Simultaneous assessment of the median annual seismicity rates and their dispersions for Taiwan earthquakes in different depth ranges

• Published in: Journal of Asian earth sciences Vol. 135; pp. 136 - 154
• Main Authors: Chang, Wen-Yen, Chen, Kuei-Pao, Tsai, Yi-Ben
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2017
• Subjects: Alternative Gutenberg-Richter relation; Arithmetic mean; Logarithmic annual seismicity rate; Taiwan earthquakes; Arithmetic mean; Alternative Gutenberg-Richter relation; Taiwan earthquakes; Logarithmic annual seismicity rate
• ISSN: 1367-9120; 1878-5786
• DOI: 10.1016/j.jseaes.2016.12.027

[Display omitted] •This is a milestone paper for presentation of Gutenberg-Richter relation.•Logarithmic mean tends to dampen the influence of spuriously high or low numbers.•Standard deviation is symmetric with logarithmic mean in the log-linear domain.•Arithmetic mean is susceptibly influenced by spuriously high or low numbers.•We explicitly incorporate the logarithmic mean and standard deviation in G-R law.•We use the catalog of Taiwan earthquakes to verify our concept for point (3)-(4). The main purpose of this study is to apply an innovative approach to assess simultaneously the median annual seismicity rates and their dispersions for Taiwan earthquakes in different depth ranges. In this approach an alternative Gutenberg-Richter (G-R) relation is explicitly expressed in terms of both the logarithmic mean annual seismicity rate and its standard deviation, instead of only by the arithmetic mean in the conventional G-R relation. Seismicity data from 1975 to 2014 in a Taiwan earthquake catalog with homogenized Mw moment magnitudes are used in this study. This catalog consists of high-quality earthquake data originally obtained by the Institute of Earth Sciences (IES) and the Central Weather Bureau (CWB). The selected seismicity data set is shown to be complete for Mw⩾3.0. The logarithmic mean annual seismicity rate and its standard deviation from the observed annual seismicity rates of individual years are obtained initially for different Mw ranges. It is shown subsequently that the logarithmic annual seismicity rates indeed possess a well-behaved lognormal distribution. It is further shown that our new approach has an added merit that tends to suppress the influences of anomalously high annual seismicity rates due to large numbers of aftershocks from major earthquake sequences. Finally, the observed logarithmic mean annual seismicity rates with their standard deviations for 3.0⩽Mw⩽5.0 are used to obtain the alternative Gutenberg-Richter relations for different depth ranges. The results are as follows: log10N=5.75-0.90Mw±(0.25-0.01Mw)for focal depth 0–300km; log10N=5.78-0.94Mw±(0.20+0.01Mw)for focal depth 0–35km; log10N=4.72-0.89Mw±(-0.08+0.08Mw)for focal depth 35–70km; log10N=4.69-0.88Mw±(-0.47+0.16Mw)for focal depth 70–300km. In above equations log10N represents the logarithmic annual seismicity rate. These G-R relations give distinctly different values of the parameters a and b for Taiwan earthquakes in different depth ranges. These analytical equations can be readily used to obtain both the mean logarithmic annual seismicity rate and its standard deviation for any given Mw. As an example, a numerical table presenting the corresponding median annual seismicity rates and their upper and lower bounds at median±one standard deviation levels, is given at the end. This table offers a concise glance at the annual seismicity rates for Taiwan earthquakes of various magnitudes and focal depths. It is interesting to point out that the seismicity rate of crustal earthquakes, which tends to contribute most hazards, accounts for only about 74% of the overall seismicity rate in Taiwan. Accordingly, direct use of the entire earthquake catalog without differentiating focal depth ranges may result in substantial overestimates of potential seismic hazards.