Analysis for the curve chart of distribution of epicenter (Magnitude)

The curve chart of the ,magnitude distribution in Iwate-oki Area including of Great East Japan Earthquake as below,

Just before Great East Japan Earthquake (M9.0), the frequency distribution curve of magnitude became almost negative quadratic function curve. The correlation coefficient (R^2) was 0.9281. It becomes 0.7697 now. M9.0 was irregular dot for these quadratic function curves. It seems to be similar with the exception of Gutenberg-Richter law in larger Magnitude zone.

The frequency distribution curves of magnitude has many patterns.

The curve chart of the ,magnitude distribution in Kumamoto region Area including of Great East Japan Earthquake as below, 

The top shape of the curve is sharper than one of quadratic function curve. The irregular plots are spread to the negative area of horizontal axis. Most of these epicenters were occurred in Aso region. So, these plots may be caused by volcanic activity of M't Aso(volcano). The irregular plots may be occurred by the difference of the earthquake mechanism.

There are other patterns like as multi peak curves, amorphous, etc. These difference should have the reasonable cause. It must be useful to solve the reasons.

Analysis for the curve chart of distribution of epicenter(Depth)

 To know a distribution of discrete values, histogram is usually used. There is Frequent tendency of the occurrence of Earthquakes in specific depth according with the local area. For such characteristics of discrete variable of the depth, the curve chart of depth class is used. 

The curve chart of the depth distribution in Iwate-oki Area including of Great East Japan Earthquake as below,

As the  deeper area's frequency is low, it seems to be redundant. So, double logarithmic graph is used as below,

This pattern seems to be ultimate one because of M9 huge earthquake. No need to say, not all curve have the peak of the curve in the shallow depth. This curve seems to be one of the reason why I believe earthquakes come from deeper epicenters. As 0km can't be used for logarithmic scale, 1km is used as the class value instead of it.

The double logarithm graph is Earthquake frequency per depth Chart in Niizima&Kozu island Area as below,

If the data of "Details unknown" with no magnitude is regarded as 1 km depth, the curve can become the similar line of blue as "in Sanriku-oki". So, I believed data of "Details unknown" as 1km depth.It seems to be too shallow to de fixed the depth, or to be slow slip epicenters. Anyway, in this site,  "Details unknown" is regarded as 1km depth data.

Analysis for the Area chart of epicenter(Magnitude)-3

The 6th "Accumulated value Chart" is for The Niigataken Chuetsu-oki Earthquake
(M6.8) in 2008 as below, 

There were 2 other area peaks in 2011/2024. They were aftershocks of Great East Japan Earthquake (M9.0) and of Noto Peninsula Earthquake (M7.6) . Both of the epicenter are outside of this Area.The main depth was shifted from Yellow area (10km) to Orange area (20km) by The Niigataken Chuetsu-oki Earthquake (M6.8) in 2008. Then, by M9.0, it was turn back to Yellow area (10km) /Red area (1km). By M7.6, it has turn to Orange area (20km) /Red area (1km) .

The 7th "Accumulated value Chart" is for The Noto Hanto Earthquake (M6.9) in 2007, and the common as the first one is for Noto Peninsula Earthquake (M7.6) in 2024.  

The 8th "Accumulated value Chart" is for The Mid Niigata prefecture Earthquake (M6.8) in 2004 as below, 

After the peak of M6.8, there are 2 major peaks of Yellow area in 2007 and of Red area in 2011. They are aftershocks of The Noto Hanto Earthquake (M6.9) and of Great East Japan Earthquake (M9.0). There is no major peak for Noto Peninsula Earthquake in 2024 (M7.6) even though nearer and larger than The Noto Hanto Earthquake (M6.9) in 2007. Maybe, both M6.9 in 2007 and M9.0 in 2011 had taken away aftershocks before it. These Red Area peaks were very remarkable.

The 9th "Accumulated value Chart" is for The Tokachi−oki Earthquake (M8.0) in 2003 as below,

There was 2 major peaks in this graph. One was the area peak of Red (1km)/Yellow(10km)/Green(40km)  caused by The Tokachi−oki Earthquake (M8.2) in 1952. The other was the area peak of Yellow green(30km)/Green(40km)/Light blue(50km) in 2003 caused by The Tokachi−oki Earthquake (M8.0) in 2003. These Tokachi−oki Earthquakes are very similar as below,

The difference of the depth area  component between them may be the order. This phenomenon is similar with the relationship between 2 earthquakes in Noto as explained above.

The 10th "Accumulated value Chart" is for The Western Tottori prefecture earthquake (M7.3) in 2000 as below, 

There are 4 major peaks of in this graph. The first one was the area peak of Red (1km) caused by Tottori earthquake (M7.2) in 1943. The 2nd one is the area peak of Red (1km)&Yellow(10km) caused by The Western Tottori prefecture earthquake (M7.3) in 2000. The 3rd one was the area peak of Yellow(10km) caused by nameless earthquake swarm (max M5.6) in 2001.The 4th one was the area peak of Red (1km)&Yellow(10km) caused by Central Tottori earthquake (M6.6) in 2016.Before M7.3 in 2000, there is small area peak of Yellow(10km) and long silent term of Red(1km) as about 11 years.

As showed 10 cases of main earthquakes in 2000-2024,  "Accumulated value Chart" is useful for the check of the mode change, and sometimes there are some advanced sign of big earthquakes.

Analysis for the Area chart of epicenter(Magnitude)-2

The 5th "Accumulated value Chart" is for The Iwate-Miyagi Nairiku Earthquake (M7.2) in 2008 as below,

There were 2 major peak. One was M7.1 in 2003. The other was M7.2 in 2008.They changed the pattern of the depth distribution in this area before and after completely. Great East Japan Earthquake changed in 2011 also, but, no remarkable peak there was. The difference between 3 earthquakes are listed in the table.

To clear the effect of the red area(1km), only 1km accumulated is picked up as below,

As the horizontal axis is non-linear, they have the different scale between full depth and only 1km. Before M7.2 in Jun 2008, there was small red area peak in Des 2007. It seems to be the advanced sign of M7.2.No peak was caused by no data of magnitude of "Details unknown". They are treated as 1 km depth class of epicenter in my site.(It's never the official opinion of Japan Meteorological Agency.)

Analysis for the Area chart of epicenter(Magnitude)-1

Most of earthquakes in the same area is single per day unless after big ones. So,the sum of magnitude per day can show the activity level in the area even though the values themselves have no meaning. Furthermore, by separating the sum per the depth class, it can show which depth is more active also. I defined the sum as "Accumulated value" of magnitude, and separate it per depth class(1km,10km,etc.).

I show will show the "Accumulated value Chart" for 10 major earthquakes after 2000 year. The first one is for Noto Peninsula Earthquake in 2024 (and The Noto Hanto Earthquake in 2007) as below,

There are more red (1km) and yellow (10km) area, especially after M7.6/M6.9. There are remarkable red area before them also, and there are long silent terms before the signs. It means red area (1km) may be the previous sign to great magnitude earthquakes.

The next chart is for Hokkaido Eastern Iburi Earthquake in 2018 as below,

There was a big peak of red area related with Eruption of M’t Usu in 2000 before the peak of the Iburi Earthquake(M6.7) in 2018. There was a long silent term (2003-2010) of red area (1km depth) also. After the silent term, there was middle peak of red area in 2014. As the epicenter of M6.7 was 37km, there was no peak of red area just after it. But, red area occurrence had great effect to M6.7.  

The 3rd chart is for Kumamoto Earthquake (M7.3) in 2016. As same as in Noto, there are much red area (1km) and yellow area (10km) totally. There were middle  peaks of red in 1975 and yellow in 2000. In 1990, Fugendake was erupted in 1991. As same as Kumamoto Earthquake,  eruption seems to have deep relationship with earthquake.

The 4th chart is for Great East Japan Earthquake(M9.0) in 2011 as below,

There are many peaks of big earthquakes more than 10 times of over M7. "Accumulated value" of magnitude per depth are added on in descending order of depth. The reason why is that less depth is more frequent and more important for the check of the activity level. As the total value itself has no great meaning, the vertical axis value is cut by 50[M]. Horizontal axis is non-liner.

Analysis for the line chart of epicenter(Magnitude)-2

For the prediction of magnitude earthquake, envelope lines seem to be useful.

The  line chart of magnitude in Sanriku-oki Area (rectangle area) with envelope lines is as below,

There are 2 kind of envelope lines. One is the top envelope lines for local maximum plots. The other is the bottom envelope lines for local minimum plots. For local period, all magnitude values with it are between top/bottom lines. Crossing these envelope lines may shows the pattern changes, and the too more/less excess values may often be the sign of sudden change like rapid increase of later value. As showed the previous page, sometimes the top envelope line of short term covers the excess value from the envelope line of long term. Around in 2007, there were rapid divergence of magnitude range between top/bottom envelope lines just after rapid convergence of them. It seems some sign of M9.0.   

Analysis for the line chart of epicenter(Magnitude)-1

The  line chart of magnitude in Sanriku-oki Area (rectangle area) as below,

For the predictive analysis of M9.0 (Great East Japan Earthquake)/M7.9 (Tokachi-oki Earthquake), some envelop lines are added on the graph as below,

3 red lines are related with M9, and one green line is related with M7.9.

3 red lines as approximation line are picked up, and extended until near M9 plot.

Each correlation coefficient(R^2) is 1.0 (because of only 2 dots). The intersections are nearby M9.0 even though there is about 3 years error against the real date of occurrence.

For M7.9 (Tokachi-oki Earthquake), one envelop line is added as green line, and picked up in the graph below,

The red line is as same as for green dots in the graph above. But, as there is only one envelop line at the occurrence of M7.9, the occurrence time couldn't be predicted.The correlation coefficient(R^2) of 3 dots is 1.0 including M7.9.

Even though I found these envelop lines, there is problems how to find out them/how to judge the extension length still. But, some candidate of envelop line may help the predict of earthquake magnitude.