Danijel Schorlemmer

Probability of Detecting an Earthquake

We present a new method for estimating earthquake detection proba- bilities that avoids assumptions about earthquake occurrence, for example, the event-size distribution, and uses only empirical data: phase data, station infor- mation, and network-specific attenuation relations. First, we determine the detection probability for each station as a function of magnitude and hypocentral distance, using data from past earthquakes. Second, we combine the detection probabilities of sta- tions using a basic combinatoric procedure to determine the probability that a hy- pothetical earthquake with a given size and location could escape detection. Finally, we synthesize detection-probability maps for earthquakes of particular magnitudes and probability-based completeness maps. Because the method relies only on detec- tion probabilities of stations, it can also be used to evaluate hypothetical additions or deletions of stations as well as scenario computations of a network crisis. The new approach has several advantages: completeness is analyzed as a function of network properties instead of earthquake samples; thus, no event-size distribution is assumed. Estimating completeness is becoming possible in regions of sparse data where meth- ods based on parametric earthquake catalogs fail. We find that the catalog of the Southern California Seismic Network (SCSN) has, for most of the region, a lower magnitude of completeness than that computed using traditional techniques, although in some places traditional techniques provide lower estimates. The network reliably records earthquakes smaller than magnitude 1.0 in some places and 1.0 in the seis- mically active regions. However, it does not achieve the desired completeness of mag- nitude ML 1:8 everywhere in its authoritative region. A complete detection is achieved at ML 3:4 in the entire authoritative region; thus, at the boundaries, earthquakes as large as ML 3:3 might escape detection.

Analysis of the Completeness Magnitude and Seismic Network Coverage of Japan

Abstract A reliable estimate of completeness magnitude, M c , above which all earthquakes are considered to be detected by a seismic network, is vital for seismicity-related studies. We show a comprehensive analysis of M c in Japan. We use the catalog maintained by the Japan Meteorological Agency (JMA) and also available information on seismic stations that report to JMA. For computing M c , we adopt a commonly used method based on the Gutenberg–Richter frequency-magnitude law. Presently, M c =1.0 might be typical in the mainland, but to have a complete catalog, one needs to use earthquakes with magnitudes of 1.9 or larger. Comparison with the Southern California Seismic Network (SCSN) suggests that the recent event detectability in the mainland generally shows similar completeness levels to that in the authoritative region of SCSN. We argue that the current M c of Japan is due to the success of network modernization over time. Particularly, we show that the spatiotemporal change of M c closely matches the addition of the Hi-net borehole stations to enhancing seismic-station density; it started in October 1997 in southwestern Japan, continuing to northeastern Japan until 2002. As suggested from this matching, we confirm that M c inversely correlates with station density. Further, we find that irrespective of the network change after 1997, this correlation is unchanged in time, demonstrating that the influence on M c from factors beyond station density does not vary in time. Contrary to Alaska and California (Wiemer and Wyss, 2000), our results do not attribute such factors simply to anthropogenic noise. Because this is due to the borehole stations that reduce ambient noise, we conclude that in Japan the anthropogenic noise has an insignificant effect on M c .

On the Probability of Detecting Picoseismicity

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< M w<-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 M P=-4.8, whereas at stope level (approximately 100xa0m from the network), the magnitude of completeness is only M P=-3.1. Variations due to the influence of local heterogeneities, for example, tunnels, are clearly resolvable.

Regional Earthquake Likelihood Models II: Information Gains of Multiplicative Hybrids

The Regional Earthquake Likelihood Models experiment in California tested the performance of earthquake likelihood models over a five‐year period. First‐order analysis showed a smoothed‐seismicity model by Helmstetter etxa0al. (2007) to be the best model. We construct optimal multiplicative hybrids involving the best individual model as a baseline and one or more conjugate models. Conjugate models are transformed using an order‐preserving function. Two parameters for each conjugate model and an overall normalizing constant are fitted to optimize the hybrid model. Many two‐model hybrids have an appreciable information gain (log probability gain) per earthquake relative to the best individual model. For the whole of California, the Bird and Liu (2007) Neokinema and Holliday etxa0al. (2007) pattern informatics (PI) models both give gains close to 0.25. For southern California, the Shen etxa0al. (2007) geodetic model gives a gain of more than 0.5, and several others give gains of about 0.2. The best three‐model hybrid for the whole region has the Neokinema and PI models as conjugates. The best three‐model hybrid for southern California has the Shen etxa0al. (2007) and PI models as conjugates. The information gains of the best multiplicative hybrids are greater than those of additive hybrids constructed from the same set of models. The gains tend to be larger when the contributing models involve markedly different concepts or data. These results need to be confirmed by further prospective tests. Multiplicative hybrids will be useful for assimilating other earthquake‐related observations into forecasting models and for combining forecasting models at all timescales.

Regional Earthquake Likelihood Models II: Information Gains of Multiplicative HybridsRegional Earthquake Likelihood Models II: Information Gains of Multiplicative Hybrids

The Regional Earthquake Likelihood Models experiment in California tested the performance of earthquake likelihood models over a five‐year period. First‐order analysis showed a smoothed‐seismicity model by Helmstetter etxa0al. (2007) to be the best model. We construct optimal multiplicative hybrids involving the best individual model as a baseline and one or more conjugate models. Conjugate models are transformed using an order‐preserving function. Two parameters for each conjugate model and an overall normalizing constant are fitted to optimize the hybrid model. Many two‐model hybrids have an appreciable information gain (log probability gain) per earthquake relative to the best individual model. For the whole of California, the Bird and Liu (2007) Neokinema and Holliday etxa0al. (2007) pattern informatics (PI) models both give gains close to 0.25. For southern California, the Shen etxa0al. (2007) geodetic model gives a gain of more than 0.5, and several others give gains of about 0.2. The best three‐model hybrid for the whole region has the Neokinema and PI models as conjugates. The best three‐model hybrid for southern California has the Shen etxa0al. (2007) and PI models as conjugates. The information gains of the best multiplicative hybrids are greater than those of additive hybrids constructed from the same set of models. The gains tend to be larger when the contributing models involve markedly different concepts or data. These results need to be confirmed by further prospective tests. Multiplicative hybrids will be useful for assimilating other earthquake‐related observations into forecasting models and for combining forecasting models at all timescales.