Abstract
Multifractal Measures of M ≥ 3 Shallow Earthquakes in the Taipei Metropolitan Area
Highlights
In 1944, the frequency-magnitude relation reported by Gutenberg and Richter (1944) was the first scaling law to represent self-similarity of earthquake phenomena
The generalized fractal dimensions are measured for the M ≥ 3 shallow earthquakes with focal depths ≤ 40 km in the Taipei Metropolitan Area (TMA) during the 1973 - 2010 period based on the spatial distribution and time series
To examine the size of a study area on multifractal measures, the earthquakes in a smaller area are taken into account
Summary
In 1944, the frequency-magnitude relation reported by Gutenberg and Richter (1944) was the first scaling law to represent self-similarity of earthquake phenomena. Mandelbrot (1983) proposed the concepts of fractal geometry and fractal dimension to describe the scale-invariant natural phenomena. This concept has been widely applied to describe the spatial distribution of earthquakes (cf Turcotte 1989; Hirabayashi et al 1992; Wang and Lin 1993; Wang and Lee 1996; Wang and Shen 1999) and time series. A fractal set is defined to be one for which the Hausdorff-Besicovitch dimension strictly exceeds the commonlyused topological dimension (Mandelbrot 1983). A similarity dimension DS is defined for an exactly self-similar set as DS = log (L) /log (N), where L is the linear size and N is the number of the similar daughters. The correlation dimension DC is defined from the correlation integral C(r) in the following relation: C(r)~rDc-d, where d is the spatial (or topological) dimension (2 and 3 for the 2D and 3D spaces) and C(r) is defined for the epicentral distribution {ri} (i=1, 2, 3, ..., N) as
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
