Properties of the aftershocks sequences of the 2000 and 2002 earthquakes in Aksehir-Afyon graben,west-central Anatolia,Turkey

The b-value of the Gutenberg–Richter’s frequency–magnitude relation and the p-value of the modified Omori law, which describes the decay rate of aftershock activity, were investigated for more than 500 aftershocks in the Aksehir-Afyon graben (AAG) following the 15 December 2000 Sultandagi–Aksehir and the 3 February 2002 Çay–Eber and Çobanlar earthquakes. We used the Kandilli Observatory’s catalog, which contains records of aftershocks with magnitudes ≥2.5. For the Çobanlar earthquake, the estimated b-values for three aftershock sequences are in the range 0.34 ≤  b ≤ 2.85, with the exception of the one that occurred during the first hour (4.77), while the obtained p-values are in the range 0.44 ≤ p ≤ 1.77. The aftershocks of the Sultandagi earthquake have a high p-value, indicating fast decay of the aftershock activity. A regular increase of b can be observed, with b < 1.0 after 0.208 days for the Çay–Eber earthquake. A systematic and similar increase and decrease pattern exists for the b- and p-values of the Çobanlar earthquakes during the first 5 days.     

Seismicity patterns associated with the September 10th, 2008 Qeshm earthquake, South Iran

The b value of the Gutenberg-Richter relation and the standard deviate, Z, were calculated to investigate the temporal and spatial variations in seismicity patterns associated with the September 10th, 2008 (Mw?=?6.1) Qeshm earthquake. The temporal variations of b value illustrate a distinct dramatic drop preceding the Qeshm earthquake, and the spatial changes in b value highlight a zone with an abnormally low b value around the epicenter of this event. The cumulative number and Z value as a function of time show a precursory seismic quiescence preceding the 2008 Qeshm earthquake that observed for 1?year in a circle with R?=?50?km around its epicenter. The spatial distribution map of the standard deviate, Z, also exhibits an obvious precursory seismic quiescence region before the 2008 Qeshm event around the epicenter of this event. Interestingly, the precursory seismic quiescence region is approximately consistent with low b value anomaly region, and both have E–W to NE–SW trend. These two precursory anomalies took place in relatively large regions, which were possibly relevant to the preparation zone of the 2008 Qeshm event.     

Assessment of the statistical earthquake hazard parameters for NW Turkey

We performed a probabilistic analysis of earthquake hazard input parameters, NW Turkey covers Gelibolu and Biga Peninsulas, and its vicinity based on four seismic sub-zones. The number of earthquakes with magnitude M ≥ 3.0 occurred in this region for the period between 1912 and 2007 is around 5130. Four seismic source sub-zones were defined with respect to seismotectonic framework, seismicity and fault geometry. The hazard perceptibility characterization was examined for each seismic source zone and for the whole region. The probabilities of earthquake recurrences were obtained by using Poisson statistical distribution models. In order to determine the source zones where strong and destructive earthquakes may occur, distribution maps for a, b and a/b values were calculated. The hazard scaling parameters (generally known as a and b values) in the computed magnitude–frequency relations vary in the intervals 4.28–6.58 and 0.59–1.13, respectively, with a RMS error percentage below 10 %. The lowest b value is computed for sub-zone three indicating the predominance of large earthquakes mostly at Gelibolu (Gallipoli) and north of Biga Peninsula (southern Marmara region), and the highest b value is computed for sub-zone two Edremit Bay (SW Marmara region). According to the analysis of each seismic sub-zone, the greatest risk of earthquake occurrence is determined for the triangle of Gelibolu–Tekirda? western part of Marmara Sea. Earthquake occurrence of the largest magnitude with 7.3 within a 100-year period was determined to be 46 % according to the Poisson distribution, and the estimated recurrence period of years for this region is 50 ± 12. The seismic hazard is pronounced high in the region extending in a NW–SE direction, north of Edremit Bay, west of Saros Bay and Yenice Gönen (southern Marmara region) in the south. High b values are generally calculated at depths of 5–20 km that can be expressed as low seismic energy release and evaluated as the seismogenic zone.     

An assessment of seismicity parameters in northwest Himalaya and adjoining regions

In this study, an assessment of seismicity parameters in the northwest Himalaya and adjoining regions using an earthquake catalog from India Meteorological Department covering a period from June 1, 1998 to June 30, 2011 has been carried out. The spatial distributions of seismicity parameters, namely magnitude of completeness, M _C, a value, b value, and correlation fractal dimension, D _C, are estimated for the studied region. The M _C, a, and b values are found to be 2.5, 4.601, and 0.83, respectively. Despite significant gaps, the spatial distributions of a and b values are seen to follow similar trend and are found scattering in between Main Boundary Thrust (MBT) and South Tibet Detachment, adjoining areas of Mahendragarh-Dehradun Fault (MDF), Delhi-Haridwar Ridge (DHR) and Moradabad Fault (MF), and the southern flank of Karakoram Fault and Indus-Tsangpo Suture Zone. The estimated spatial distribution of b and a values is within 90 % of confidence level, thereby indicating non-uniform stress accumulation or higher rock fracturing density in the studied region caused by strong tectonization following several earthquakes. Negative correlation between low b value and high D _C is observed predominantly in the region between the MBT and Munsiari Thrust or Main Central Thrust-I of Garhwal and Kumaon Himalaya, adjoining zones of MDF, DHR, and MF of Indo-Gangetic plain, and the eastern flank of the studied region, suggesting the presence of asperities in the zone. At the same time, active creeping process can be inferred in between the MBT and Main Central Thrust of Garhwal Himalaya and the surrounding areas of Shimla region of the Himalayan arc to the northwestern part of the studied region from the positive correlation between b value and D _C. The results indicate that the structural heterogeneity caused by different stress accumulation and rock fracturing densities exists due to continuous tectonic adjustments between different geomorphic features of the studied region. An attempt has also been made to classify the studied region into smaller seismic zones by observing the spatial patterns of b value and D _C that are fractal properties of the observed seismicity, along with the prevalent fault networks.     

Fractal variogram-based time–space of aftershock sequences analysis—case study: the May 21, 2003 Boumerdes–Algeria earthquake, M w = 6.8

The most of shallow earthquakes are followed, just after the main shock, by increased residual seismicity known as “aftershocks” or “aftershock sequences”. Because of their disparity in time and space, aftershock sequences are more or less obvious and their productivity is spread out in time. Several studies have been regularly proposed to explain or to understand the mechanisms of the occurrence and the behaviour of these small earthquakes. In a theoretical context, many factors can induce the aftershock triggering: residual friction, subcritical crack growth, pore fluid flow etc. Just after the occurrence of the most destructive main shock of the 21 May 2003 Boumerdes (Algeria) earthquake, a wide sequence of aftershocks was recorded at different geographical locations and with various magnitudes. Based on the fact that the region of Boumerdes (40 km east of the capital Algiers) did not develop major earthquakes in the past, a geostatistical investigation of the data for this aftershock sequence is a valuable input for better seismogeological identification of this area. In the present analysis, after an overview of the geological factors in the likely occurrence of the earthquake, fundamental statistical parameters were chosen: the b value from the Gutenberg–Richter law, the p factor of the extracted respectively from the b value and the fractal variogram defined as a graphic tool to describe the continuity or the roughness of data. Jointly to the geostatistical parameters provided by the variogram like the fractal dimension. The main objective of the calculation and interpretation of these parameters is oriented towards a better understanding of the seismicity of the region of Boumerdes (Algeria) now classified as seismogenic zone.     

Geodetic and seismological investigation of crustal deformation near Izmir (Western Anatolia)

The Aegean region including western Turkey, mainland Greece, and the Hellenic Arc is the most seismological and geodynamical active domain in the Alpine Himalayan Belt. In this study, we processed 3 years of survey-mode GPS data and present the analysis of a combination of geodetic and seismological data around Izmir, which is the third most populated city in Turkey. The velocities obtained from 15 sites vary between 25 mm/yr and 28 mm/yr relative to the Eurasian plate. The power law exponent of earthquake size distribution (b-value) ranges from 0.8 to 2.8 in the Izmir region between 26.2°E and 27.2°E. The lowest b-value zones are found along Karaburun Fault (b = 0.8) and, between Seferihisar and Tuzla Faults (b = 0.8). A localized stress concentration is expected from numerical models of seismicity along geometrical locked fault patches. Therefore, areas with lowest b-values are considered to be the most likely location for a strong earthquake, a prediction that is confirmed by the 2005 M_w = 5.9 Seferihisar earthquake sequences, with epicentres located to the south of the Karaburun Fault. The north–south extension of the Izmir area is corroborated by extension rates up to 140 nanostrain/yr as obtained from our GPS data. We combined the 3-year GPS velocity field with the published velocity field to determine the strain rate pattern in the area. The spatial distribution of b-value reflects the normal background due to the tectonic framework and is corroborated by the geodetic data. b-Values correlate with strain pattern. This relationship suggests that decrease of b-values signifies accumulating strain.     

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 D ₂ was also estimated for each zone. From the ratio D ₂/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 seismic b-value and its correlation with Bouguer gravity anomaly over the Shillong Plateau area: Tectonic implications

Clues to the understanding of intra- and inter-plate variations in strength or stress state of the crust can be achieved through different lines of evidence and their mutual relationships. Among these parameters Bouguer gravity anomalies and seismic b-values have been widely accepted over several decades for evaluating the crustal character and stress regime. The present study attempts a multivariate analysis for the Shillong Plateau using the Bouguer gravity anomaly and the earthquake database, and establishes a causal relationship between these parameters. Four seismic zones (Zones I–IV), with widely varying b-values, are delineated and an excellent correlation between the seismic b-value and the Bouguer gravity anomaly has been established for the plateau. Low b-values characterize the southwestern part (Zone IV) and a zone (Zone III) of intermediate b-values separates the eastern and western parts of the plateau (Zones I and II) which have high b-values. Positive Bouguer anomaly values as high as +40 mgal, a steep gradient in the Bouguer anomaly map and low b-values in the southwestern part of the plateau are interpreted as indicating a thinner crustal root, uplifted Moho and higher concentration of stress. In comparison, the negative Bouguer anomaly values, flat regional gradient in the Bouguer anomaly map and intermediate to high b-values in the northern part of the plateau are consistent with a comparatively thicker crustal root and lower concentration of stress, with intermittent dissipation of energy through earthquake shocks. Further, depth wise variation in the b-value for different seismic zones, delineated under this study, allowed an appreciation of intra-plateau variation in crustal thickness from ∼30 km in its southern part to ∼38 km in the northern part. The high b-values associated with the depth, coinciding with lower crust, indicate that the Shillong Plateau is supported by a strong lithosphere.     

Analysis of the characteristics of self-similarity of seismicity and the active fault network of Eurasia

An analysis of the possible relationship between fractal dimensions of the active fault network, spatial distribution of earthquake epicenters, and parameter b in the Gutenberg-Richter law is presented. The quantitative characteristics of self-similarity of the seismic process and the active fault network of seismically active areas of Eurasia are obtained. This self-similarity manifests itself over a range of at least two orders of spatial scales and magnitudes. The obtained estimations of the fractal dimensions of the fault network D _f and epicenter field D _e are close for all the areas analyzed. It is established that the average value connecting values D and b for all the investigated areas is slightly higher than the theoretical value (2.0) and varies within the range of 1.7–2.4.     

Evaluation of earthquake potential along the Northern Anatolian Fault Zone in the Marmara Sea using comparisons of GPS strain and seismotectonic parameters

Seismotectonic parameters including the Gutenberg-Richter b-value and multifractal dimensions D₂ and D₁₅ of seismicity patterns (both spatial and temporal) were compared to GPS-derived maximum shear and dilatation strains measured in the Marmara Sea region of western Turkey along the Northern Anatolian Fault Zone (NAFZ). Comparisons of seismotectonic parameters and GPS-derived maximum shear and dilatation strain along the NAFZ in the vicinity of the 1999 M7.4 Izmit earthquake reveal a positive correlation (r = 0.5, p = 0.05) between average dilatation and the Gutenberg-Richter b-value. Significant negative correlation (r = − 0.56, p = 0.03 and r = − 0.56, p = 0.02) was also observed between the spatial fractal dimension D₂ and GPS-derived maximum geodetic and shear strain. This relationship suggests that, as maximum geodetic and shear strains increase, seismicity becomes increasingly clustered.Anomalous interrelationships are observed in the Marmara Sea region prior to the Izmit event along a bend in the NAFZ near the eastern end of the Marmara Sea known as the Northern Boundary Fault (NBF). An asperity is located near the northwest end of the NBF. Along the 50-km length of the NBF, GPS strains become slightly compressive. The correlation between b-value and GPS-derived dilatation suggests that regions in compression have increased probability of larger magnitude rupture. The NBF appears to serve as an impediment to the transfer of strain from east to west along the NAFZ. Recurrence times for large earthquakes along the NBF are larger than in surrounding areas. Temporal clustering of seismicity in the vicinity of the NBF may represent foreshocks of an impending rupture.     

The 1998 Hida Mountain, Central Honshu, Japan, earthquake swarm: Double-difference event relocation, frequency–magnitude distribution and Coulomb stress changes

By using the double-difference relocation technique, we have determined the fine structure of seismicity during the 1998 Hida Mountain earthquake swarm. The distribution of seismic activity defines two main directions (N–S and E–W) that probably correspond to the regional stress pattern. The detailed structure of seismicity reveals intense spatio-temporal clustering and earthquake lineations. Each cluster of events contains a mainshock and subsequent aftershock activity that decays according to the Omori law. The seismicity and the b-value temporal and spatial patterns reflect the evolution of the static stress changes during the earthquake swarm. About 80% of the swarm's best-relocated events occur in regions of increased ΔCFF. The smaller value of b found in the northern part of the swarm region and a larger b-value observed to the south, for the same period of time, could be well explained by the static stress changes caused by the larger events of the sequence. We argue that the state of stress in the crust is the main factor that controls the variation of b-value.     

Spatial mapping of earthquake hazard parameters in the Hindukush–Pamir Himalaya and adjacent regions: Implication for future seismic hazard

The study deals spatial mapping of earthquake hazard parameters like annual and 100-years mode along with their 90% probability of not being exceeded (NBE) in the Hindukush–Pamir Himalaya and adjoining regions. For this purpose, we applied a straightforward and most robust method known as Gumbel’s third asymptotic distribution of extreme values (GIII). A homogeneous and complete earthquake catalogue during the period 1900–2010 with magnitude M_W ⩾ 4.0 is utilized to estimate these earthquake hazard parameters. An equal grid point mesh, of 1° longitude X 1° latitude, is chosen to produce detailed earthquake hazard maps. This performance allows analysis of the localized seismicity parameters and representation of their regional variations as contour maps. The estimated result of annual mode with 90% probability of NBE is expected to exceed the values of M_W 6.0 in the Sulaiman–Kirthar ranges of Pakistan and northwestern part of the Nepal and surroundings in the examined region. The 100-years mode with 90% probability of NBE is expected to exceed the value of M_W 8.0 in the Hindukush–Pamir Himalaya with Caucasus mountain belt, the Sulaiman–Kirthar ranges of Pakistan, northwestern part of the Nepal and surroundings, the Kangra–Himanchal Pradesh and Kashmir of India. The estimated high values of earthquake hazard parameters are mostly correlated with the main tectonic regimes of the examined region. The spatial variations of earthquake hazard parameters reveal that the examined region exhibits more complexity and has high crustal heterogeneity. The spatial maps provide a brief atlas of the earthquake hazard in the region.     

The 2007 Talala,Saurashtra, western India earthquake sequence: Tectonic implications and seismicity triggering

A damaging and widely felt moderate (M_w 5.0) earthquake occurred in the Talala region of Saurashtra, Gujarat (western India) on November 6, 2007. The highly productive sequence comprised about 1300 micro earthquakes (M > 0.5) out of which 325 of M ? 1.5 that occurred during November 6, 2007–January 10, 2008 were precisely located. The spatial aftershock distribution revealed a NE–SW striking fault in accordance with the centroid moment tensor solution, which in turn implies left-lateral motion. The orientation and sense of shear are consistent with similarly orientated geological fault identified in the area from satellite imagery and field investigation.The aftershocks temporal decay, b-value of frequency–magnitude distribution, spatial fractal dimension, D, and slip ratio (ratio of the slip occurred on the primary fault to the total slip) were examined with the purpose to identify the properties of the sequence. The high b-value (1.18 ± 0.01) may be attributed to the paucity of the larger (M ? 4.0) aftershocks and reveals crustal heterogeneity and low stress regime. The high p-value (1.10 ± 0.39), implying fast decay rate of aftershocks, evidences high surface heat flux. A value of the spatial fractal dimension (D) equal to 2.21 ± 0.02 indicates random spatial distribution and source in a two-dimensional plane that is being filled-up by fractures. A slip ratio of 0.42 reveals that more slip occurred on secondary fault systems.The static Coulomb stress changes due to the coseismic slip of the main shock, enhanced off fault aftershock occurrence. The occurrence of a moderate earthquake (M_w 4.3) on October 5, 2008 inside a region of positive Coulomb stress changes supports the postulation on aftershock triggering. When the stress changes were resolved on a cross section including the stronger (M4.8) foreshock plane that is positioned adjacent to the main fault, it became evident that the activity continued there due to stress transfer from the main rupture.     

Variation of b and p values from aftershocks sequences along the Mexican subduction zone and their relation to plate characteristics

Aftershock sequences along the Mexican subduction margin (between coordinates 110ºW and 91ºW) were analyzed by means of the p value from the Omori–Utsu relation and the b value from the Gutenberg–Richter relation. We focused on recent medium to large (M_w > 5.6) events considered susceptible of generating aftershock sequences suitable for analysis. The main goal was to try to find a possible correlation between aftershock parameters and plate characteristics, such as displacement rate, age and segmentation. The subduction regime of Mexico is one of the most active regions of the world with a high frequency of occurrence of medium to large events and plate characteristics change along the subduction margin. Previous studies have observed differences in seismic source characteristics at the subduction regime, which may indicate a difference in rheology and possible segmentation. The results of the analysis of the aftershock sequences indicate a slight tendency for p values to decrease from west to east with increasing of plate age although a statistical significance is undermined by the small number of aftershocks in the sequences, a particular feature distinctive of the region as compared to other world subduction regimes. The b values show an opposite, increasing trend towards the east even though the statistical significance is not enough to warrant the validation of such a trend. A linear regression between both parameters provides additional support for the inverse relation. Moreover, we calculated the seismic coupling coefficient, showing a direct relation with the p and b values. While we cannot undoubtedly confirm the hypothesis that aftershock generation depends on certain tectonic characteristics (age, thickness, temperature), our results do not reject it thus encouraging further study into this question.     

Analysis of Izmit aftershocks 25 days before the November 12th 1999 Düzce earthquake, Turkey

We investigate spatial clustering of 2414 aftershocks along the Izmit M_w = 7.4 August 17, 1999 earthquake rupture zone. 25 days prior to the Düzce earthquake M_w = 7.2 (November 12, 1999), we analyze two spatial clusters, namely Sakarya (SC) and Karadere–Düzce (KDC). We determine the earthquake frequency–magnitude distribution (b-value) for both clusters. We find two high b-value zones in SC and one high b-value zone in KDC which are in agreement with large coseismic surface displacements along the Izmit rupture. The b-values are significantly lower at the eastern end of the Izmit rupture where the Düzce mainshock occurred. These low b-values at depth are correlated with low postseismic slip rate and positive Coloumb stress change along KDC. Since low b-values are hypothesized with high stress levels, we propose that at the depth of the Düzce hypocenter (12.5 km), earthquakes are triggered at higher stresses compared to shallower crustal earthquake. The decrease in b-value from the Karadere segment towards the Düzce Basin supports this low b-value high stress hypothesis at the eastern end of the Izmit rupture. Consequently, we detect three asperity regions which are correlated with high b-value zones along the Izmit rupture. According to aftershock distribution the half of the Düzce fault segment was active before the 12 November 1999 Düzce mainshock. This part is correlated with low b-values which mean high stress concentration in the Düzce Basin. This high density aftershock activity presumably helped to trigger the Düzce event (M_w = 7.2) after the Izmit M_w 7.4 mainshock.     

Spatial analysis of the frequency–magnitude distribution of aftershock activity of 2003 Bam earthquake: southeast Iran

The Bam earthquake (2003 December 26, M _W = 6.6) was one of the largest earthquakes that occurred in southeast of Iran during last century. It took place along an N–S trending right-lateral strike-slip fault, almost near the southern end of Nyband–Gowk fault. In this study, we mapped the frequency–magnitude distribution of aftershock events spatially across the Bam aftershock zone. The b-value varies between 0.6 and 1.1 across the Bam rupture zone. The overall depth distribution of b-value in Bam aftershock zone reveals two distinct increases in b-value: (1) at depths of 8–10 km and (2) shallower than 4 km beneath the Bam city. There is no correlation between high b- value anomalies found in this study and the region of largest slip, whereas the spatial correlation between high b-value anomalies and the zone of low V _s and high σ (in earlier tomography study) is obvious. This correlation reveals that material properties and increasing heterogeneity are more important in controlling b-value distribution in Bam earthquake rupture zone. The high b-value anomaly near the surface of northern part of rupture zone may be related to unconsolidated and water-rich quaternary alluvial sediments and probable low-strength rocks beneath them. The high b-value anomaly at depth range 8–10 km can be correlated with fractured and fluid-filled mass, which may result from the movement of magma during Eocene volcanism in the Bam area. In this study, the induced changes in pore fluid pressure due to main shock are suggested as a mechanism for aftershock generation.     

Structure and peculiarities of the seismic regime in the source zone of the Takoe earthquake on September 1, 2001 (M W 5.2)

The Takoe earthquake (M _W 5.2) occurred between two en-echelon segments of the active Aprelovskii fault on September 1, 2001, and was accompanied by an earthquake swarm, which was successfully recorded by a local network of digital seismic stations located on the southern part of Sakhalin Island. Modern methods were applied to relocate the parameters of the sources for the earthquake swarm event and significantly specify their spatial distribution and relations to the structural-geological features of the complex system of interacting faults. New data on the correlation between the source mechanism and the modern geodynamic setting in the southern part of Sakhalin were obtained.     

Probabilistic seismic hazard assessment in the Constantine region,Northeast of Algeria

This paper presents a seismic hazard evaluation and develops an earthquake catalogue for the Constantine region over the period from 1357 to 2014. The study contributes to the improvement of seismic risk management by evaluating the seismic hazards in Northeast Algeria. A regional seismicity analysis was conducted based on reliable earthquake data obtained from various agencies (CRAAG, IGN, USGS and ISC). All magnitudes (M _l, m _b) and intensities (I ₀, I _MM, I _MSK and I _EMS) were converted to M _s magnitudes using the appropriate relationships. Earthquake hazard maps were created for the Constantine region. These maps were estimated in terms of spectral acceleration (SA) at periods of 0.1, 0.2, 0.5, 0.7, 0.9, 1.0, 1.5 and 2.0 s. Five seismogenic zones are proposed. This new method differs from the conventional method because it incorporates earthquake magnitude uncertainty and mixed datasets containing large historical events and recent data. The method can be used to estimate the b value of the Gutenberg-Richter relationship, annual activity rate λ(M) of an event and maximum possible magnitude M _max using incomplete and heterogeneous data files. In addition, an earthquake is considered a Poisson with an annual activity rate λ and with a doubly truncated exponential earthquake magnitude distribution. Map of seismic hazard and an earthquake catalogue, graphs and maps were created using geographic information systems (GIS), the Z-map code version 6 and Crisis software 2012.     

On the importance of continuity of magnitude scales

To describe an individual earthquake or the seismicity of a region, simple parameters such as magnitudes are necessary. In seismicity studies observations for as long as possible time intervals should be at disposal and subsequently the continuity of the parameters' quality should be guaranteed. M_GR or M_S can be such parameters. m_b(sp) of USGS and ISC is another one, but it has been accumulated only since the 1960s. An international proposal to introduce or revive classical m_b asks to change the traditional procedure of measuring the P maximum within a few seconds from the P onset. Some confusion appears to exist for recent m_b-data in EDR of USGS. It is strongly hoped that the traditional procedure of USGS for m_b(sp)-determination will not be discontinued and that the new m_b will be introduced only as an additional parameter.     

A new procedure to best-fit earthquake magnitude probability distributions: including an example for Taiwan

Since the year 1973, more than 54,000 M _w ≥ 3.0 earthquakes have occurred around Taiwan, and their magnitude–frequency relationship was found following with the Gutenberg–Richter recurrence law with b value equal to 0.923 from the least-square calculation. However, using this b value with the McGuire–Arabasz algorithm results in some disagreement between observations and expectations in magnitude probability. This study introduces a simple approach to optimize the b value for better modeling of the magnitude probability, and its effectiveness is demonstrated in this paper. The result shows that the optimal b value can better model the observed magnitude distribution, compared with two customary methods. For example, given magnitude threshold = 5.0 and maximum magnitude = 8.0, the optimal b value of 0.835 is better than 0.923 from the least-square calculation and 0.913 from maximum likelihood estimation for simulating the earthquake’s magnitude probability distribution around Taiwan.