Estimation of the recording completeness of seismic catalogs recorded with small networks in a heterogeneous observation volume, for example, in mines, is difficult. Local heterogeneities have a strong influence on the wave path and attenuation and must be taken into account. In order to analyze the spatially varying completeness of such catalogs in three dimensions, we present a new approach based on the probability-based magnitude of completeness (PMC) method of Schorlemmer and Woessner (2008). We demonstrate that the traditional approach of Schorlemmer and Woessner (2008) is insufficient in very complex and heterogeneous settings. To account for this problem, we extend the PMC method, taking into account the direction of incoming seismic waves. This allows us to analyze the influence of small heterogeneities on the recording completeness in high resolution. We compare the results with results obtained by a traditional Gutenberg–Richter frequency-magnitude analysis for the JAGUARS catalog: The Japanese German Underground Acoustic Emission Research in South Africa (JAGUARS) project recorded approximately 500,000 seismic events with magnitudes -5<Mw<-1 in the Mponeng gold mine (Carletonville, South Africa) at -3.5 km depth. The network is surrounded by several cavities and is located partly in the Pink-Green dike, a local geological feature. We estimate that the completeness of the JAGUARS catalog varies significantly in space. In the center of the network, we estimate a magnitude of completeness of MP=-4.8, whereas at stope level (approximately 100 m from the network), the magnitude of completeness is only MP=-3.1. Variations due to the influence of local heterogeneities, for example, tunnels, are clearly resolvable.

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