact suggest this area around the structure around the Singularity should have the ability of the transmission/redistributuin of the similar huge stress.
Though the Singularity itself has the less possibility of a origin of the next M7+, it should have the greater possibility of becoming the stress bypass along the north-south direction relatively because of the weaker struction in some future.
