# Regression Analysis

December 11, 2011
By

(This article was first published on Knowledge Discovery » R, and kindly contributed to R-bloggers)

## Regression Analysis

~about Long term data of earthquakes~

## 1 Introduction

I have attempted gaining a deeper understanding of seismic activity.
As one of the approach, I showed a “Japan Quake Map” on R-bloggeres,
which visualized infomation about epicenter and magnitude of earthquakes.

Please pay attention before and after “Tohoku Earthquake” on March 11, 2011 (1:03).

Using very long term data about earthquakes in Japan, I drew a Magnitude-Frequency Distribution in ggplot2 of R. Besides, I estimated coefficient of Gutenberg-Richter law.
Gutenberg-Richter law is a regression analysis model between the magnitude and total number of earthquakes of at least that magnitude.

## 2 Data

The term of analysis is the latest 126 years (from January 1885 through April 2011), number of sample is 41136. This dataset is included only data larger than Magnitude 4.0.

## 3 Results

First is Magnitude-Frequency Distribution. This aesthetic graph is drew with ggplot2 of R.
Second, using a graph taking a semilog scale, I estimated Gutenberg-Richter law’s b-value.
Coefficient of Gutenberg-Richter model was estimated by ordinary least squares(OLS).
Consequently, Gutenberg-Richter’s b-value was 0.918 in the sample period.

## 4 Conclusion

There are several published studies about estimating of the b-value.
For example, P Bak(2002) shows that b=0.95 using a dataset covering the period 1984 –2000 in a region of California.

In case of before and after “The 2011 off the Pacific coast of Tohoku Earthquake” on March 11, 2011, b-value was 0.795 in the same way.
Gutenberg-Richter law’s b-value is one of characteristic of seismic in any given region and time period.

## 5 Gratitude

Invaluable long term data I used was gathered by Prof.Teruo Kamada at Fukuyama University in Japan.The data source is mostly as follows.

• National Astronomical Observatory of Japan : Chronological Scientific Tabels
• Books(Author : Tatsuo Usami) : University of Tokyo Press
• Japan Meteorological Agency

He has published the data and software about earthquakes. I’d like to pay respect to his contributions.

## 6 Donate

After “Tohoku Earthquake”, many earthquakes have occured until today.
More than 15,841 people confirmed died, more than 3400 people is still missing
(According to infomation released by Japan National Police Agency on December 9, 2011),
and there’re a lot of people who are victims.

If you kindly wish to send your donations, I’d like to introduce two website below.
First is Japanese Red Cross Society.
Second is Google Crisis Response.

Finally, I’d like to express our thanks to all of you for helping us.

Only Seismic of Magnitude 9.0 is “The 2011 off the Pacific coast of Tohoku Earthquake” on March 11, 2011. This is the largest earthquake in Japan.

To leave a comment for the author, please follow the link and comment on their blog: Knowledge Discovery » R.

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