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.

Analysis for the line chart of epicenter(Depth)

As showed ""Analysis for the line chart of epicenter(Lat/Lng)", the trend of 0km(1km) data of epicenters is very important. The trend graph in Sanriku-Area(1919-2015) is showed as below,

There is the longest silent term of 0km(1km) epicenter in the black circle.The graph area without 0km(1km) epicenter looks like blank area towards deeper epicenters.The next graph shows MD trend. MD is defined as the product between the magnitude and the depth of each epicenter. closed up the blank area is as below,

To show the blank area of  0km(1km) in details is as below, 

MD range is limited to close up the blank area.2 red lines are envelope lines to be connected of local minimum values in the blank area. It seems they may be useful for the prediction of Great East Japan Earthquake(M9.0).

* All data was downloaded from the site of Japan Meteorological Agency. I have arranged the data into graphs.Please see this page.

Analysis for the line chart of epicenter(Lat/Lng)-2

For the analysis of Noto Peninsula Earthquake(M7.6) in 2024/1/1, the time series graph of the epicenter(Lng) in Noto-pen.Area (1919/1-2025/1) is as below, 

The first graph is all data in the area.

The next graph is only 1km epicenter.

1km graph shows the graph pattern change more clearly.Earthquake swarm in 2007 was caused by M6.9 in Noto Offsure.After long silent term,the epicenter' s Longitude moved near to East side once. Then they returned to West side again and M6.9 was occurred. M6.9 is the second scale in all data of Noto-pen. Area. M7.6 in 2024 is the largest one in this Area.

Before M7.6(Noto Peninsula Earthquake), the abnormal earthquake swarm has started since around Aug/2021.But, in the graph with only 1km data, there had been the longest silent term exists just after M7.6.The term was broken only after  14 minutes from M7.6.

The time series graph of the epicenter(Lat) in Noto-pen. Area (1919/1-2025/1) as below, 

The first graph is all data in the area.

The next graph is only 1km epicenter(Lat).

* All data was downloaded from the site of Japan Meteorological Agency. I have arranged the data into graphs.M7.6 was occurred in land area as Noto-resion, and M6.9 was occurred in sea area near by the coast.About area definition, please see this page.

Analysis for the line chart of epicenter(Lat/Lng)-1

To predict future phenomenon, time series graph is very important.

For the analysis of Great East Japan Earthquake(M9), the time series graph of the epicenter in Sanriku-oki (1919/1-2011/3) Area as below,

Even just before Great East Japan Earthquake,it seems there is no previous indication of it in these above graphs. The some increase of occurrence has been seen, but data in 1969 was far more. So, I tried to classified the data per the depth level per 10km. As I showed, 0km(treated as 1km) is the main data. In this case, 1km data showed the most remarkable results as below,

There is long silent term before M9. For easy finding, these charts are for in 1919-2025. Unfortunately, the end of this long silent term was just after about 3hours. But, in other cases, the end times are before big earth quakes. Anyway,long silent term can show the possibility of great earthquakes as far as I have checked other data.The same pattern before M9 can be found along Japan Trench in many area.

There is another long silent term in 2012-2025 also.The outer-rise earthquake against M9 has not been confirmed. 

Epicenter location vs Magnitude graph

Huge earthquake seems to be occurred as the result of chain of many earthquakes.To make clear the relationship with other ones, graph is one of the most important tools.

The below graph shows the dependency of Epicenter location(Longitude) to the magnitude in Sanriku-oki area. Horizontal axis is epicenter's longitude, and vertical logarithmic axis is Magnitude.These earthquake data are between 1/1/2019 - 3/11/2011 (until Great East Japan Earthquake) in Sanriku-oki area,downloaded from Japan Meteorological Agency.  

The black circle in graph shows the gap between M9.0 and M6.2 on 142.9E. The gap reflects one of the exception of Gutenberg-Richter law in larger Magnitude zone.Colored lines are connecting with some peaks of Magnitude in each location.It might be some possibility of the prediction of large Magnitude before the occurrence. To show the linearity of these colored lines,the related plots are picked up in the graph below,

Dots on the blue line are data as below,

• 1933/ 3/ 3 144.8E/39.5N M6.7 0km
• 1935/10/18 144.4E/40.3N M7.1 7km
• 2011/ 3/11 142.9E/38.1N M9.0 24km

Blue line's correlation coefficient of 3 points is 0.9998 (almost 1).

Dots on orange line are as below,

• 1958/ 4/ 8 143.5E/38.4N M6.5 0km
• 1992/ 7/18 143.4E/39.4N M6.9 0km
• 2011/ 3/ 9 143.3E/38.3N M7.3 8km
• 2011/ 3/11 142.9E/38.1N M9.0 24km

Orange line's correlation coefficient of 4 points is 0.9993 (almost 1). In the case of 3 points without M6.5 0km (older than M6.9 0km), it becomes 0.9998.

M9.0 on 142.9E may be predicted by the intersecting point of Blue/Orange lines. But, there is no way to know the estimated time of the occurrence only by these graphs.

As same as for Epicenter location(Longitude)  above, the below graph shows the dependency of Epicenter location(Latitude) to the magnitude in Sanriku-oki area. Horizontal axis is epicenter's latitude, and vertical logarithmic axis is Magnitude. Others are common with the case of  location(Longitude).

 

 

The black circle in graph shows the gap between M9.0 and M6.2 on 38.1N. The related plots on the colored lines are picked up in the graph below,

 

Dots on the Pink line are data as below,

• 1931/ 3/ 9 143.3E/40.2N M7.2 0km
• 1933/ 3/ 3 145.1E/39.1N M8.1 0km
• 1935/10/18 144.4E/40.3N M7.1 7km
• 2011/ 3/11 142.9E/38.1N M9.0 24km
  

Pink line's correlation coefficient of 5 points is 0.9998 (almost 1).

Dots on the Green line are data as below,

• 1958/ 4/ 8 143.5E/38.4N M6.5 0km
• 2011/ 3/ 9 143.3E/38.3N M7.3 8km
• 2011/ 3/11 142.9E/38.1N M9.0 2.4km

Green line's correlation coefficient of 5 points is 0.9973 (almost 1). 

 

M9.0 on 38.1N may be predicted by the intersecting point of Pink/Green lines. As M9.0 on 142.9E can be done also, the prediction of the epicenter should be able to fix without the timing.This result makes me believe the prediction including the timing should be possible also in the future.  

Area data of Great East Japan Earthquake

Sanriku-oki as rectangle area including the epicenter of Great East Japan Earthquake is as below,

This picture was downloaded from the database of Japan Meteorological Agency(JMA).

Orange circle shows the epicenter of Great East Japan Earthquake(M9.0).

Great East Japan Earthquake(M9.0) was occurred in 3/11/2011.The depth was 24km.The epicenter was in 142.9E/38.1N.

I will explain the analysis of earthquake using real data of Great East Japan Earthquake mainly.

Earthquake data treatment

All fundamental original data have download from database of Japan Meteorological Agency (JMA). I use only felt earthquakes in Japan as possible data size.

Original data is a set of data as below,

• Date and time of occurrence
• Location Name of epicenter
• latitude longitude of epicenter
  
• Depth of epicenter ([km])
  
• Magnitude (M0.0-M9.9)
• Japanese earthquake scale（10steps） 

I give some arrangements for these basic data as below,

• Date and time of occurrence => Some data are treated as the total value per day
• Location Name of epicenter (Original ones are amorphous, for example, separated land area from sea area) => New rectangle area defined including all original area
• latitude longitude of epicenter => Sometimes used as rounding off to the first decimal place for classification
• Depth of epicenter ([km]) => Sometimes used as rounding off for classification like as 0km/10km/20km/etc. Sometime 1km is used instead of 0km for usage of logarithm scale or product value
  
• Magnitude (M0.0-M9.9) => as is numerical value　
• Japanese earthquake scale（10steps）  => only reference because of secondary parameter

"Details Unknown" with unknown depth as Location Name of epicenter are included in JMA database. The quantity is about 90 thousands against about 220 thousands of all data. "Details Unknown" with no magnitude data is regarded as 0[km] or 1[km].

 

Database of Japan Meteorological Agency (JMA) is sometimes updated.Some data have been added lucking data, and some of them have been deleted.   

 

Image of Earthquake as Plate Tectonics

Plate Tectonics theory is the most popular one as well known generally. Near Japan, both Pacific plate and Philippine sea plate is going down below continental plate slowly.These plates are carried by mantle convection under them.The going down plates are pulling down continental plate also. But, if the stress becomes over than friction force between these plates, the continental plate will spring back. In the case of the spring back with long time deflection all at once, the huge earthquake should be occurred. On the other hand, if the spring back goes slowly, only small earthquake should be occurred. The phenomenon called as "Slow Slip" is such one. 

Before huge earthquake, micro earthquakes with Slow slip had often been occurred as the sign of huge one. It seems to be similar that the full drawing bow must be allowed only micro moving. As I wrote in Image of Earthquake as cracking phenomenon (2) , there are many data of Details Unknown" with unknown depth in database of Japan Meteorological Agency (JMA). I guessed the reason why the depth are unknown that too shallow epicenters might be not enough to calculate the depths from the time lags between S-wave and P-wave. But, I wonder if some of them might be Slow Slip because of the slow process. 

Image of Earthquake as cracking phenomenon (3)

 As I wrote in (2), there are cracking origins of Earthquakes near the plate edges in deep area.In the deeper area of earth's crust, the higher pressure there is. So, stress of plates should go towards to shallower area. In the other hand, earthquake energy  is distributed from deeper area to shallower area. It seems to be similar with the domino from a large piece to smaller pieces.In the ends of domino, the falling domino makes stopped by the bigger pieces. Except the falling down near ground surface, most of energy should be stocked as all the accumulation including past other stacked pieces. Only it is open end, and others in deeper area are fixed end by neighborhood crust.

The loss energy by shaking near ground surface is very small because of far smaller mass than the Magnitude except tsunami with huge mass of sea water. This may be the reason why most of the biggest earthquakes wouldn't follow with Gutenberg-Richter law. The loss energy by friction between sinking continental plates around the edge may be small ratio of the total Magnitude energy. Its dynamic friction coefficient in slipping phenomenon is very small in general (If it were large, the phenomenon should be called not "slipping", but "slow slipping" without large magnitude ).  

Image of Earthquake as cracking phenomenon (2)

One big earthquake induces many other earthquakes around it.Sometimes, it induces bigger ones.The dynamics seems to be similar with domino's one.Big domino piece can push down the same or smaller pieces.Sometimes, high speed pieces can push down even bigger one.If not pushed down,tilted piece can stock the kinetic energy as potential energy.It seems to be similar with earthquake dynamics.

In my understanding, stress comes from deep Earth crust area.In deeper area, there is higher pressure.So, every movement of Earth crust should be limited.In fact,most of earthquakes came from deeper area in Japan.Based on the database of Japan Meteorological Agency(JMA), the numbers of earthquakes per the depth are as the graph as below,

(note)The counts are done by me.The earthquakes of 0km includes "Details Unknown" with unknown depth just as my judgment.

The number of class of 0km is more than 100 thousands,and it's almost half of the total number.On the other hand, the numbers of deeper than 100km is only less than 2%. This result may reflect the fact that deeper earthquakes are primordial than the shallower ones.

The 2 figures shows the results selected with 100km deeper from JMA database directly as below,

(Condition 1) Results : N=355

Period : 1/1/1919-1/6/2025

Magnitude : M6.0-M9.9

Depth : 100km-999km

 

(Condition 2)Results : N=855

Period : 1/1/1919-1/6/2025

Magnitude : M0.0-M4.0

Depth : 100km-999km

Even though the number of earthquakes with M0.0-M4.0 (condition 2) are 2 times more than with M6.0-M9.9 (condition 1), the distribution on the map are less than.As I described above, the every movement are limited, less magnitude should mean near the origins of cracking. The curve of epicenters shows the plate edge.In M6.0-M9.9 (condition 1), most of epicenters also stay near the plate edge curves.

As you know, continental plate movement is the main cause of earthquakes near the Pacific-rim, and Pacific Ring of Fire exists along it.

 

    

Image of Earthquake as cracking phenomenon (1)

Earthquake is usually described with the data set of its start time, epicenter, depth, magnitude, and seismic intensity.But,the epicenter/depth is just only a starting point of cracking area or block.Earthquake phenomenon is a cracking/slipping in Earth crust.For example,Great East Japan Earthquake in 2011 had the broken area with almost 450km length and 200km width according with Japan Meteorological Agency's analysis.Earthquake energy is depended on the length of the earthquake fault.Earthquake energy is defined as magnitude scale.Seismic intensity is depended on the distance between the observation point and the epicenter including the depth.So,we need to predict the magnitude before the seismic intensity. 

In general,cracking starts from the weakest points.Folded paper can be cut along with the folding line easily.Light selects the route with the shortest time required according with Fermat's principle.As same as Light, crack selects the route with the minimum work according with principle of least action.This may be the reason why there are some epicenters are on a line and others are not on a line against the complicated geological structure.One of the weakest line in the area should be the earthquake fault as the scar of the ground.The large fault can be the cause of big earthquake.

Introduction to Earthquake study

This blog has a purpose to share with my individual understanding for Earthquake nature.It still includes many estimation,and incomplete one.But, I believe it may be useful for the future Earthquake study progress.

My study started after Great East Japan Earthquake in 2011 when I was a ordinary office worker having no relation with Earthquake study.I had been a interest in the nature of the linearity between the epicenters of some major Earthquakes.It seems to be natural that they came into a line as one kind of cracking phenomenon.So,I believed there should be some rules of their occurrences.

My first study job was just input all felt earthquake data day by day in my private time after returning home.It was very simple,but very hard work because of manual input of too many data. On 3/11/2011,more than 500 times earthquake was occurred in a day.The counts in 2011 was more than 10 thousands.

Now, based on down load data set from Japan Meteorological Agency site, my private study is on going.Though data comes form them, the analysis has being performed by myself unless any additional note.I can't give any guarantee for the accuracy for my estimation and my prediction.Because I don't know if it's true or not also.I hope your own judgment for my opinion by yourself after reading it.

On 1/6/2025,  Keigetu Sansui (pen name)