A Study of Data Analysis by the Fractal Dimension Method

• Main Authors: Bing-Hai Chen, 陳冰海
• Other Authors: Tian-Wei Sheu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/81662971053604091636

碩士 === 國立臺中教育大學 === 教育測驗統計研究所 === 98 === This study is proposed for detecting P-wave’s arrival time and estimating the azimuth of an earthquake and apparent velocity near station by combining fractal dimension with correlation function technique. In addition, we apply the 2D fractal dimension technique to analyze children’s drawings to find out the developing stages of children. Research results are summarized as follows: 1. Applying fractal dimension method to seismic recordings, we find that the place where fractal dimension curve changes suddenly indicates the P-wave arrival. The fractal dimension method can identify the first arrival P-wave from background noises up to S/N ratio 1.25 after several theoretical testes. 2. The results of analyzing the earthquake recordings by fractal dimension method are that the time differences between theoretical and calculated are smaller than 0.1 second when the epicentral distances are smaller than 86 km, and the time error are smaller than 0.5 second when the epicentral distances are smaller than 113 km. Therefore, we conclude that the fractal dimension technique is an efficient method to detect the first P-wave arrival. 3. Estimating the azimuth of epicenter and apparent velocity near station, we can infer two important results. The first, the error of azimuth is smaller than 6 degrees when the epicentral distance is smaller than 95 km. The error of azimuth is more than 6 degrees when the epicentral distance is larger than 95km. The epicentral distance will influence the accuracy of the estimates of azimuth and apparent velocity. The second, the apparent velocity is correlative to the near surface P-wave’s velocity and incidence angle of seismic wave. Estimated apparent velocity in this research is about 3~3.5km/sec which is close to the surface P-wave velocity when the epicentral distance is smaller than 35 km. 4. For the children’ developing stage, the grade is significant to the dimension. Sixth grade shows the highest average dimension, and second grade reveals the lowest average dimension. In addition, we can conclude that the sexual difference is not significant to the fractal dimension of graphs.