Estimating maximum magnitude earthquakes in Iraq using extreme value statistics

Summary. Extreme value theory is used to estimate maximum magnitude earthquakes in Iraq (29–38°N, 39–48°E). The seismicity file for the period 1905–1982 is used to determine the recurrence relationship as well as the parameters of Gumbel types I and III asymptotic distributions.
The statistical parameters are estimated by both least squares and maximum likelihood techniques. Results show that although the least squares upper magnitude is closer in value to actual earthquake magnitude, the maximum likelihood approximation to the third distribution appears to show a better overall fit to the data sample. This result is reflected in the calculated probability of occurrence of earthquake risk over various design periods.     

Perceptible earthquakes in the United Kingdom

Summary. Earthquake occurrence in the United Kingdom is analysed using Gumbel's third type asymptotic distribution of extreme values. Uncertainties in both the parameters and predictions derived from the Gumbel distribution are obtained and it is shown that an earthquake with body-wave magnitude slightly over five is the one most likely to be perceived at any point in the United Kingdom.     

Mixture distributions - an alternative approach for estimating maximum magnitude earthquake occurrence

Summary. Gumbel's theory of extreme value has been employed in the statistical forecasting of maximum-magnitude earthquake occurrence. The basic working hypothesis behind this method assumes that observations follow either Gumbel type I or type III asymptotic distributions. In certain cases, however, it is found that neither type of distribution fits the data well enough to produce accurate parameter-estimates, particularly in the larger earthquake range. This article proposes an alternative approach based on finite-mixture distributions whereby a more realistic prediction of upper earthquake magnitudes (at given return periods) is expected using a combined analysis of both Gumbel types I and III extremal distributions.     

The first and third asymptotic distributions of extremes as applied to the seismic source regions of India and adjacent areas

The seismic source regions are identified on the basis of spatial and temporal distributions of shocks (1900–1989), recurrence relations and the tectonic architecture of the Indian subcontinent and adjoining areas. The probable occurrence of the maximum magnitude earthquake is estimated using the theory of extreme values of Gumbel. The parameters of the first and third asymptotic distributions of extremes and their uncertainty values are computed for the seven identified seismic source regions of India and adjacent areas. The third-type distribution curve is preferable to the first type in all the regions, as revealed by the χ² test. The results of the third asymptotic distribution indicate the upper bound to earthquake magnitude w is equal to 8.94 ± 0.21 for Assam, 8.56 ± 0.29 for Bihar-Nepal, 8.43 ± 0.10 for Kangra, 8.97 ± 0.27 for Hindukush, 7.61 ± 0.24 for Pakistan-Cutch, 7.34 ± 0.12 for Koyna and 8.98 ± 0.27 for Andaman Sea seismic source regions. The predicted most probable largest earthquake magnitude is computed for return periods of 10, 20, 50, 75 and 100 yr in each source region.     

The role of seismicity models in probabilistic seismic hazard estimation: comparison of a zoning and a smoothing approach

Seismic hazard estimations are compared using two approaches based on two different seismicity models: one which models earthquake recurrence by applying the truncated Gutenberg-Richter law and a second one which smoothes the epicentre location of past events according to the fractal distribution of earthquakes in space ( Woo 1996 ). The first method requires the definition of homogeneous source zones and the determination of maximum possible magnitudes whereas the second method requires the definition of a smoothing function. Our results show that the two approaches lead to similar hazard estimates in low seismicity regions. In regions of increased seismic activity, on the other hand, the smoothing approach yields systematically lower estimates than the zoning method. This epicentre-smoothing approach can thus be considered as a lower bound estimator for seismic hazard and can help in decision making in moderate seismicity regions where source zone definition and estimation of maximum possible magnitudes can lead to a wide variety of estimates due to lack of knowledge. The two approaches lead, however, to very different earthquake scenarios. Disaggregation studies at a representative number of sites show that if the distributions of contributions according to source–site distance are comparable between the two approaches, the distributions of contributions according to magnitude differ, reflecting the very different seismicity models used. The epicentre-smoothing method leads to scenarios with predominantly intermediate magnitudes events (5 ≤ M ≤ 5.5) while the zoning method leads to scenarios with magnitudes that increase with the return period from the minimum to the maximum magnitudes considered. These trends demonstrate that the seismicity model used plays a fundamental role in the determination of the controlling scenarios and ways to discriminate between the most appropriate models remains an important issue.     

Resolution and significance assessment of precursory changes in mean earthquake magnitudes

The Loma Prieta earthquake (magnitude 7.0), which occurred in October 1989 in central California, was preceded by a period during which the mean magnitude of background seismicity in a small region near the eventual epicentre was abnormally low. This period may have begun as early as 1979, and it continued until mid-1988, after which the mean magnitude increased to a higher than normal value until the main earthquake. These changes were observed in the seismicity of an area 40  km in radius, centred on the Loma Prieta epicentre, and are consistent with the predictions of fracture mechanics studies. The 1988 change correlates with a reported change in long-term strain.
  A procedure has been developed for resolving such temporal changes in seismicity using CUSUM statistics. It demonstrates that the anomaly was highly significant, on the basis of analyses of two independent catalogues. There was also a significant anomaly before the 1994 Northridge earthquake.
  The hypothesis that large earthquakes are preceded by periods in which the mean magnitude of background activity is abnormally low, in the immediate vicinity of the eventual epicentre, is a tantalizing one. The analysis tool examined here may be useful for resolving such changes. Care needs to be taken, however, in routine surveillance of earthquake populations that contain large aftershock sequences.     

Seismic hazard in central southern Africa

Seismic hazard maps of central-southern Africa where hazard has been expressed in terms of peak ground acceleration for an annual probability in excess of 10^-1 show relatively high values that distinguish the seismic hazard potential of the Deka fault zone, the mid-Zambezi basin-Luangwa rift and western central Mozambique. In areas such as central-southern Africa where little is known about the geology of the region and the fault systems have not been fully mapped, seismic hazard potential may be estimated from seismicity and broad-scale fault features. For this region, such potential is based on earthquake magnitude M_s ≥ 6. Events of such magnitude have recently occurred in the mid-Zambezi basin, southern Zimbabwe and western-central Mozambique. This paper follows the conventional probabilistic hazard analysis procedure, defining seismic source zones from seismicity based on instrumental records from a cataloque that spans a period of 83 years. Geological and geomorphological features in the region are described on the mesoscale and are correlated with the seismicity as broad fault zones. The scarcity of strong-motion accelerogram data necessitated the formulation of attenuation values based on random vibration theory (RVT).     

Seismic reflection studies using local earthquake sources

Summary. A method is presented for processing three-component digital recordings of micro-earthquakes to obtain near-vertical reflection profiles in regions of shallow seismicity. The processing includes magnitude and focal-depth normalization and event stacking, where stacking is by small localized groups, with ray theoretical time and distance corrections applied to compensate for varying focal depths. In areas with high seismicity, this procedure allows earthquakes to be treated as "controlled" sources to probe layered structures of the deep crust and upper mantle. The validity of our approach is demonstrated using S-waves from aftershocks of the Borah Peak, Idaho, earthquake (Ms = 7.3) of 1983.     

Statistical analysis of seismicity in a wide region around the 1998 Mw 8.1 Balleny Islands earthquake in the Antarctic Plate

A large earthquake (Mw 8.1) that occurred off the North Coast of the Antarctic continent near the Balleny Islands on 25 March 1998 was the largest intra-plate earthquake ever recorded in the Antarctic Plate. The earthquake hypocenter catalog for this area shows a marked change in seismicity following the main shock in a large area around the Balleny aftershock region. However, the earthquake catalog includes many aftershocks and is affected by a variable detection rate. To overcome these limitations, we applied statistical models and methods, including Gutenberg–Richter’s magnitude frequency distribution, the Epidemic-Type Aftershock Sequences (ETAS) model, and the space–time ETAS model, thereby enabling calculation of the change in detection rate. The results show a change in the spatial pattern of background seismicity over a large region after the 1998 event.     

Likelihood analysis of earthquake catalogues

We apply several classes of stochastic multidimensional models to statistical analysis of earthquake catalogues using likelihood methods. We investigate the importance of including different earthquake parameters in the model: epicentral coordinates, hypocentral depth, time limits for interearthquake interaction, and especially spatial distribution of earthquakes as well as spatial aftershock patterns. Results of this study combined with other investigations, suggest that most distributions controlling earthquake interaction have a fractal or scale-invariant form. Developed models are used for statistical analysis of several earthquake catalogues to evaluate parameters of earthquake occurrence. These parameters are shown to be similar for shallow earthquakes of different magnitude ranges and seismogenic regions, confirming self-similarity of the earthquake process. Whereas intermediate earthquakes seem to emulate the pattern of shallow earthquake occurrence, albeit at a much smaller aftershock rate, deep earthquakes differ significantly in their properties. Predictability of standard shallow earthquake catalogues has been analysed; we present evidence that for the best available catalogues the predictability is close to 10 bits per earthquake. Several synthetic earthquake catalogues have been created and processed through the likelihood inversion scheme. The results from likelihood analysis of these catalogues confirm our approach.     

Determination of earthquake early warning parameters, τc and Pd, for southern California

We explore a practical approach to earthquake early warning in southern California by determining a ground-motion period parameter  τ _c   and a high-pass filtered displacement amplitude parameter Pd from the initial 3 s of the P waveforms recorded at the Southern California Seismic Network stations for earthquakes with M > 4.0. At a given site, we estimate the magnitude of an event from  τ _c   and the peak ground-motion velocity ( PGV ) from Pd . The incoming three-component signals are recursively converted to ground acceleration, velocity and displacement. The displacements are recursively filtered with a one-way Butterworth high-pass filter with a cut-off frequency of 0.075 Hz, and a P -wave trigger is constantly monitored. When a trigger occurs,  τ _c   and Pd are computed. We found the relationship between  τ _c   and magnitude ( M ) for southern California, and between Pd and PGV for both southern California and Taiwan. These two relationships can be used to detect the occurrence of a major earthquake and provide onsite warning in the area around the station where onset of strong ground motion is expected within seconds after the arrival of the P wave. When the station density is high, the methods can be applied to multistation data to increase the robustness of onsite early warning and to add the regional warning approach. In an ideal situation, such warnings would be available within 10 s of the origin time of a large earthquake whose subsequent ground motion may last for tens of seconds.     

Statistical analysis of time-dependent earthquake occurrence and its impact on hazard in the low seismicity region Lower Rhine Embayment

The time-dependence of earthquake occurrence is mostly ignored in standard seismic hazard assessment even though earthquake clustering is well known. In this work, we attempt to quantify the impact of more realistic dynamics on the seismic hazard estimations. We include the time and space dependences between earthquakes into the hazard analysis via Monte Carlo simulations. Our target region is the Lower Rhine Embayment, a low seismicity area in Germany. Including aftershock sequences by using the epidemic type aftershock-sequence (ETAS) model, we find that on average the hypothesis of uncorrelated random earthquake activity underestimates the hazard by 5–10 per cent. Furthermore, we show that aftershock activity of past large earthquakes can locally increase the hazard even centuries later. We also analyse the impact of the so-called long-term behaviour, assuming a quasi-periodic occurrence of main events on a major fault in that region. We found that a significant impact on hazard is only expected for the special case of a very regular recurrence of the main shocks.     

Upper-crustal structure of the Benevento area (southern Italy): fault heterogeneities and potential for large earthquakes

The Benevento region is part of the southern Apennines seismogenic belt, which experienced large destructive seismic events both in historical and in recent times. The study area lies at the northern end of the Irpinia fault, which ruptured in 1980 with a M_s = 6.9 normal faulting event, which caused about 3000 casualties. The aims of this paper are to image lateral heterogeneities in the upper crust of the Benevento region, and to try to identify the fault segments that are expected to generate such large earthquakes. This work is motivated by the recognition that lithological heterogeneities along major fault zones, inferred from velocity anomalies, reflect the presence of fault patches that behave differently during large rupture episodes. In this paper, we define the crustal structure of the Benevento region by using the background seismicity recorded during 1991 and 1992 by a local seismic array. These data offer a unique opportunity to investigate the presence of structural discontinuities of a major seismogenic zone before the occurrence of the next large earthquake. The main result that we obtained is the delineation of two NW-trending high-velocity zones (HVZs) in the upper crust beneath the Matese limestone massif. These high velocities are interpreted as high-strength regions that extend for 30-40 km down to at least 12 km depth. The correspondence of these HVZs with the maximum intensity regions of historical earthquakes (1688 AD, 1805 AD) suggests that these anomalies delineate the extent of two fault segments of the southern Apenninic belt capable of generating M = 6.5⁻⁷ earthquakes. The lateral offset observed between the two segments from tomographic results and isoseismal areas is possibly related to transverse right-lateral faults.     

Earthquake nests

Summary. Making use of extensive observations of micro-earthquakes available in the Tokyo region, Usami & Watanabe constructed a simple but effective method of exhibiting those regions where small earthquakes have clustered during a 4.5 yr period. Such clusters are defined by contour surfaces, and for convenience are termed earthquake nests .
If we accept the assumption that the magnitude of an earthquake is directly related to the volume previously undergoing intensified strain, and if we regard the nests as measures of such volumes, we can make rough estimates of the magnitudes of potential earthquakes in different parts of the Tokyo region. This method of assigning seismicity can be one way of calculating local risk. Repeated investigations can also detect changes in the tress field.     

Seismicity and seismic gap in the Lesser Antilles arc and earthquake hazard in Guadeloupe

Summary. A seismic study of the Lesser Antilles arc has been carried out, first for the period 1950–1978, for which we can use local seismic networks to draw maps of instrumental seismicity, then for the period 1530–1950, for which we have catalogues of felt earthquakes. The striking feature of the spatial distribution of foci is the cluster of epicentres in the northern half of the arc; all large earthquakes ( M > 7.5) are located north of 14° latitude. Seismicity cross-sections through the arc show a variable dipping subduction zone along the arc; the deep seismic zone is steeper in the centre of the arc than on the extremity.
The time-space diagram for historical seismicity, and the evidence of a seismic gap at the east of Guadeloupe lead us to consider the northern half arc as a likely site for a large earthquake in the near future.
The seismic slip rate calculated from all major earthquakes since 1530 is of much greater value than that obtained from recent plate tectonic models, suggesting that the recurrence rate of earthquakes is more than many hundreds of years with a possible aseismic creep.     

Precursory seismic quiescence in the Mudurnu Valley, North Anatolian fault zone, Turkey

The seismicity rate in the Mudurnu Valley of Turkey was studied using an earthquake catalogue that reports events homogeneously down to magnitude 2.3 for the years 1985–1989, and covers the area between latitudes 40.2° and 41.0°N, and longitudes 30.0° and 31.5°E. During this period the only two main shocks, M = 4.0 and M = 4.3, occurred on 1988 September 6 and 1988 December 9 within about 30km of each other. A highly significant seismic quiescence is evident in the area surrounding these main shocks, while the seismicity rate in the rest of the area covered by the catalogue remains constant. the quiescence becomes more pronounced the smaller the area around the main shocks that is studied. the smallest areas that can be studied contain about 60 earthquakes and have dimensions of approximately 25km on each side. the decreases in seismicity rates are 50–80 per cent depending on the volume and period used for defining the quiescence. the quiescence started in 1988 January and lasted about seven months, with approximately 4.5 months of normal activity separating it from the main shock of December. the precursor time of 12 months for an M = 4.3 main shock is similar to those observed in California. It is concluded that it is possible to resolve precursory quiescence before moderate and large earthquakes in the Mudurnu area with the existing seismograph network.     

Low detection capability of global earthquakes after the occurrence of large earthquakes: investigation of the Harvard CMT catalogue

We investigated the detection capability of global earthquakes immediately after the occurrence of a large earthquake. We stacked global earthquake sequences after occurrences of large earthquakes obtained from the Harvard centroid-moment tensor catalogue, and applied a statistical model that represents an observed magnitude–frequency distribution of earthquakes to the stacked sequence. The temporal variation in model parameters, which corresponds to the detection capability of earthquakes, was estimated using a Bayesian approach. We found that the detection capability of global earthquakes is lower than normal for several hours after the occurrence of large earthquakes; for instance, the duration of lowered detection capability of global earthquakes after the occurrence of an earthquake with a magnitude of seven or larger is estimated to be approximately 12 hr.     

中国地震发生频率与烈度的空间分布

考虑不同区域地震记录具有时间长度不等的特点,对“震中分布分震级网格点密集值”算法进行改进,结合 GIS 的空间分析方法将地震目录中的点数据空间化为能反映地震发生频率的栅格数据;依据地震震级和烈度的关 系以及地震烈度在空间上的椭圆衰减模型,选择逼近和近似的计算手段,并结合空间插值方法得到中国地震烈度 分布的栅格图。从地震频率分布结果上看,大致以宁夏、甘肃、四川和云南为界,中国西部地区3 级以上的地震发生 频率要高于东部地区;从地震烈度分布结果看,中国甘肃、陕西、宁夏、山西、河北、四川、云南等位于地震带内的区 域在发生地震时产生的烈度较高。     

Application of the negative binomial to earthquake occurrences in the Alpide-Himalayan belt

Summary . Shallow focus earthquakes ( h ≤ 60 km) of magnitude range M = 4.0–6.0, occurred during 1954–75 in various high seismicity zones of the Alpide-Himalayan belt have been tested by the Poisson and the negative binomial laws. When the clustering of events make the simple Poisson model inapplicable in most of the high seismicity zones of the Alpide-Himalayan belt it has been shown that the negative binomial entries provide an excellent model for describing the earthquake occurrences. The chi-square ( X ²) test is employed for testing the actual observations with theoretical distributions.     

A multidisciplinary study of a slow-slipping fault for seismic hazard assessment: the example of the Middle Durance Fault (SE France)

Assessing seismic hazard in continental interiors is difficult because these regions are characterized by low strain rates and may be struck by infrequent destructive earthquakes. In this paper, we provide an example showing that interpretations of seismic cross sections combined with other kinds of studies such as analysis of microseismicity allow the whole seismogenic source area to be imaged in this type of region. The Middle Durance Fault (MDF) is an 80-km-long fault system located southeastern France that has a moderate but regular seismicity and some palaeoseismic evidence for larger events. It behaves as an oblique ramp with a left-lateral-reverse fault slip and has a low strain rate. MDF is one of the rare slow active fault system monitored by a dedicated dense velocimetric short period network. This study showed a fault system segmented in map and cross section views which consists of staircase basement faults topped by listric faults ramping off Triassic evaporitic beds. Seismic sections allowed the construction of a 3-D structural model used for accurate location of microseismicity. Southern part of MDF is mainly active in the sedimentary cover. In its northern part and in Alpine foreland, seismicity deeper than 8 km was also recorded meaning active faults within the crust cannot be excluded. Seismogenic potential of MDF was roughly assessed. Resulting source sizes and estimated slip rates imply that the magnitude upper limit ranges from 6.0 to 6.5 with a return period of a few thousand years. The present study shows that the coupling between 3-D fault geometry imaging and accurate location of microseismicity provides a robust approach to analyse active fault sources and consequently a more refined seismic hazard assessment.