Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case

The area-characteristic, maximum possible earthquake magnitude $T_M$ is required by the earthquake engineering community, disaster management agencies and the insurance industry. The Gutenberg-Richter law predicts that earthquake magnitudes $M$ follow a truncated exponential distribution. In the geophysical literature several estimation procedures were proposed, see for instance Kijko and Singh (Acta Geophys., 2011) and the references therein. Estimation of $T_M$ is of course an extreme value problem to which the classical methods for endpoint estimation could be applied. We argue that recent methods on truncated tails at high levels (Beirlant et al., Extremes, 2016; Electron. J. Stat., 2017) constitute a more appropriate setting for this estimation problem. We present upper confidence bounds to quantify uncertainty of the point estimates. We also compare methods from the extreme value and geophysical literature through simulations. Finally, the different methods are applied to the magnitude data for the earthquakes induced by gas extraction in the Groningen province of the Netherlands

Estimation of earthquake hazard parameters from incomplete data files. Part III. Incorporation of uncertainty of earthquake-occurrence model

Most probabilistic seismic-hazard analysis procedures require that at least three seismic source parameters be known, namely the mean seismic activity rate λ, the Gutenberg–Richter b-value, and the area-characteristic (seismogenic source) maximum possible earthquake magnitudemmax. In almost all currently used seismic-hazard assessment procedures that utilize these three parameters, it is explicitly assumed that all three remain constant over time and space. However, closer examination of most earthquake catalogs has indicated that significant spatial and temporal variations existed in the seismic activity rate λ, as well as in the Gutenberg–Richter b-value. In this study, the maximum likelihood estimation of these earthquake hazard parameters considers the incompleteness of the catalogs, the uncertainty in the earthquake magnitude determination, as well as the uncertainty associated with the applied earthquake-occurrence models. The uncertainty in the earthquake-occurrence models is introduced by assuming that both the mean seismic activity rate λ and the Gutenberg–Richter b-value are random variables, each described by the gamma distribution. This approach results in the extension of the classic frequency–magnitude Gutenberg–Richter relation and the Poisson distribution of the number of earthquakes with their compounded counterparts (Benjamin, 1968; Campbell, 1982, 1983). The proposed procedure was applied in the estimation of the seismicity parameters in an area that had experienced the strongest and most devastating earthquake in contemporary South African history, namely the 29 September 1969 Mw 6.3 Ceres–Tulbagh event. In this example, it was shown that the introduction of uncertainty in the earthquake-occurrence model reduced the mean return periods, leading to an increase of the estimated seismic hazard. Additionally, this study confirmed that accounting for magnitude uncertainties had the opposite effect, that is, it brought about increases in the return periods, or, equivalently, a reduction of the estimated seismic hazard.The National Research Foundation of South Africa (Grant Numbers 76906 and 94808).http://www.seismosoc.orgpublications/bssa/am2016Geolog

Extension of the Aki-Utsu b-value estimator for incomplete catalogs

The Aki (1965) maximum likelihood estimate of the Gutenberg–Richter b-value is extended for use in the case of multiple catalogs with different levels of completeness. The most striking feature of this newly derived estimator is its simplicity—it is more manageable than the well-known and already easy to use Weichert (1980) solution to the analogs problem. In addition, confidence intervals for the newly derived estimator are provided.http://www.seismosoc.orgpublications/bssa/am2017Geolog

First-order regional seismotectonic model for South Africa

A first-order seismotectonic model was created for South Africa. This was done using four logical steps: geoscientific data collection, characterisation, assimilation and zonation. Through the definition of subunits of concentrations of earthquake foci and large neotectonic and structural domains, seismotectonic structures, systems and domains were created. Relatively larger controls of seismicity exist between the Great Escarpment and the coast. In the south, this region is characterised by large aeromagnetic anomalies and large EW trending faults. In the west, it is characterised by the NW–SE trending Wegener stress anomaly, radial-trending dykes and earthquake clusters. In the east, it is characterised by a large neotectonic domain where several large historical earthquakes occurred. In the centre of South Africa, several clusters of earthquake activity are found, often related to mining activity. Further north, seismicity is related to both mining activity and neotectonic deformation. This work contributes to the development of a seismotectonic model for South Africa by (1) bringing together, digitally, several data sets in a common GIS platform (geology, geophysics, stress, seismicity, neotectonics, topography, crustal and mantle structure and anisotropy), (2) understanding the significance of data sets for seismotectonic zonation and limitations thereof and (3) obtaining a reasonable regional model for use in seismic hazard assessments.The Council for Geoscience (CGS) and the National Research Foundation.http://www.springer.com/earth+sciences+and+geography/hydrogeology/journal/11069http://www.springerlink.com/content/0921-030x/nf201

Guest Editorial: Special Issue on “Lithosphere Dynamics and Earthquake Hazard Forecasting”

Brilliant scientific ideas coupled with quantitative modelling and laboratory experiments have determined progress in seismology and geodynamics for the last several decades. Methods of nonlinear geophysics, inverse problems, mathematical statistics, extreme theory and data analysis have improved knowledge of the structure of the Earth’s lithosphere, earthquake generation, predictability, and seismic hazards. This Special Issue of Surveys in Geophysics “Lithosphere Dynamics and Earthquake Hazard Forecasting” is dedicated to the 100th anniversary of the birth of Professor Vladimir (Volodya) Keilis-Borok (1921–2013), a distinguished mathematical geophysicist. For more than 60 years, the topics of seismology, nonlinear dynamics of the lithosphere, and earthquake prediction were central in Keilis-Borok's research.Open Access funding enabled and organized by Projekt DEAL.https://www.springer.com/journal/10712hj2022Geolog

Statistical evaluation of seismic event location accuracy by the South African National Seismograph Network over four decades

We analyzed the changes/improvements of seismic event detection and location accuracy of the South African National Seismograph Network over the last four decades. The effect of three regional velocity models on epicentral solutions was tested during the initial study. It is shown that the hypocentral depth considered during this study, viz. at 2 km for mining related events, and 5 km to 10 km for tectonic earthquakes, have a negligible effect on the error in epicentre location. Further, three detection distances were evaluated during this study, viz. 300, 500 and 1000 km. The location errors decreased significantly by increasing the detecting distance. This study highlights the importance of including 5-phase arrival times to better constrain seismic event locations. This observation is of particular value for the 1970 to 1997 period, when only P-phases were considered during the location procedure. Lastly, it is shown how the errors in epicentre location decrease with an increase in the number and geographical distribution of seismic stations.The South African National Seismograph Network operated by the Geophysics Competency of the Council for Geoscience.http://sajg.geoscienceworld.orgam2017Geolog

Probabilistic tsunami hazard assessment from incomplete and uncertain historical catalogues with application to tsunamigenic regions in the Pacific Ocean

The paper presents a new method for empirical assessment of tsunami recurrence parameters, namely the mean tsunami activity rate λT, the Soloviev–Imamura frequency–magnitude power law bT-value, and the coastline-characteristic, maximum possible tsunami intensity imax. The three coastline-characteristic recurrence parameters are estimated locally by maximum likelihood techniques using only tsunami event catalogues. The method provides for incompleteness of the tsunami catalogue, uncertainty in the tsunami intensity determination, and uncertainty associated with the parameters in the applied tsunami occurrence models. Aleatory and epistemic uncertainty is introduced in the tsunami models by means of the use of mixture distributions. Both the mean tsunami activity rate λT of the Poisson occurrence model, and the bT-value of the Soloviev–Imamura frequency–intensity power law are random variables. The proposed procedure was applied to estimate the probabilities of exceedance and return periods for tsunamis in the tsunamigenic regions of Japan, Kuril–Kamchatka, and South America.The National Research Foundation of South Africa (Grant Numbers 76906 and 94808).https://link.springer.com/journal/242018-08-30hj2017GeologyStatistic

Probabilistic tsunami risk assessment from incomplete and uncertain historical impact records : Mediterranean and connected seas

DATA AVAILABILITY : The data sets used in this paper and the relevant citations are explained in the main text and summarized in Supplementary file 1.Tsunami risk is considered as the probability of a particular coastline being struck by a tsunami that may cause a certain level of impact (destructiveness). The impact metric of a tsunami is expressed in terms of tsunami intensity values, K, assigned on a 12-degree scale. To calculate tsunami risk we are based on the tsunami history of the region codified in tsunami catalogues. The probabilistic model adopted was used successfully for hazard assessment of earthquakes (Kijko et al. in Bull Seismol Soc Am 79:645–654, 2016) and of tsunamis (Smit et al. in Environmetrics 30:e2566, 2019) by considering seismic magnitude and tsunami height as metrics of the respective hazards. In this model, instead of hazard metrics we inserted risk metric, i.e. wave impact in terms of intensity values. The procedure allows utilization of the entire data set consisting not only from the complete (recent) part of tsunami catalogue but also from the highly incomplete and uncertain historical part of the catalogue. Risk is assessed in terms of probabilities of exceedance and return periods of certain intensity values in specific time frames. We applied the model using catalogues for the Mediterranean and connected seas. Sensitivity analysis showed that using complete data sets generally provided more realistic results than using entire data sets. Results indicated that the risk level depends on the seismicity level and not on the size of individual ocean basin. The highest tsunami risk level was found in the eastern Mediterranean (EM), with a significantly lower risk in the western Mediterranean (WM). In the Marmara Sea (MS), the tsunami risk was low, and the lowest was in the Black Sea (BS). The risk in the small Corinth Gulf (CG, Central Greece) was comparable to that of WM. The return period of damaging tsunamis (i.e. K ≥ 7) was 22 years in the entire Mediterranean basin and 31, 118, 135, 424, and 1660 years in the EM, WM, CG, MS, and BS basins, respectively.Open access funding provided by HEAL-Link Greece.http://link.springer.com/journal/24hj2024GeologySDG-14:Life below wate

Estimation techniques for seismic recurrence parameters for incomplete catalogues

Please read the abstract in the article.http://link.springer.com/journal/10712hj2021Geolog

Energetic and spatial characterization of seismicity in the Algeria–Morocco region

We estimate the energetic and spatial characteristics of seismicity in the Algeria–Morocco region using a variety of seismic and statistical parameters, as a first step in a detailed investigation of regional seismic hazard. We divide the region into five seismotectonic regions, comprising the most important tectonic domains in the studied area: the Moroccan Meseta, the Rif, the Tell, the High Plateau, and the Atlas. Characteristic seismic hazard parameters, including the Gutenberg–Richter b-value, mean seismic activity rate, and maximum possible earthquake magnitude, were computed using an extension of the Aki–Utsu procedure for incomplete earthquake catalogs for each domain, based on recent earthquake catalogs compiled for northern Morocco and northern Algeria. Gutenberg–Richter b-values for each zone were initially estimated using the approach of Weichert (Bull Seismol Soc Am 70:1337–1346, 1980): the estimated b-values are 1.04 ± 0.04, 0.93 ± 0.10, 0.72 ± 0.03, 0.87 ± 0.02, and 0.77 ± 0.02 for the Atlas, Meseta, High Plateau, Rif, and Tell seismogenic zones, respectively. The fractal dimension D2 was also estimated for each zone. From the ratio D2/b, it appears that the Tell and Rif zones, with ratios of 2.09 and 2.12, respectively, have the highest potential earthquake hazard in the region. The Gutenberg–Richter relationship analysis allows us to derive that in the Tell and Rif, the number of earthquake with magnitude above Mw 4.0, since 1925 normalized to decade and to square cell with 100-km sides is equal to 2.6 and 1.91, respectively. This study provides the first detailed information about the potential seismicity of these large domains, including maximum regional magnitudes, characteristics of spatial clustering, and distribution of seismic energy release.The Algerian CRAAG, the Spanish Seismic Hazard and Active Tectonics research group, and the Spanish MINECO CGL2015- 65602-R project.http://link.springer.com/journal/110692018-04-30hb2016Physic