Near-surface wave attenuation (kappa) of Far West Rand micro-events

Abstract

Brandt (2015) and Birch, Cichowicz, and Grobbelaar (2015) recently undertook studies to determine the quality factor Q and attenuation parameter , which describe the attenuation of seismic waves with distance, for South African earthquakes and mining-related seismic events, respectively. Brandt (2015) derived an attenuation relation of Q( f ) 400f 0.7 , whereas Birch, Cichowicz, and Grobbelaar (2015) estimated the relation Q( f ) = 327f 0.81 for the Kaapvaal Craton. However, both these studies determined Q without knowledge of the near-surface attenuation, which is quantified by the factor k (kappa). The general decrease in amplitude of seismic waves caused by attenuation may be described by using the quality factor Q, as was proposed over 50 years ago (e.g. Havskov and Ottemöller, 2010b):where A 0 is the initial amplitude, A(t) the amplitude after the waves have travelled for time t, f represents the frequency, and Q( f) is the general frequency-dependent quality factor. Q has been observed to have strong regional variations in the crust and a frequency dependence of the form(e.g. Kvamme and Havskov, 1989;Kvamme, Hansen, and Bungum, 1995;Malagnini, Herrmann, and Koch, 2000) when f > 1 Hz and Q( f ) is nearly constant for 0.1 Hz < f < 1.0 Hz (e.g. Stein and Wysession, 2003). The frequency dependence is often found to be stronger with increasing tectonic activity and is thought to be related to the decrease in homogeneity within the crust (e.g. Kvamme and Havskov, 1989;Birch, Cichowicz, and Grobbelaar, 2015). Q is also thought to be mostly constant along the ray path for local seismology observations, with the exception of the near-surface layers (1-3 km), which generally have a much lower Q than the rest of the path and tend to filter out high-frequency energy between 5-25 Hz (e.g. Havskov and Ottemöller, 2010b). The attenuation term in Equation [1] may be separated into surface and deeper crust effects: [3] with k representing the near-surface attenuation. The parameter k describes the asymptotic high-frequency slope of the spectrum of a seismogram. A low value for k corresponds to a seismogram with abundant high-frequency energy, whereas a high value corresponds to a minimal amount of highfrequency energy (Kilb et al., 2012). Kappa varies with region (stable continental area vs. Kappa, near-surface attenuation, mining-related seismic event, spectral analysis.

Near-surface wave attenuation (kappa) of an earthquake near Durban, South Africa

“…For the analysis, the author selected a 30-second window for the S-phase portion of the vertical component seismogram. The result was an average = 0.021 ± 0.0007 seconds, which is lower than = 0.048 seconds for micro-events in the Far West Rand and much lower than = 0.098 seconds for explosions at Sasolburg coal mines (Brandt, 2017). Kappa was found to be higher than for a stable continental region ( = approx.…”

“…kappa, near-surface seismic attenuation, tectonic earthquake, spectral analysis. The present study is a continuation of the work previously completed by Brandt (2017). The reader is referred to that article for the definition of near-surface wave attenuation, , the two routine methods used to determine , the advanced method to determine , and how shapes the source spectrum of a small earthquake.…”

“…Atkinson, 1996;Douglas et al, 2010). Brandt (2017) ascribed this higher value obtained for to (1) additional near-surface wave attenuation at the shallow focus of both micro-events and explosions; and (2) the effect of the implosive component (micro-events) or explosive component (explosions) not accounted for in the Brune source model (Brune, 1970(Brune, , 1971. These two factors differentiate mining-related events and explosions from tectonic earthquakes that have (1) deeper focal depths (Brandt, 2014) and (2) a source mechanism that may be described by a double couple (McGarr, 2002).…”

“…These two factors differentiate mining-related events and explosions from tectonic earthquakes that have (1) deeper focal depths (Brandt, 2014) and (2) a source mechanism that may be described by a double couple (McGarr, 2002). The purpose of the initial investigation by the author (Brandt, 2017) was to derive a value for mining-related that will be useful in determining the attenuation relation required by spectral analysis when calculating moment magnitude, M w , for S-waves using the seismograms recorded by the South African National Seismograph Network (SANSN).…”

“…The reader is referred to that article for the definition of near-surface wave attenuation, , the two routine methods used to determine , the advanced method to determine , and how shapes the source spectrum of a small earthquake. In this study, is determined by means of definition (1) in Brandt (2017). This is the original definition given by Anderson and Hough (1984), but modified here for signals originating from a moderate size earthquake of M L 3.4 rather than for events larger than magnitude 5.…”