[Macro Analysis]
In the 1930 North Izu Earthquake (北伊豆地震M7.3), the magnitude within the corresponding grid (139.0°E, 35°N, depth 1 km) jumped abruptly from an initial 2nd-stage value of M3.7 to a 3rd-stage M7.3. This gap cannot be explained without considering the ripple effect (which we call the "Domino Effect") from large surrounding earthquakes.
Therefore, before the micro-analysis near the singularity, I will briefly conduct a macro-analysis of the surrounding area. The following describes the M6.7+ epicenters, their list, and the transition graph within a rectangular area including the Izu region(伊豆地方) and the 1923 Kanto Earthquake (Great Kanto Earthquake関東大震災 epicenter), based on the JMA Felt Earthquake Database.
From the 1923 Kanto Earthquake M7.9 to the subsequent Izu-Oshima Nearshore M6.8, and up to the East Off Izu Peninsula M6.7, the epicenters draw a counter-clockwise loop enclosing a large triangular area. A similar transition surrounding a counter-clockwise triangular area is also observed in the Neighberhood of Iki-Oki (壱岐・隠岐近海) and the 12 Singular Epicenter groups. Additionally, epicenters relatively close to the M7.9 event show magnitudes of M7.3, while those further away scale down slightly to the M6.7–M6.9 range.
Regarding the "stages" of each grid: the Tanzawa Earthquake (M7.3), closest to the M7.9, is the 1st stage. The North Izu Earthquake (M7.3), occurring next, is a 3rd stage rising from a 2nd-stage M3.7. This shows a process where both M7.3 events were induced by the M7.9 in a domino fashion. Furthermore, the dominoes induced a 1st stage M6.9 in Suruga Bay (near Irozaki(石廊崎)). From there, both the Izu-Oshima(伊豆大島) Nearshore M7.0 and the nearby East Off Izu Peninsula (伊豆東方沖)M6.7 were induced as 2nd stages.
In the area near Izu-Oshima(伊豆大島), magnitudes have been updated—3rd stage M6.8 in 1930, 2nd stage M7.0 in 1978, and 2nd stage M6.7 in the East Off Izu Peninsula (伊豆東方沖)—showing how the maximum M in surrounding grids increased through a domino chain within the M6.7–M7.0 range.
The initial ripple from the M7.9 to the distant M6.8 was an energy transfer where energy dispersed and accumulated in surrounding grids was concentrated like dominoes and transmitted with a time lag. The phenomenon where the loop "returns to its original scale" near M6.7 after starting from M6.8 can be seen as a visualization of the process where the energy conservation of the entire system and the stress balance within the crust reach equilibrium and stabilize. Since the M6.7 in 1980, no earthquake of M6.7 or higher has occurred in this analyzed rectangular area.
Now that the macro-process analysis of the surge from 2nd-stage M3.7 to 3rd-stage M7.3 is complete, we move to the micro-analysis of the North Izu Earthquake.
[Micro Analysis]
To confirm interactions in the vertical direction, the analysis range is expanded beyond the 1 km depth to include the vertical grid hierarchy. There are 42 total earthquakes in this grid (same Lon/Lat), with 11 at 0 km and 7 at 1 km. We begin analyzing from the shallowest 0 km layer.
After three consecutive "Unknown" (unlabeled) events, the activity moved south to M3.8. Following a yellow-labeled "Unknown," it proceeded counter-clockwise, closing a rectangular area at M3.6, then moved north clockwise to M3.2. Subsequently, the pattern shifted gently toward the southwest (blue labels).
Next, we confirmed the transition of Magnitude (M) relative to Longitude. The correlation of the three points on the red line is extremely high, with a correlation coefficient of 0.9992. This constant rate of change in magnitude accompanying longitudinal movement likely reflects the existence of an extremely homogeneous gradient in stress distribution (or friction characteristics) on the fault plane.
Next, we confirmed the transition of M relative to Latitude. These are two sets of three-point correlations on the red lines. They share the M3.6 epicenter, and the correlation coefficients for the positive/negative slopes are remarkably high at 0.9998 and 0.9985, respectively. Surprisingly, both sets consist of the same magnitude combination: M3.2, M3.6, and M3.8.
The fact that two linear epicenter groups cross and share specific magnitudes suggests that the stress field at 0 km depth—directly above the singularity—possessed a mathematically rigorous geometric structure. It marks the junction of "two different structural lines (fault systems or stress axes)." The shared M3.6 epicenter may have acted as a "fixed point" where the energy gradients of longitude and latitude perfectly coincided.
Analysis of the 1 km Layer (Singularity Grid)
The number of epicenters in the 1 km singularity grid is seven. The activity is concentrated in a very short period in 1930.
Similar to the 0 km layer, the 1 km layer shows a counter-clockwise loop forming a trapezoidal area. The North Izu Earthquake (M7.3) occurred near the point where the loop closed. The subsequent transition moved south-southeast, deviating significantly from the trapezoidal area. This loop can be interpreted as tracing the outline of an asperity (locked zone).
Regarding M vs. Longitude at 1 km, we confirmed two sets of highly correlated epicenter groups sharing one epicenter (unlike the single set at 0 km). The correlation coefficients are 1.0 and 0.9993. With only six epicenters having recorded magnitudes, such high correlations cannot be a coincidence.
The trajectory shows M3.6 (1st stage initial) and M3.7 (2nd stage initial), followed by M3.2 and M3.4 on a line with a correlation of 1.0, before abruptly expanding to the M7.3 North Izu Earthquake.
Mechanisms Near the North Izu Earthquake
The two M3.8 earthquakes (November 25 and November 26) that occurred at a depth of 0 km played a decisive role in the process of constructing the "geometric framework (outer frame)" over a 24-hour period.
1. Distinction and Roles of the Two M3.8 Events in the 0 km Layer
1st Event: November 25, 1930 (Previous Day) M3.8 (Depth: 0 km)
Role: The starting point of the "negative slope" line in the correlation diagram of the 0 km layer.
Significance: Approximately 24 hours before the mainshock, it placed the first "maximum load point" on the singularity grid and determined the endpoints of the North-South and East-West stress gradients.
2nd Event: November 26, 1930 (Day of the Event) M3.8 (Depth: 0 km)
Role: The starting point of the "positive slope" line in the correlation diagram of the 0 km layer.
Significance: In the activity on the day of the mainshock, it placed "another maximum load point" to pair with the first M3.8 (from the previous day). This completed the outer frame of the "X-shaped cross structure (screw-tightening structure)" shown in later analyses.
2. Chronological Reorganization: Linkage from the 0 km Layer to the 1 km Layer
By distinguishing between the two M3.8 events, the dynamic process until the singularity was completed as a "singularity" has become clearer.
Setting the Framework (Nov 25): The M3.8 (0 km) on the previous day set one "strain boundary condition" near the surface.
Completion of the Diagonal Axis (Early morning, Nov 26): The M3.8 (0 km) of the day occurred, pairing with the point from the previous day, completing the geometric preparation to "sandwich" the inside of the grid.
Precise Convergence (Nov 26, 01:00 to before 04:00): Subsequently, hypocenters such as the M3.6 (shared hypocenter) and M3.2 occurred in "descending order of magnitude" and "symmetrically" along the axes established by the M3.8 events, completely eliminating any slack within the grid.
Mainshock Occurrence in the 1 km Layer (Nov 26, 04:02): Immediately after the "screw-tightening (cross structure)" in the 0 km layer was completed and the surface side became an immovable "lid," the energy's escape route was transferred to the layer 1 km below. At this point, the M7.3 (3rd stage) occurred simultaneously with the M3.8 (reference value) of the 1 km layer.
Supplementary Explanation
Although there seems to be little numerical difference between hypocenter depths of 0 km and 1 km, the 0 km depth differs in that it acts as an <u>open end</u> for waves.
The counter-clockwise rotation of the hypocenters is observed at both macro and micro levels, suggesting the fractal nature of earthquake characteristics.
While this analysis focused on earthquakes with a hypocenter depth of 1 km, the next analysis will cover a depth of 37 km, from which I expect to gain different insights.
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