Violations of Gutenberg–Richter Relation in Anthropogenic Seismicity

Abstract

Anthropogenic seismicity (AS) is the undesired dynamic rockmass response to technological processes. AS environments are shallow hence their heterogeneities have important impact on AS. Moreover, AS is controlled by complex and changeable technological factors. This complicated origin of AS explains why models used in tectonic seismicity may be not suitable for AS. We study here four cases of AS, testing statistically whether the magnitudes follow the Gutenberg-Richter relation or not. The considered cases include the data from Mponeng gold mine in South Africa, the data observed during stimulation of geothermal well Basel 1 in Switzerland, the data from Acu water reservoir region in Brazil and the data from Song Tranh 2 hydropower plant region in Vietnam. The cases differ in inducing technologies, in the duration of periods in which they were recorded, and in the ranges of magnitudes. In all four cases the observed frequency-magnitude distributions statistically significantly differ from the Gutenberg-Richter relation. Although in all cases the Gutenberg-Richter b-value changed in time, this factor turns out to be not responsible for the discovered deviations from the Gutenberg-Richter born exponential distribution model. Though the deviations from Gutenberg-Richter law are not big, they substantially diminish the accuracy of assessment of seismic hazard parameters. It is demonstrated that the use of non-parametric kernel estimators of magnitude distribution functions improves significantly the accuracy of hazard estimates and therefore these estimators are recommended to be used in probabilistic analyses of seismic hazard caused by AS.

Time-dependent seismic hazard in Bobrek coal mine, Poland, assuming different magnitude distribution estimations

“…Evidences for the existence of multimodal earthquake size distribution were presented in many papers (e.g., Gibowicz and Kijko 1994;Gibowicz and Lasocki 2001;Lasocki and Orlecka-Sikora 2008). Magnitude distribution may statistically significantly differ from the exponential distribution but the differences may be small (Urban et al 2016). G-R model seems often inadequate to describe the earthquake size distribution.…”

“…First, we used KolmogorovSmirnov (K-S) goodness-of-fit one-sample test to check whether earthquake size distribution statistically differs from the exponential distribution. Details of this procedure and the corresponding findings in several cases of induced seismicity are described in the paper of Urban et al (2016). Second, we examined the earthquake size distribution for its complexity using smoothed bootstrap test for multimodality.…”

Interval Estimation of Seismic Hazard Parameters

“…Haege et al 2012;Urban et al 2015). The second model corresponds for instance to the seismicity triggered by a surface reservoir impoundment of the hydropower plant Song Tranh 2 in Central Vietnam (e.g.…”

“…The second model corresponds for instance to the seismicity triggered by a surface reservoir impoundment of the hydropower plant Song Tranh 2 in Central Vietnam (e.g. Wiszniowski et al 2015;Urban et al 2015). The third model is a mixture of two one-side truncated exponential distributions, and reads:…”

“…The two considered approaches to CI estimation of hazard functions have been applied to two actual sets of earthquakes related to anthropogenic seismicity accompanying, respectively, (1) underground exploitation of copper ore in the Legnica-Głogów Copper District (LGCD) in Poland (Orlecka-Sikora et al 2012) and (2) Song Tranh 2 in Vietnam reservoir impoundment (Wiszniowski et al 2015;Urban et al 2015). The first dataset from LGCD is associated with mining exploitation in section G-11/8 of Rudna mine.…”