Scaling relations of moment magnitude,local magnitude,and duration magnitude for earthquakes originated in northeast India

In this study, we aim to improve the scaling between the moment magnitude (M _W), local magnitude (M _L), and the duration magnitude (M _D) for 162 earthquakes in Shillong-Mikir plateau and its adjoining region of northeast India by extending the M _W estimates to lower magnitude earthquakes using spectral analysis of P-waves from vertical component seismograms. The M _W-M _L and M _W-M _D relationships are determined by linear regression analysis. It is found that, M _W values can be considered consistent with M _L and M _D, within 0.1 and 0.2 magnitude units respectively, in 90 % of the cases. The scaling relationships investigated comply well with similar relationships in other regions in the world and in other seismogenic areas in the northeast India region.     

Empirical Global Relations Converting M S and m b to Moment Magnitude

The existence of several magnitude scales used by seismological centers all over the world and the compilation of earthquake catalogs by many authors have rendered globally valid relations connecting magnitude scales a necessity. This would allow the creation of a homogeneous global earthquake catalog, a useful tool for earthquake research. Of special interest is the definition of global relations converting different magnitude scales to the most reliable and useful scale of magnitude, the moment magnitude, M _W. In order to accomplish this, a very large sample of data from international seismological sources (ISC, NEIC, HRVD, etc.) has been collected and processed. The magnitude scales tested against M _W are the surface wave magnitude, M _S, the body wave magnitude, m _b, and the local magnitude, M _L. The moment magnitudes adopted have been taken from the CMT solutions of HRVD and USGS. The data set used in this study contains 20,407 earthquakes, which occurred all over the world during the time period 1.1.1976–31.5.2003, for which moment magnitudes are available. It is shown that well-defined relations hold between M _W and m _b and M _S and that these relations can be reliably used for compiling homogeneous, with respect to magnitude, earthquake catalogs.     

Magnitude estimation of Koyna-Warna earthquakes, India

The paper presents the current state of magnitude estimation for Koyna earthquakes exceeding magnitude 3.0. We estimate coda duration magnitude from analogue seismograms recorded on the short period vertical (SPZ) seismometer at Hyderabad seismic observatory HYB and determine moment magnitude using very broad-band (VBB) data from the Geoscope station (HYB)and short period digital data from the local seismic network of NationalGeophysical Research Institute (NGRI) around the Koyna and Warna reservoirs.Firstly, the seismograms of 97 Koyna earthquakes exceeding magnitude 4.0 havebeen used to establish a new empirical coda duration magnitude scale which includes the higher order terms of log₁₀, where is the coda length in seconds. Four background noise levels (1, 2, 6 and 10 mm) areconsidered to estimate the coda duration. We found that the duration magnitudes for 1 mm background level are more stable than those for 2, 6 and 10 mm. The new coda duration magnitude (M_dnew) scale, for 1 mmlevel, is:M_dnew = –0.594 + 2.04 log₁₀ – 0.0435 (log₁₀)²The estimated M_dnew are compatible with the reported M_S values of the NGRI observatory and the m_b values of the United States Geological Survey (USGS). These magnitudes can be obtained within the standard deviation of ± 0.26 units of M_S (NGRI). A new relatively homogeneous catalog for Koyna earthquakes of M_dnew 4.0 is obtained. The momentmagnitudes for 34 Koyna-Warna events of M_dnew ranging from 3.0 to 5.4 have been estimated using two techniques. The first utilizes amplitudes of band-pass filtered (between 15 and 30 sec) velocity traces of moderate Koyna-Warna earthquakes of M_W} 4.4 to 5.4, we abbreviate the magnitude using M_A. The second is based on the S-wave spectrum of short period seismograms of local earthquakes (M_W < 3.8). Moment magnitudes estimated by spectral analysis mainly depend on the estimation of event's long-period spectral level and appears to saturate for moderate Koyna-Warnaearthquakes (M_W > 3.8). We recommend the use of both techniques whenever possible. The estimated moment magnitudes and M_dnew show an almost linear relationship with a standard deviation of ± 0.05.     

The Conversion Relationship between the Local Earthquake Magnitude and Surface Wave Magnitude in the Inner Mongolia Digital Seismic Network

Using 116 earthquakes over M_L3.8 in the Inner Mongolia region from 2008 to 2015, the local earthquake magnitude M_L and surface wave magnitude M_S are remeasured. Based on norm linear regression(SR1 and SR2) and norm(OR) orthogonal regression method, we established the conversion relationship between M_L and M_S. The results were tested with Gaussian disturbance. The result shows that the orthogonal regression method(OR) result has the best fitting curve, and the conversion relation is M_S=0.96 M_L-0.10. The difference between our result and Guo Lücan's(M_S=1.13 M_L-1.08) may be caused by regional tectonic characteristics. M_(S Inner Mongolia) value is significantly higher than the M_(S empirical) value, with an average difference of 0.23, the difference distribution of empirical relation and the rectified relation is in the range of 0.2-0.3.     

内蒙古中西部地区中小地震矩震级研究

基于S震相"S窗"内的波形信号识别、品质因子Q(f)和22个台站场地响应,利用2009~2016年3月内蒙古中西部地区地震的波形资料,反演了182次中小地震的震源波谱参数,得到这些小震的零频幅值及其拐角频率,据此计算了这些地震的地震矩M_0、矩震级M_W和应力降Δσ。利用回归分析方法得到了近震震级与矩震级、矩震级与应力降的关系式。分析表明,近震震级与矩震级、矩震级与应力降呈线性关系。可见,将矩震级纳入地震的快报与正式目录中,可以丰富地震观测报告内容,更好地为地震应急和地震科研服务。     

宁夏地区近震震级短周期量规函数的研究与修正

选取宁夏"十五"宽频带数字地震台网2009年1月—2016年12月的1 782个地震事件、7 345条地震记录资料,通过震级残差统计和多元回归分析计算各台站单台震级与台网平均震级的偏差、平均偏差和标准偏差,分析震级偏差的频次分布,修正M_L量规函数,得到宁夏地区的地方性均匀震级量规函数和台基改正量。且采用多元回归分析方法,得到最大地动位移的衰减关系及与之对应的量规函数。结果表明,修正后的震级均方差由原来的0.237 0降低为0.228 9,震级修正最大值为0.51。     

Magnitude reassessment of New Zealand earthquakes

The surface-wave magnitudes of a selection of New Zealand earthquakes have been determined on a consistent basis using the ‘Prague formula’ and station corrections. The earthquakes range in magnitude from about 5 to 7.8, covering the instrumental period 1901–1988. Magnitudes for many of the earlier events had not been properly determined previously; and some significant discrepancies from the traditional magnitudes were found. The use of European station data (160° < D < 175°) is important to New Zealand because of its geographical isolation. These distant data were found to give consistently slightly higher M_s than closer stations, but could be used without bias through the station correction procedure. The relationship between M_s and M_L was found for 31 ‘shallow’ New Zealand events and much of the scatter was explained as a function of depth. Significant differences in M_s/M_L expressions from Europe and California were also found. The limited New Zealand data for M_w and M₀ related well to Californian and global relationships with M_s.     

The rupture process and asperity distribution of three great earthquakes from long-period diffracted P-waves

Maximum earthquake size varies considerably amongst the subduction zones. This has been interpreted as a variation in the seismic coupling, which is presumably related to the mechanical conditions of the fault zone. The rupture process of a great earthquake indicates the distribution of strong (asperities) and weak regions of the fault. The rupture process of three great earthquakes (1963 Kurile Islands, M_W = 8.5; 1965 Rat Islands, M_W = 8.7; 1964 Alaska, M_W = 9.2) are studied by using WWSSN stations in the core shadow zone. Diffraction around the core attenuates the P-wave amplitudes such that on-scale long-period P-waves are recorded. There are striking differences between the seismograms of the great earthquakes; the Alaskan earthquake has the largest amplitude and a very long-period nature, while the Kurile Islands earthquake appears to be a sequence of magnitude 7.5 events.The source time functions are deconvolved from the observed records. The Kurile Islands rupture process is characterized by the breaking of asperities with a length scale of 40–60 km, and for the Alaskan earthquake the dominant length scale in the epicentral region is 140–200 km. The variation of length scale and M_W suggests that larger asperities cause larger earthquakes. The source time function of the 1979 Colombia earthquake (M_W = 8.3) is also deconvolved. This earthquake is characterized by a single asperity of length scale 100–120 km, which is consistent with the above pattern, as the Colombia subduction zone was previously ruptured by a great (M_W = 8.8) earthquake in 1906.The main result is that maximum earthquake size is related to the asperity distribution on the fault. The subduction zones with the largest earthquakes have very large asperities (e.g. the Alaskan earthquake), while the zones with the smaller great earthquakes (e.g. Kurile Islands) have smaller scattered asperities.     

Correlating Precursory Declines in Groundwater Radon with Earthquake Magnitude

Both studies at the Antung hot spring in eastern Taiwan and at the Paihe spring in southern Taiwan confirm that groundwater radon can be a consistent tracer for strain changes in the crust preceding an earthquake when observed in a low‐porosity fractured aquifer surrounded by a ductile formation. Recurrent anomalous declines in groundwater radon were observed at the Antung D1 monitoring well in eastern Taiwan prior to the five earthquakes of magnitude (M_w): 6.8, 6.1, 5.9, 5.4, and 5.0 that occurred on December 10, 2003; April 1, 2006; April 15, 2006; February 17, 2008; and July 12, 2011, respectively. For earthquakes occurring on the longitudinal valley fault in eastern Taiwan, the observed radon minima decrease as the earthquake magnitude increases. The above correlation has been proven to be useful for early warning local large earthquakes. In southern Taiwan, radon anomalous declines prior to the 2010 M_w 6.3 Jiasian, 2012 M_w 5.9 Wutai, and 2012 M_L 5.4 Kaohsiung earthquakes were also recorded at the Paihe spring. For earthquakes occurring on different faults in southern Taiwan, the correlation between the observed radon minima and the earthquake magnitude is not yet possible.     

Frequency analysis of annual maximum earthquakes within a geographical region

The risk formula, expressing the probability of at least one occurrence of earthquakes of greater-than-design-value magnitudes over the economic life of a structure, is modified taking into consideration the probability of no-earthquake years. The annual maximum earthquake magnitudes of three scales: Richter magnitude, also known as local magnitude (M_L), body-wave magnitude (M_b), and moment magnitude (M_M) in a geographical area encompassing the Bingöl Province in Turkey are taken from two sources: (1) report by Kalafat et al. (2007) [14] and (2) the web site reporting data by Kandilli Observatory which has been recording earthquakes occurring in and around Turkey since 1900. Statistical frequency analyses are applied on the three sample series using various probability distribution models, and magnitude versus average return period relationships are determined. The values of the M_L, M_b, and M_M series for 10% and 2% risk are computed to be around 7.2 and 8.3. The tectonic structure and seismic properties of the Bingöl region are also given briefly.     

Estimation of Maximum Earthquakes in Northeast India

We attempt to estimate possible maximum earthquakes in the northeast Indian region for four seismic source zones, namely EHZ, MBZ, EBZ, and SHZ, which encapsulates the various seismogenic structures of the region and also for combined source zones taken as a single seismic source regime. The latter case exhibits a high maximum earthquake estimate of M_W 9.4 (±0.85) through Bayesian interpretation of frequency magnitude distribution with Gamma function implicating a moderate deviation from the standard Gutenberg Richter model at the higher magnitudes. However, tapering Gutenberg Richter models with corner magnitudes at M_W 8.01, 8.7 and 9.1, respectively indicated maximum values corresponding to M_W 8.4, 9.0, and 9.3. The former approach was applied to each of the source zones wherein the data are presented in parts according to the data completeness, thereof. EHZ, MBZ, EBZ and SHZ are seen with maximum earthquakes of M_W 8.35 (±0.59), 8.79 (±0.31), 8.20 (±0.50), and 8.73 (±0.70), respectively. The maximum possible earthquakes estimated for each individual zone are seen to be lower than that estimated for the single regime. However, the pertaining return periods estimated for the combined zone are far less than those estimated for the demarcated ones.     

Calibration of an M L scale for South Africa using tectonic earthquake data recorded by the South African National Seismograph Network: 2006 to 2009

A relation to determine local magnitude (M _L) based on the original Richter definition is empirically derived from synthetic Wood–Anderson seismograms recorded by the South African National Seismograph Network. In total, 263 earthquakes in the distance range 10 to 1,000 km, representing 1,681 trace amplitudes measured in nanometers from synthesized Wood–Anderson records on the vertical channel were considered to derive an attenuation relation appropriate for South Africa through multiple regression analysis. Additionally, station corrections were determined for 26 stations during the regression analysis resulting in values ranging between ?0.31 and 0.50. The most appropriate M _L scale for South Africa from this study satisfies the equation: $$ {M_{{{\bf L}}}} = {\text{lo}}{{\text{g}}_{{10}}}(A) + 1.149\;{\text{lo}}{{\text{g}}_{{10}}}(R) + 0.00063R + 2.04 - S $$ The anelastic attenuation term derived from this study indicates that ground motion attenuation is significantly different from Southern California but comparable with stable continental regions.     

Source parameters for the 2013–2015 earthquake sequence in Nógrád county,Hungary

Between 2013 June and 2015 January, 35 earthquakes with local magnitude M _L ranging from 1.1 to 4.2 occurred in Nógrád county, Hungary. This earthquake sequence represents above average seismic activity in the region and is the first one that was recorded by a significant number of three-component digital seismographs in the county. Using a Bayesian multiple-event location algorithm, we have estimated the hypocenters of 30 earthquakes with M _L ≥1.5. The events occurred in two small regions of a few squared kilometers: one to the east of Érsekvadkert and the other at Iliny. The uncertainty of the epicenters is about 1.5–1.7 km in the E-W direction and 1.8–2.1 km in the N-S direction at the 95 % confidence level. The estimated event depths are confined to the upper 3 km of the crust. We have successfully estimated the full moment tensors of 4 M _w ≥3.6 earthquakes using a probabilistic waveform inversion procedure. The non-double-couple components of the retrieved moment tensor solutions are statistically insignificant. The negligible amount of the isotropic component implies the tectonic nature of the investigated events. All of the analyzed earthquakes have strike-slip mechanism with either right-lateral slip on an approximately N-S striking or left-lateral movement on a roughly E-W striking nodal plane. The orientations of the obtained focal mechanisms are in good agreement with the main stress pattern published for the epicentral region. Both the P and T principal axes are horizontal, and the P axis is oriented along a NE-SW direction.     

Determination of source duration and moment of earthquakes in the Indian Peninsula using love waveforms

Love waves recorded by a long-period seismograph at New Delhi (NDI) from seven earthquakes of magnitude 4.3 to 5.2 in Koyna and Bhatsa on the western coast and one earthquake in Ongole on the eastern coast of the Indian Peninsula have been used to determine the seismic moment for each of the earthquakes by waveform modeling. Transverse component of the synthetic seismogram shows that the maximum amplitude of waveform decreases with an increase of source duration. Thus for an evaluation of the seismic moment by equating the amplitude level of the observed and synthetic waveforms, we must know the source duration. The synthetic seismogram also indicates that a short source duration gives rise to a small but sharp pulse and this pulse is interpreted as anLg wave. Comparison of the observed and synthetic waveforms has been used for a simultaneous evaluation of the source duration and seismic moment. The source durations are found to vary between 2.2 and 4.4 s; for earthquakes with a magnitude range between 4.3 and 5.2 these durations are slightly higher than normal. We obtain moment (M ₀) of Ongole earthquake (M _L =5.1)as 1.7×10²⁴ dyne-cm; moments of Koyna and Bhatsa earthquakes (4.3M _L 5.2) on the western coast lie between 0.7×10²³ and 3.6×10²³ dyne-cm. Moment (M ₀)-magnitude (M _L ) relation logM ₀=1.5M _L +16.0 for the western United States region agrees as well, in general, with the results for the earthquakes in the Indian Peninsula.     

Moment Magnitude and Its Calculation

In this paper, we give a brief introduction to the proposal and development history of the earthquake magnitude concept. Moment magnitude M_W is the best physical quantity for measuring earthquakes. Compared with other magnitude scales used traditionally, moment magnitude is not saturated for all earthquakes, regardless of big and small earthquakes, deep and shallow earthquakes, far field and near field seismic data, geodetic and geological data, moment magnitude can be measured, and can be connected with well-known magnitude scales such as surface wave magnitude M_S. Moment magnitude is a uniform magnitude scale, which is suitable for statistics with wide magnitude range. Moment magnitude is the preferred magnitude selected by the International Seismological community, and it is preferred by the departments responsible for publishing seismic information to the public.Moment magnitude is a uniform magnitude scale, which is suitable for statistics with wide magnitude range. Moment magnitude is a preferred magnitude for international seismology, it is preferred by the agency responsible for providing information about earthquakes to the public. We provide all formulas used in the calculation of moment magnitude, and the calculation steps in detail. We also analyzed some problems and rules to solve these problems by using different formulas and numerical value calculation steps.     

Magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> in metropolitan France

The recent seismicity catalogue of metropolitan France Sismicité Instrumentale de l’Hexagone (SI-Hex) covers the period 1962–2009. It is the outcome of a multipartner project conducted between 2010 and 2013. In this catalogue, moment magnitudes (M _w) are mainly determined from short-period velocimetric records, the same records as those used by the Laboratoire de Détection Géophysique (LDG) for issuing local magnitudes (M _L) since 1962. Two distinct procedures are used, whether M _L-LDG is larger or smaller than 4. For M _L-LDG >4, M _w is computed by fitting the coda-wave amplitude on the raw records. Station corrections and regional properties of coda-wave attenuation are taken into account in the computations. For M _L-LDG ≤4, M _w is converted from M _L-LDG through linear regression rules. In the smallest magnitude range M _L-LDG <3.1, special attention is paid to the non-unity slope of the relation between the local magnitudes and M _w. All M _w determined during the SI-Hex project is calibrated according to reference M _w of recent events. As for some small events, no M _L-LDG has been determined; local magnitudes issued by other French networks or LDG duration magnitude (M _D) are first converted into M _L-LDG before applying the conversion rules. This paper shows how the different sources of information and the different magnitude ranges are combined in order to determine an unbiased set of M _w for the whole 38,027 events of the catalogue.     

Updated earthquake catalogue for seismic hazard analysis in Pakistan

A reliable and homogenized earthquake catalogue is essential for seismic hazard assessment in any area. This article describes the compilation and processing of an updated earthquake catalogue for Pakistan. The earthquake catalogue compiled in this study for the region (quadrangle bounded by the geographical limits 40–83° N and 20–40° E) includes 36,563 earthquake events, which are reported as 4.0–8.3 moment magnitude (M_W) and span from 25 AD to 2016. Relationships are developed between the moment magnitude and body, and surface wave magnitude scales to unify the catalogue in terms of magnitude M_W. The catalogue includes earthquakes from Pakistan and neighbouring countries to minimize the effects of geopolitical boundaries in seismic hazard assessment studies. Earthquakes reported by local and international agencies as well as individual catalogues are included. The proposed catalogue is further used to obtain magnitude of completeness after removal of dependent events by using four different algorithms. Finally, seismicity parameters of the seismic sources are reported, and recommendations are made for seismic hazard assessment studies in Pakistan.     

Spatial relation between source regions of strong earthquakes (M ≥ 7) on Southern Kamchatka and the distribution of velocities and elastic moduli in the Benioff zone

The presence of a phenomenological relationship between high velocity regions in the Benioff zone and sources of relatively strong earthquakes (M ≥ 6) was established for the first time from the comparison of such earthquakes with the velocity structure of central Kamchatka in the early 1970s. It was found that, in the region with P wave velocities of 8.1–8.5 km/s, the number of M ≥ 6 earthquakes over 1926–1965 was 2.5 times greater than their number in the region with velocities of 7.5–8.0 km/s. Later (in 1979), within the southern Kurile area, Sakhalin seismologists established that regions with V _P = 7.3–7.7 km/s are associated with source zones of M = 7.0–7.6 earthquakes and regions with V _P = 8.1–8.4 km/s are associated with M = 7.9–8.4 earthquakes. In light of these facts, we compared the positions of M = 7.0–7.4 earthquake sources in the Benioff zone of southern Kamchatka over the period 1907–1993 with the distribution of regions of high P velocities (8.0–8.5 to 8.5–9.0 km/s) derived from the interpretation of arrival time residuals at the Shipunskii station from numerous weak earthquakes in this zone (more than 2200 events of M = 2.3–4.9) over the period 1983–1995. This comparison is possible only in the case of long-term stability of the velocity field within the Benioff zone. This stability is confirmed by the relationship between velocity parameters and tectonics in the southern part of the Kurile arc, where island blocks are confined to high velocity regions in the Benioff zone and the straits between islands are confined to low velocity regions. The sources of southern Kamchatka earthquakes with M = 7.0–7.4, which are not the strongest events, are located predominantly within high velocity regions and at their boundaries with low velocity regions; i.e., the tendency previously established for the strongest earthquakes of the southern Kuriles and central Kamchatka is confirmed. However, to demonstrate more definitely their association with regions of high P wave velocities, a larger statistics of such earthquakes is required. On the basis of a direct correlation between P wave velocities and densities, the distributions of density, bulk modulus K, and shear modulus μ in the upper mantle of the Benioff zone of southern Kamchatka are obtained for the first time. Estimated densities vary from 3.6–3.9 g/cm³ in regions of high V _P values to 3.0–3.2 g/cm³ for regions of low V _P values. The bulk modulus K in the same velocity regions varies from (1.4–1.8) × 10¹² to (0.8–1.1) × 10¹² dyn/cm², respectively, and the shear modulus μ varies from (0.8–1.0) × 10¹² to (0.5–0.7) × 10¹² dyn/cm², respectively. Examination of the spatial correlation of the source areas of southern Kamchatka M = 7.0–7.4 earthquakes with the distribution of elastic moduli in the Benioff zone failed to reveal any relationship between their magnitudes and the moduli because of the insufficient statistics of the earthquakes used.     

Relative seismic moment tensor determination for Vrancea intermediate depth earthquakes

The method of relative seismic moment tensor determination proposed byStrelitz (1980) is extended a) from an interactive time domain analysis to an automated frequency domain procedure, and b) from an analysis of subevents of complex deep-focus earthquakes to the study of individual source mechanism of small events recorded at few stations.The method was applied to the recovery of seismic moment tensor components of 95 intermediate depth earthquakes withM _L=2.6–4.9 from the Vrancea region, Romania. The main feature of the obtained fault plane solutions is the horizontality ofP axes and the nonhorizontal orienaation ofT axes (inverse faulting). Those events with high fracture energy per unit area of the fault can be grouped unambiguously into three depth intervals: 102–106 km, 124–135 km and 141–152 km. Moreover, their fault plane solutions are similar to ones of all strong and most moderate events from this region and the last two damaging earthquakes (November 10, 1940 withM _W=7.8 and March 4 1977 withM _W=7.5) occurred within the third and first depth interval, respectively. This suggests a possible correlation at these depths between fresh fracture of rocks and the occurrence of strong earthquakes.