Estimation of the Tapered Gutenberg-Richter Distribution Parameters for Catalogs with Variable Completeness: An Application to the Atlantic Ridge Seismicity

The use of the tapered Gutenberg-Richter distribution in earthquake source models is rapidly increasing, allowing overcoming the definition of a hard threshold for the maximum magnitude. Here, we expand the classical maximum likelihood estimation method for estimating the parameters of the tapered Gutenberg-Richter distribution, allowing the use of a variable through-time magnitude of completeness. Adopting a well-established technique based on asymptotic theory, we also estimate the uncertainties relative to the parameters. Differently from other estimation methods for catalogs with a variable completeness, available for example for the classical truncated Gutenberg-Richter distribution, our approach does not need the assumption on the distribution of the number of events (usually the Poisson distribution). We test the methodology checking the consistency of parameter estimations with synthetic catalogs generated with multiple completeness levels. Then, we analyze the Atlantic ridge seismicity, using the global centroid moment tensor catalog, finding that our method allows better constraining distribution parameters, allowing the use more data than estimations based on a single completeness level. This leads to a sharp decrease in the uncertainties associated with the parameter estimation, when compared with existing methods based on a single time-independent magnitude of completeness. This also allows analyzing subsets of events, to deepen data analysis. For example, separating normal and strike-slip events, we found that they have significantly different but well-constrained corner magnitudes. Instead, without distinguishing for focal mechanism and considering all the events in the catalog, we obtain an intermediate value that is relatively less constrained from data, with an open confidence region.

Analisis Tingkat Kegempaan Wilayah Jawa Timur berbasis Distribusi Spasial dan Temporal Magnitude Of Completeness (Mc), A-Value Dan B-Value

<p class="AbstractText">Distribusi spasial dan temporal dari parameter seismisitas yang terdiri dari <em>magnitude of completeness</em> (Mc), <em>a-value</em>, dan <em>b-value </em>telah dihitung sebagai upaya untuk menganalisis tingkat kegempaan wilayah Jawa Timur. Parameter tersebut dihitung berdasarkan data katalog gempa bumi <em>International Seismological Center</em> (ISC) dalam rentang waktu antara tahun 1980-2020. Tujuan dari penelitian iniadalah untuk menentukan parameter seismisitas dan distribusi spasial dan temporalnya sehingga proses deteksi dan peringatan dini gempa bumi di Jawa Timur dapat berjalan secara optimal. Parameter seismistas dihitung dengan menggunakan metode <em>Maximum Curvature</em> (MaxC). Metode MaxC dalam menentukan parameter seismisitas terdiri dari proses menentukan titik kelengkungan maksimum dengan menghitung nilai maksimum dari turunan pertama kurva distribusi Frekuensi-Magnitudo (FMD). Variasi parameter seismisitas kemudian dipetakan secara spasial dan temporal setiap sepuluh tahun dalam kurun waktu 50 tahun terakhir untuk melihat perubahan variasi parameter seismisitas. Hasil penelitian menunjukkan Mc-<em>value</em> 3,4 – 4,8; a-<em>value</em> 5,560 - 8,244; dan b-<em>value</em> (0,73 – 0,82 ± 0.13). Daerah yang memiliki <em>b-value</em> rendah (0,73 ± 0.13) berada di sekitar wilayah selatandai Jawa Timur. Wilayah ini diindikasikan sebagai daerah dengan pelepasan momen seismik yang tinggi dan memiliki akumulasi tingkat <em>stress</em> batuan yang tinggi. Mengetahui dan memahami hubungan antara parameter seismistas dan struktur tektonik dapat membantu kita untuk menentukan tingkat resiko bencana gempa bumi di wilayah Jawa Timur.</p>

A homogeneous earthquake catalogue for Turkey

A new homogenized earthquake catalogue for Turkey is compiled for the period 1900–2018. The earthquake parameters are obtained from the Bulletin of International Seismological Centre that was fully updated in 2020. New conversion equations between moment magnitude and the other scales (md, ML, mb, Ms, and M) are determined using the general orthogonal regression method to build up a homogeneous catalogue, which is the essential database for seismic hazard studies. The 95 % confidence intervals are estimated using the bootstrap method with 1000 samples. The equivalent moment magnitudes (Mw*) for the entire catalogue are calculated using the magnitude relations to homogenize the catalogue. The magnitude of completeness is 2.7 Mw*. The final catalogue is not declustered or truncated using a threshold magnitude in order to be a widely usable catalogue. It contains not only Mw* but also the average and median of the observed magnitudes for each event. Contrary to the limited earthquake parameters in the previous catalogues for Turkey, the 45 parameters of ∼378 000 events are presented in this study.

A grid-based b-value approximation through Southern and Northern Norway: preliminary results

&lt;p&gt;The Gutenberg &amp;#8211; Richter&amp;#8217;s b-value is commonly used to analyze the frequency-magnitude distribution of earthquakes, describing the proportion of small and large seismic events as the first estimation of seismic hazard. Additionally, the b-value has been used as a stress meter, giving some insights into the stress regime in different regions around the world. In this research, a grid-based spatial distribution for the b &amp;#8211; value was estimated in three different areas of Norway: northern (74&amp;#176;-81&amp;#176; N/ 12&amp;#176;-26&amp;#176; E), southern (57&amp;#176;-64&amp;#176;N/3&amp;#176;-12&amp;#176; E), and the ridge zones of Mohns and Knipovich. For this, we used a complete catalog from the years 2000 to 2019, which was obtained from the Norwegian National Seismic Network online database. The magnitude of completeness was estimated separately for each zone both in time and space, covering a total area of ~425,000 km&lt;sup&gt;2&lt;/sup&gt;. Our results show a regional variation of the mean b-value for northern (b&lt;sub&gt;north&lt;/sub&gt; = 0.79) and southern (b&lt;sub&gt;south&lt;/sub&gt; = 1.03) Norway, and the Ridge (b&lt;sub&gt;ridge&lt;/sub&gt; = 0.73), which can be interpreted in terms of the predominant stress regime in the different zones. So far, a few calculations regarding the b-value were previously done in Norway to analyze local intraplate sequences. Then, according to our knowledge, this research corresponds to the first estimation of a regional spatial variation of the b &amp;#8211; value in the country.&lt;/p&gt;

Do spatial and/or temporal b-value variations exist within the Groningen induced earthquake catalogue?

&lt;p&gt;We present a data-driven analysis to derive whether statistically significant spatial and/or temporal Gutenberg-Richter b-value variations exist within the induced earthquake catalogue of the Groningen gas field. We utilize the method developed by Kamer and Hiemer (2015; J. Geophys. Res. Solid Earth, 120, doi:10.1002/2014JB011510 ) which is based on optimal partitioning using Voronoi tessellation, penalized likelihood, and wisdom of the crowd philosophy. Our implementation derives both the magnitude of completeness and the b-values simultaneously. The magnitude of completeness is computed with the maximum curvature method with a correction applied to avoid bias due to catalogue incompleteness. Finally, following Marzocchi et al. (2020; Geophys. J. Int. 220, doi: 10.1093/gji/ggz541) the b-values computed are corrected for bin size and small sample sizes.&lt;/p&gt;&lt;p&gt;In a first step we have limited the analysis to spatial variations in the b-values. A significant advantage of the approach taken is that it is feasible to also derive b-values in regions of very low data density. We will show that a statistically significant variation in b-values is obtained. Very low b-values (b&lt;0.8) are observed in the central-northern part of the gas field. However, in the west near the production cluster Eemskanaal (EKL) and in the east near the city of Delfzijl significantly higher b-values (b&gt;1.1) are observed. A Kolmogorov-Smirnov test of frequency-magnitude distributions for the two areas obtains a p-value of 1.5 10-13 and 2.3 10-12 for the EKL region and Delfzijl regions, respectively, rendering the difference more than statistically significant at the 99% confidence level.&lt;/p&gt;&lt;p&gt;In a second step we extended the spatial analysis to a spatial-temporal analysis. The results of the analysis show that the Groningen earthquake database is too small to derive meaningful spatial results for the full Groningen gas field based on multiple random temporal nodes.&amp;#160; We divided the dataset in two almost equal datasets: both containing roughly 50% of the data and of comparable spatial resolution. Spatial analysis of these two subsets of the catalogue shows a significant decrease of the b-values in the central and southern regions. Particularly in the western EKL region the b-value decreases from 1.2 to 0.92. The decrease is close to significant at the 90% confidence level. The northern region exhibits comparable low b-values in both periods. As the data in the first decade is primarily concentrated in the northern region, we have attempted to assess the spatial b-value here in the period prior to 2005. We find the high b-value area is significantly smaller and the minimum value is higher (b = 0.96 pre-2005 versus b = 0.88 post-2012). The difference is significant only at the interquartile level, but the model resolution is low.&lt;/p&gt;&lt;p&gt;Based on our results, we could conclude a spatial and temporal variation in b-value is observed. However, despite our efforts to limit bias in the derivation, variations could still result from the presence of a truncation. Hence, we will extend the current analysis by a comparable analysis assuming a constant b-value and estimating the corner magnitude of a taper truncation.&lt;/p&gt;

KAMCHATKA AND COMMANDER ISLANDS

The seismicity review of Kamchatka and surrounding territories for 2014 is given. In Kamchatka earthquake catalogue minimum local magnitude of completeness is MLmin=3.5, and for earthquakes under the Okhotsk sea with h≥350 kmMLmin=3.6. The Kamchatka earthquake catalogue for 2014 with ML3.5, published in the Appendix to this annual, includes 1114 events. 86 earthquakes of the catalogue with ML=3.35–6.2 were felt in Kamchatka and surrounding areas with seismic intensity I ranged from 2 to 5 according the MSK-64 scale. For all events with ML5.0 occurred in the area of responsibility of the KB GS RAS in 2014, an attempt to calculate the seismic moment tensor (SMT) was made. There are 40 such events in the regional catalogue. For 36 earthquakes, the SMT and depth h of the equivalent point source were calculated successfully. The calcu-lations were performed for the SMT double-couple model using a nonlinear algorithm. In 2014, a typical location of the earthquake epicenters was observed in the Kamchatka zone. In 2014, the seismicity level in all selected zones and in the region as a whole corresponded to the background one according to the “SESL’09” scale. The number of recorded events with ML3.6 and strong earthquakes with ML5.1 is close to the average annual value. Anomalous and outstanding events were not recorded.

A Homogeneous Earthquake Catalogue for Turkey and Surrounding Region

A new earthquake catalogue for Turkey and surrounding region (32°–47° N, 20°–52° E) is compiled for the period 1900–2017. The earthquake parameters are obtained from the Bulletin of International Seismological Centre that is fully updated in 2020. New conversion equations between moment magnitude and the other scales (md, ML, mb, Ms and M) are determined using in the General Orthogonal Regression method to build up a homogeneous catalogue, which is the essential data for seismic hazard studies. The 95 % confidence intervals are estimated using the bootstrap method with 1000 samples. The equivalent moment magnitudes (Mw*) for the entire catalogue are calculated using the magnitude relations to homogenise the catalogue. The magnitude of completeness is 2.9 Mw* and 3.0–3.2 Mw* for Turkey and Greece generally. The final dataset is not declustered or truncated using a threshold magnitude because of motivation for generating a widely usable catalogue. It contains not only Mw*, but also the average and median of the observed magnitudes for each event. Contrary to the limited earthquake parameters in the previous catalogues, the 45 parameters of approximately 700 k events occurred in a wide area from the Balkans to the Caucasus are presented.