Downscaling of slip distribution for strong earthquakes
Abstract
We intend to develop a downscaling model to enhance the earthquake slip distribution resolution. Slip distributions have been obtained by other researchers using various inversion methods. As a downscaling model, we are discussing fractal models that include mono-fractal models (fractional Brownian motion, fBm; fractional Lévy motion, fLm) and multi-fractal models as candidates. Log - log-linearity of k (wave number) versus E (k) (power spectrum) is the necessary condition for fractality: the slip distribution is expected to satisfy log - log-linearity described above if we can apply fractal model to a slip distribution as a downscaling model. Therefore, we conducted spectrum analyses using slip distributions of 11 earthquakes as explained below. 1) Spectrum analyses using one-dimensional slip distributions (strike direction) were conducted. 2) Averaging of some results of power spectrum (dip direction) was conducted. Results show that, from the viewpoint of log - log-linearity, applying a fractal model to slip distributions can be inferred as valid. We adopt the filtering method after Lavallée (2008) to generate fBm/ fLm. In that method, generated white noises (random numbers) are filtered using a power law type filter (log - log-linearity of the spectrum). Lavallée (2008) described that Lévy white noise that generates fLm is more appropriate than the Gaussian white noise which generates fBm. In addition, if the 'alpha' parameter of the Lévy law, which governs the degree of attenuation of tails of the probability distribution, is 2.0, then the Lévy distribution is equivalent to the Gauss distribution. We analyzed slip distributions of 11 earthquakes: the Tohoku earthquake (Wei et al., 2011), Haiti earthquake (Sladen, 2010), Simeulue earthquake (Sladen, 2008), eastern Sichuan earthquake (Sladen, 2008), Peru earthquake (Konca, 2007), Tocopilla earthquake (Sladen, 2007), Kuril earthquake (Sladen, 2007), Benkulu earthquake (Konca, 2007), and southern Java earthquake (Konca, 2006)). We obtained the following results. 1) Log - log-linearity (slope of the linear relationship is ' - ν') of k versus E(k) holds for all earthquakes. 2) For example, ν = 3.70 and α = 1.96 for the Tohoku earthquake (2011) and ν = 4.16 and α = 2.00 for the Haiti earthquake (2010). For these cases, the Gauss' law is appropriate because alpha is almost 2.00. 3) However, ν = 5.25 and α = 1.25 for the Peru earthquake (2007) and ν = 2.24 and α = 1.57 for the Simeulue earthquake (2008). For these earthquakes, the Lévy law is more appropriate because α is far from 2.0. 4) Although Lavallée (2003, 2008) concluded that the Lévy law is more appropriate than the Gauss' law for white noise, which is later filtered, our results show that the Gauss law is appropriate for some earthquakes. Lavallée and Archuleta, 2003, Stochastic modeling of slip spatial complexities for the 1979 Imperial Valley, California, earthquake, GEOPHYSICAL RESEARCH LETTERS, 30(5). Lavallée, 2008, On the random nature of earthquake source and ground motion: A unified theory, ADVANCES IN GEOPHYSICS, 50, Chap 16.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFM.S51A2313Y
- Keywords:
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- 7215 SEISMOLOGY Earthquake source observations;
- 4475 NONLINEAR GEOPHYSICS Scaling: spatial and temporal;
- 7260 SEISMOLOGY Theory;
- 4440 NONLINEAR GEOPHYSICS Fractals and multifractals