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The earthquake magnitude data for Sudan Territory includes four types of magnitude scales (Moment Magnitude Mw, Surface wave magnitude Ms, Local magnitude ML and Body wave Magnitude mb ). Unifying the magnitude scale of the compiled earthquake catalogue requires converting these scales to one appropriate scale, usually moment magnitude scale. Therefore, the current paper is presented to retrieve plausible magnitude regression relationships for Sudan Territory. For this reason, all earthquakes that reported by Mw and any other type of magnitude scale are separated and used to derive the earthquake magnitude regression relationships for studied area. The conversion equations are derived using three types of regressions; the standard least-square regression, the inverted standard least-square regression and the particular orthogonal regression. The residual analysis and the log-likelihood method are performed to judge the goodness of fit for each model. The analysis indicated that the models derived by the standard least-square regression for each data-set are well represent the magnitude data within the study area followed by those yielded by the orthogonal regression.

The earthquake early warning (EEW) system is difficult to provide consistent magnitude estimate in the early stage of an earthquake occurrence because only few stations are triggered and few seismic signals are recorded. One of the feasible methods to measure the size of earthquakes is to extract amplitude parameters using the initial portion of the recorded waveforms after P-wave arrival. However, for a large-magnitude earthquake (M w > 7.0), the time to complete the whole ruptures resulted from the corresponding fault may be very long. The magnitude estimations may not be correctly predicted by the initial portion of the seismograms. To estimate the magnitude of a large earthquake in real-time, the amplitude parameters should be updated with ongoing waveforms instead of adopting amplitude contents in a predefined fixed-length time window, since it may underestimate magnitude for large-magnitude events. In this paper, we propose a fast, robust and less-saturated approach to estimate earthquake magnitudes. The EEW system will initially give a lower-bound of the magnitude in a time window with a few seconds and then update magnitude with less saturation by extending the time window. Here we compared two kinds of time windows for measuring amplitudes. One is P-wave time window (PTW) after P-wave arrival; the other is whole-wave time window after P-wave arrival (WTW), which may include both P and S wave. One to ten second time windows for both PTW and WTW are considered to measure the peak ground displacement from the vertical component of the waveforms. Linear regression analysis are run at each time step (1- to 10-s time interval) to find the empirical relationships among peak ground displacement, hypocentral distances, and magnitudes using the earthquake records from 1993 to 2012 in Taiwan with magnitude greater than 5.5 and focal depth less than 30 km. The result shows that considering WTW to estimate magnitudes has smaller standard deviation than PTW. The magnitude estimations using 1-s time widow have larger uncertainties. Progressively adopting peak displacement amplitudes (P d ) from 2- to 10-s WTW is suggested for EEW systems.

Attempts have been made to investigate the relationships between various earthquake magnitude scales for the region of the Gulf of Guinea, namely moment magnitude (Mw), surface wave magnitude (Ms), body wave magnitude (mb) and local magnitude (ML). The study involves a sum of 535 earthquake data from the period of 1918 to 2016. It was found that M s − M w ; M w − M L and m b − M w scales are in fairly good agreement while m b − M s magnitude scale differs by a magnitude unit of 1.45. Since the region of study is seismically active and mainly under the ocean, comprising of the mid-Atlantic ridges and the plate boundary, the seismo-tectonics of the study region is inferred from the obtained Gutenberg-Richter (GR) recurrence parameters. The inferences made are the prime input to the seismic hazard assessment of the region.

In this article, the seismic records of Japan’s Kik-net are selected to measure the acceleration, displacement, and effective peak acceleration of each seismic record within a certain time after P wave, then a continuous estimation is given on earthquake early warning magnitude through statistical analysis method, and Wenchuan earthquake record is utilized to check the method. The results show that the reliability of earthquake early warning magnitude continuously increases with the increase of the seismic information, the biggest residual happens if the acceleration is adopted to fit earthquake magnitude, which may be caused by rich high-frequency components and large dispersion of peak value in acceleration record, the influence caused by the high-frequency components can be effectively reduced if the effective peak acceleration and peak displacement is adopted, it is estimated that the dispersion of earthquake magnitude obviously reduces, but it is easy for peak displacement to be affected by long-period drifting. In various components, the residual enlargement phenomenon at vertical direction is almost unobvious, thus it is recommended in this article that the effective peak acceleration at vertical direction is preferred to estimate earthquake early warning magnitude. Through adopting Wenchuan strong earthquake record to check the method mentioned in this article, it is found that this method can be used to quickly, stably, and accurately estimate the early warning magnitude of this earthquake, which shows that this method is completely applicable for earthquake early warning.

Homogenization of earthquake catalog being a pre-requisite for seismic hazard assessment requires region based magnitude conversion relationships. Linear Standard Regression (SR) relations fail when both the magnitudes have measurement errors. To accomplish homogenization, techniques like Orthogonal Standard Regression (OSR) are thus used. In this paper a technique is proposed for using such OSR for preparation of homogenized earthquake catalog in moment magnitude Mw. For derivation of orthogonal regression relation between mb and Mw, a data set consisting of 171 events with observed body wave magnitudes (mb,obs) and moment magnitude (Mw,obs) values has been taken from ISC and GCMT databases for Northeast India and adjoining region for the period 1978–2006. Firstly, an OSR relation given below has been developed using mb,obs and Mw,obs values corresponding to 150 events from this data set. M w = 1.3 ( ± 0.004 ) m b,proxy - 1.4 ( ± 0.130 ) , where mb,proxy are body wave magnitude values of the points on the OSR line given by the orthogonality criterion, for observed (mb,obs, Mw,obs) points. A linear relation is then developed between these 150 mb,obs values and corresponding mb,proxy values given by the OSR line using orthogonality criterion. The relation obtained is m b,proxy = 0.878 ( ± 0.03 ) m b,obs + 0.653 ( ± 0.15 ) . The accuracy of the above procedure has been checked with the rest of the data i.e., 21 events values. The improvement in the correlation coefficient value between mb,obs and Mw estimated using the proposed procedure compared to the correlation coefficient value between mb,obs and Mw,obs shows the advantage of OSR relationship for homogenization. The OSR procedure developed in this study can be used to homogenize any catalog containing various magnitudes (e.g., ML, mb, MS) with measurement errors, by their conversion to unified moment magnitude Mw. The proposed procedure also remains valid in case the magnitudes have measurement errors of different orders, i.e. the error variance ratio is different from unity.

The project “Seismic Hazard Assessment for Almaty” has a main objective to improve existing seismic hazard maps for the region of northern Tien Shan and especially for the surroundings of Almaty and to generate a new geodynamic model of the region. In the first step a composite seismic catalogue for the northern Tien Shan region was created, which contains about 20,000 events and is representative for strong earthquakes for the period back to the year 500. For the period of instrumental observation 1911–2006 the catalogue contains data for earthquakes with a body wave magnitude larger than 4. For smaller events with magnitudes up to 2.2 the data are only available since 1980. The composite catalogue was created on the basis of several catalogues from the United States Geologic Survey (USGS), local catalogues from the Kazakh National Data Centre (KNDC) and the USSR earthquake catalogue. Due to the different magnitudes used in several catalogues a magnitude conversion was necessary. Event density maps were created to rate the seismicity in the region and to identify seismic sources. Subsurface fault geometries were constructed using tectonic model which uses fault parallel material flow and is constrained by GPS data. The fault geometry should improve the estimation of the expected seismic sources from seismic density maps. First analysis of the earthquake catalogue and the density maps has shown that nearly all large events are related to fault systems. Annual seismicity distribution maps suggest different processes as the cause for the seismic events. Apart from tectonics, also fluids play a major part in triggering of the earthquakes. Beneath the Issyk-Kul basin the absence of strong seismic activity suggests aseismic sliding at the flat ramp in a ductile crust part and low deformation within the stable Issyk-Kul micro-continent which underthrust the northern ranges of Tien Shan. First results suggest a new partition of the region in tectonic units, whose bounding faults are responsible for most of the seismic activity.

The differences between true travel-times of P and times predicted from travel-time tables (path effects) can be estimated for groups of closely spaced explosions with known hypocentres and origin times, if the onsets are observed at large signal-to-noise ratios (SNR) and read by analysts. Reading error can also be estimated and is usually assumed to be normally distributed with zero mean. Two experiments have been carried out to look at how reading error in P times from explosions varies with magnitude – taken as a measure of SNR – when read by analysts and by automatic systems. Although at low magnitudes there is some evidence of analyst readings being biased late, the largest variation in reading error with magnitude is found for automatic systems. The results show just how difficult it can be to estimate path effects free from observational bias, at least using bulletin data. The current programme to estimate path effects to improve epicentre location for verification of the Comprehensive Test Ban needs to include checks to ensure that apparent variations in path effects with location, are not due to bias from systematic reading error.

The large 1940 Vrancea event with body wave magnitude mB = 7.3 was investigated in terms of the depth of rupture initiation and extent. It was found that the rupture started at 150 km depth and propagated downwards. The ruptured zones of the 1977, 1986 and 1990 Vrancea events were estimated from the distribution of aftershocks located with the joint hypocentre determination method. Their depth ranges are 90–110 km, 130–150 km and 70–90 km, respectively. Because the body wave magnitudes mb were saturated for the last three events and the surface wave magnitudes MS were underestimated (not being corrected for depth) we chose the moment magnitudes to quantify the four events: 7.7 (1940), 7.4 (1977), 7.1 (1986) and 6.9 (1990), respectively. The depth interval 110–130 km is found to be unbroken since at least 1838 or 1802 and therefore is expected to accommodate the next large moment release (Mw = 7.0 to 7.4). The strain in the vertical and in the SE-NW directions is about 0.0003, giving a moderate strain rate of about 10−13 s−1. A correlation between the depth interval of the large events and the year of occurrence in a century is suggested, offering a physical basis to the observed quasi-cyclicity.

A probability seismic hazard map of Uganda is presented, based on instrumentally-derived data. The Uganda catalogue, compiled by Twesigomwe for the period 1900 to 1991, has been used. The magnitudes in the catalogue have been homogenised to surface wave magnitude (Ms); the conversion of body wave magnitude (mb) and local magnitude (ML to Ms were carried out where necessary using formulae derived for the Ugandan earthquakes. Based on seismicity and tectonics, the region was divided into 13 seismic source areas, each of which contributes to the seismic hazard throughout Uganda according to its specific seismicity. The uncertainties in the input parameters were accounted for by using a logic tree approach. On the logic tree, each uncertain parameter is represented by a node and branches emanating from that node represent alternative values on that parameter value and their assigned likelihood of being correct. Due to a lack of strong motion data, a semi-theoretical approach was used to develop an attenuation relation for the region. The mean peak ground acceleration (PGA), which is exceeded on average once every 50 years, was calculated. The resulting hazard map suggests that the whole of Uganda except in or close to the rifts, can expect to experience a PGA of between 0.5 and 0.6 m s−2, equivalent to an earthquake of intensity V–VI (slight damage) on average once every 50 years. In or close to the Western Rift, the expected PGA is between 1.0 and 2.2 m s−2, equivalent to an earthquake of intensity VII–VIII (moderate to heavy damage) on average once every 50 years. The frequency of occurrence of a PGA=2.0 m s-2 (heavy damage earthquake) for various parts of Uganda was also calculated. The results indicate that northeast Uganda can expect a destructive earthquake on average once in more than 3000 years, while south of latitude 0.5°N, except in and close to the Western Rift, can expect a destructive earthquake on average once every ∼1000–1500 years. In or close to the Western Rift the return period for destructive earthquake is on average less than about 50 years.

We investigate the effect on Gutenberg and Richter's parameter b of the saturation of moment-magnitude relationships caused by source finiteness. Any conventional magnitude scale measured at a constant period features a saturation which results in a stepwise increase in the slope of the log10 moment-magnitude relationship. We predict that this leads to an increase in b value with earthquake size. This is in addition to the effect of the physical saturation of the transverse dimension of the fault, previously described in the literature. A number of scaling models are used to predict the behavior of b with increasing magnitude, in the case of both the 20 s surface-wave magnitude Ms, and the 1 s body-wave magnitude mb. We show in particular that a b value of unity can be expected only in a range of earthquake size where the relevant magnitude has already started to saturate: it should be the exception, not the rule, and cannot be extended to a wide range of magnitudes, except at the cost of significant curvature in the frequency-magnitude curve. The widely reported b = 1 stems from the common practice of using a heterogeneous magnitude scale, e.g. Ms for large events and m1 for smaller ones.

Short term spatial and temporal variations in seismicity prior to the three sequences of earthquakes of m b ⩾ 5.8 of the Burma—Szechwan region are studied. Six years (1971–1976) of ISC seismicity data, as reported in the Regional Catalogue of Earthquakes, are considered. During the period, six earthquakes of body wave magnitude m b ⩾ 5.8 occurred in four sequences. Of these, three sequences are preceded by swarm activity in the epicentral regions. Evison (1977b) suggested that the swarm before the sequences of large shocks is a possible long-term precursor. He derived the conclusion by analyzing earthquakes in New Zealand and California. The analysis of the seismicity data for the region under investigation supports Evison's view and suggests that a relation between swarms and sequences of large events exists. The precursory time period (i.e. the time from beginning of the swarm to the main shock) for the Szechwan earthquakes of m b = 5.9 (Feb. 6, 1973) and m b = 5.8 (May 10, 1974) and the Burma earthquake of m b = 6.2 (Aug. 12, 1976) are 305, 317 and 440 days, respectively.

We present a linear moment tensor inversion method that incorporates both body and surface wave data. The source coordinates are fixed during the inversion, and the source depth is determined by applying the inversion at several depths and taking the depth that produces the minimum residual. The inversion is carried out in the time domain for body wave data and in the frequency domain for surface wave data. The fundamental Rayleigh waves at the period of 256 s from IDA stations and the long-period P-waves from WWSSN and GDSN stations, whose angular distances are from 30 to 90°, are used as the data. The simultaneous inversion of both body and surface wave data sets has several merits. Because of the body wave constraints, the present method gives reasonable solutions at shallow depths (< 30 km) where long-period surface wave inversions become unstable. Although the inversion using only body wave data is unstable in the sense that it allows for a variety of solutions with a slight change in the assumed depth, probably because of the noise present and poor coverage of body wave data to determine the source mechanisms, the inclusion of surface wave data makes the solution stable. This is because the surface wave data constrain nodal-plane strikes. We may also expect better resolution in source depth by including the body wave data because the local crustal structure above the source can be taken into account to generate the Green's function. We applied our method to two large earthquakes, one occurring at the triple junction off Boso Peninsula, Central Honshu, on 18 September 1984 and another at the outer rise area off the Chile trench on 16 October 1981. The scalar moments of the Boso-Oki and Chile earthquakes are estimated to be 3.2 × 1026 dyn cm and 6.3 × 1026 dyn cm, respectively. The ratio of the minimum absolute eigenvalue of the moment tensor to the maximum, which may measure the non-double-couple component, is less than 10% for both earthquakes. This suggests that their sources are essentially a double couple. The source depths of both events are determined as ∼ 30 km. The Boso-Oki event is indicative of hinge faulting within the Pacific slab at the triple junction. The Chile event is consistent with compressional bending stress in the deeper part of the lithosphere at the trench-outer rise area off Chile.

Probability distribution of maximum earthquake magnitude is first derived for an unspecified probability distribution of earthquake magnitude. A model for energy release of large earthquakes, similar to that of Adler-Lomnitz and Lomnitz, is introduced from which the probability distribution of earthquake magnitude is obtained. An extensive set of world data for shallow earthquakes, covering the period from 1904 to 1980, is used to determine the parameters of the probability distribution of maximum earthquake magnitude. Because of the special form of probability distribution of earthquake magnitude, a simple iterative scheme is devised to facilitate the estimation of these parameters by the method of least-squares. The agreement between the empirical and derived probability distributions of maximum earthquake magnitude is excellent.

P-wave magnitude spectra of a foreshock-mainshock-aftershock sequence on 7 and 8 May 1986 in the Aleutian Islands are determined using broad-band seismograms recorded at the GRF-array. The magnitude spectra are compared for different stations of the array. The maximum magnitude is stable with a standard deviation below 1%. The reliability of other source parameters (fault length, seismic moment and stress drop) derived from the magnitude spectrum m(f) depends on the determination of the corner period. Different methods to derive the corner period are compared. Best suited and most stable is the one based on the formula: T c = ∫ 0 ∞ E s (f) df ∫ 0 ∞ E s (f) f df where Es(f) = 102mf−14 is the energy density spectrum of the P-wave, and mf, the spectral P-wave magnitude of the earthquake at the respective period.

Synthetic calibration functions for body-wave magnitudes are presented. They have been obtained from computations made under the assumption that the variation of amplitude spectra along the earth's surface is due to radial velocity heterogeneity and radial changes of the dissipation factor Q inside the earth only. The new calibration functions depend on the epicentral distance and the focal depth of the earthquake, as well as on the period of the body-wave under consideration. No single calibration function exists which would produce magnitude figures identical for all Fourier components of a body-wave. Observations on several hundreds of strong earthquakes in recent years show that the P-wave magnitudes vary systematically with the period of the wave. With the application of the synthetic calibration function a general increase of the teleseismically determined P-wave magnitudes with frequency is observed. This fact reconciles acceleration response spectra from narrowband strong-motion analyzers in the near-field of an earthquake and spectral magnitudes determined from far-field observations by sensitive narrow-band seismographs. The strength of high-frequent spectral components generally exceeds the strength of low-frequent components determined in both cases.

The strain produced by body waves in the vicinity of the earthquake is employed in the definition of the earthquake volume. The definition is applicable to artificial seismic events. Distances from the focus at which a given maximum strain was attained during the event, are presented as a function of magnitude and focal depth. The computed strains are compared with strains measured and reported for a number of earthquakes and nuclear explosions. The earthquake volume shows a distinct decrease with focal depth. The strains produced by body waves during the earthquake throw some light on the stress state in the vicinity of the focus, and are considered to be able to yield information of the rate of tectonic strain accumulation.

Various magnitude scales commonly used and the interrelationships among them are reviewed. It is shown that problems exist with all of the magnitude scales being used in the United States. When using regional catalogs, for example, it is often necessary to determine how the reported magnitudes were determined. Often such information is not available, although the potential errors are quite large. Both the MS and the mb scales were designed to be universal scales. However, both MS and mb magnitudes are often determined beyond the applicable range of the equations used to define the two scales. Furthermore, the MS magnitudes are not generally available for moderate to small earthquakes in most earthquake catalogs. The mb magnitudes are more generally available than MS values; however, there is also much greater variation in the way mb is determined. In particular, a significant change in the mb scale occurred in the early 1960’s when the World-Wide Standard Seismograph Network (WWSSN) was established. This change in instrumentation used to determine mb values had a significant effect on estimated magnitudes (post-1960 values are lower) and the saturation level of the mb scale. The older, longer-period instruments recorded larger mb magnitudes than can be recorded with the WWSSN instruments. In addition, great care must be taken when selecting the mb magnitudes of western U.S. earthquakes, because the values are often in considerable error owing to the fact that they were determined at distances less than 25° and were not properly corrected for attenuation in the upper mantle, or asthenosphere. The seismic body wave magnitude mb of an earthquake is strongly affected by regional variations in the Q structure, composition, and physical state within the earth. Therefore because of differences in attenuation of P waves between the western and eastern United States, a problem arises when comparing mb values for the two regions. A regional mb magnitude bias exists which, depending on where the earthquake occurs and where the P waves are recorded, can lead to magnitude errors as large as ⅓ unit. There is also a significant difference between mb and ML values for earthquakes in the western United States. An empirical link between the mb of an eastern U.S. earthquake and the ML of an equivalent western earthquake is given by ML = 0.57 + 0.92(mb)east. This result is important when comparing ground motion between the two regions and for choosing a set of real western U.S. earthquake records to represent eastern earthquakes.