A note on computed magnitude ML from strong motion records

It is shown that a new definition of M_L^SM (Trifunac¹⁴), which is computed from recorded strong motion earthquake accelerograms, leads to stable and unbiased estimates of the local earthquake magnitude M_L (Richter⁸) for epicentral distance R < 100 km and for 3 M_nL < 6.5. Tables of the uniform estimates using this new M_L^SM are presented for all earthquakes contributing to the current data base of free field strong motion accelerograms in EQINFOS files (Lee and Trifunac⁶).     

Calibration of Local Magnitude M<Subscript>L</Subscript> in the Azores Archipelago Based on Recent Digital Recordings

—The development of the digital seismic network in the Azores Archipelago during recent years made it possible to obtain the amplitudes (waveform) of recorded motion in a large set of stations. With this new data, maximum amplitudes of the Wood Anderson seismograph are computed, for each station/component, which, together with epicentral distances, allows for the estimation of local magnitude M _L . We used data recorded in 8 digital permanent three-component stations, with inter-stations distances up to 300 km, in the period June 1998 – June 2000, corresponding to a set of 1315 events with magnitude (M _L or M _D ) 2<M<5.8 and epicenters located in the Azores region, to estimate the coefficients of the equation to compute M _L , as well as to determine the corrections to be applied to each station. The new set of parameters, formed by attenuation coefficients and station corrections, were introduced in the calculations of the M _L , leading to smaller dispersions in the analyzed dataset. We also conclude that the attenuation in the first 150 km is similar to the California values, although higher for longer distances.     

2015年11月23日青海祁连MS5.2地震震源机制解及发震构造初步探讨

采用CAP（Cut and Paste）方法反演了2015年11月23日青海祁连M_S5.2主震的震源机制解,其最佳双力偶解：节面Ⅰ走向109°、倾角58°、滑动角21°,节面Ⅱ走向8°、倾角72°、滑动角146°,矩震级M_W5.16,矩心震源深度约为9 km。结合震区的活动构造,判定发震断层面为节面Ⅰ,推测托勒山北缘活动断裂中段为此次地震的发震断裂。     

The empirical relationships between M s, m b and M L for China and vicinity

Data from 753 earthquakes are used to determine a relationship between surface-wave magnitude (M _s) and bodywave magnitude (m _b), and from 541 earthquakes to determine a relationship between surface-wave magnitude (M _s) and local magnitude (M _L) for China and vicinity: M _s=0.9883 m _b-0.0420, M _s=0.9919 M _L-0.1773. The relationship of M _s versus m _b is obtained for 292 events occurred in the Chinese mainland in the time period from 1964 to 1996, 291 events occurred in Taiwan in the time period from 1964 to 1995 and 170 events occurred in the surrounding area. Standard deviation of the fitting is 0.445. Relationship of M _s versus M _L is obtained for 36 events occurred in the Chinese mainland, 293 events occurred in Taiwan, China and 212 events occurred in the surrounding area. The total amount is 541 events. Standard deviation of the fitting is 0.4673. The uncertainties of the converted M _s in different magnitude intervals can be estimated using complementary cumulative distribution function (CCDF). In the relationship of M _s versus m _b, taking ±0.25 as a range of uncertainties, in magnitude interval m _b 4.0–4.9, the probabilities for the converted M _s taken value less than (M _s-0.25) and more than (M _s+0.25) are 17% and 27% respectively. Similarly, we have probabilities for m _b 5.0–5.9 are 34% and 20% and that for m _b 6.0–6.9 are 11% and 47%. In the relationship of M _s versus M _L, if the range of uncertainties is still taken as ±0.25, the corresponding probabilities for magnitude interval M _L 4.0–4.9 are 22% and 38%, for M _L 5.0–5.9 are 20% and 15% and for magnitude interval M _L 6.0–6.9, are 15% and 29%, respectively. The relationships developed in this paper can be used for the conversion of one magnitude scale into another magnitude scales conveniently. The estimation of uncertainties described in this paper is more accurate and more objective than the usual estimation expressed by deviation. The estimations described in this paper indicate various dispersions in different magnitude intervals of original data. The estimations of uncertainties described by probabilities can be well connected with the total estimations of uncertainties in seismic hazard assessment.     

Lg magnitude determination for the eastern six Provinces of China (part 2)

Any pair ofm _{L gz} ,m _{L g} b,mmxz andmm x h in the eastern six provinces of China show good linear relation this makes it easy to convert from one scale to another.mm x h may replaceM _L (ECH) as the local earthquake magnitude scale for the eastern six provinces, yet retaining the level ofM _L (ECH). The scalemm x h is 0.36 magnitude units higher thanM _L (SC) for southern California. By comparingRm a x (Δ) withR ₃ (Δ) of Yunnan, it is found that the γ-value ofMAX phase of about 1 section in Yunnan region is half as large as that in the eastern six provinces of China. Observation indicates thatmm x h≈mb for magnitude 4–5. It follows therefore thatmb (ECH)≈mb (WUS). This is supported by the result that the attenuation coefficient, the γ-value in eastern China is the same as in western United States.     

The instability of the <Emphasis Type="Italic">M</Emphasis><Subscript>W</Subscript> and <Emphasis Type="Italic">M</Emphasis><Subscript>L</Subscript> comparison for earthquakes in Greece for the period 1969 to 2007

We use 576 earthquakes of magnitude, M _w, 3.3 to 6.8 that occurred within the region 33° N–42.5° N, 19° E–30° E in the time period 1969 to 2007 to investigate the stability of the relation between moment magnitude, M _w, and local magnitude, M _L, for earthquakes in Greece and the surrounding regions. We compare M _w to M _L as reported in the monthly bulletins of the National Observatory of Athens (NOA) and to M _L as reported in the bulletins of the Seismological Station of the Aristotle University of Thessaloniki. All earthquakes have been analyzed through regional or teleseismic waveform inversion, to obtain M _w, and have measured maximum trace amplitudes on the Wood–Anderson seismograph in Athens, which has been in operation since 1964. We show that the Athens Wood–Anderson seismograph performance has changed through time, affecting the computed by NOA M _L by at least 0.1 magnitude units. Specifically, since the beginning of 1996, its east–west component has been recording systematically much larger amplitudes compared to the north–south component. From the comparison between M _w and M _L reported by Thessaloniki, we also show that the performance of the sensors has changed several times through time, affecting the calculated M _L’s. We propose scaling relations to convert the M _L values reported from the two centers to M _w. The procedures followed here can be applied to other regions as well to examine the stability of magnitude calculations through time.     

Calibration of magnitude scales for earthquakes of the Mediterranean

In order to provide the tools for uniform size determination for Mediterranean earthquakes over the last 50-year period of instrumental seismology, we have regressed the magnitude determinations for 220 earthquakes of the European-Mediterranean region over the 1977–1991 period, reported by three international centres, 11 national and regional networks and 101 individual stations and observatories, using seismic moments from the Harvard CMTs. We calibrate M(M₀) regression curves for the magnitude scales commonly used for Mediterranean earthquakes (M_L, M_WA, m_b, M_S, M_LH, M_LV, M_D, M); we also calibrate static corrections or specific regressions for individual observatories and we verify the reliability of the reports of different organizations and observatories. Our analysis shows that the teleseismic magnitudes (m_b, M_S) computed by international centers (ISC, NEIC) provide good measures of earthquake size, with low standard deviations (0.17–0.23), allowing one to regress stable regional calibrations with respect to the seismic moment and to correct systematic biases such as the hypocentral depth for M_S and the radiation pattern for m_b; while m_b is commonly reputed to be an inadequate measure of earthquake size, we find that the ISC m_b is still today the most precise measure to use to regress M_W and M₀ for earthquakes of the European-Mediterranean region; few individual observatories report teleseismic magnitudes requiring specific dynamic calibrations (BJI, MOS). Regional surface-wave magnitudes (M_LV, M_LH) reported in Eastern Europe generally provide reliable measures of earthquake size, with standard deviations often in the 0.25–0.35 range; the introduction of a small (±0.1–0.2) static station correction is sometimes required. While the Richter magnitude M_L is the measure of earthquake size most commonly reported in the press whenever an earthquake strikes, we find that M_L has not been computed in the European-Mediterranean in the last 15 years; the reported local magnitudes M_WA and M_L do not conform to the Richter formula and are of poor quality and little use, with few exceptions requiring ad hoc calibrations similar to the M_S regression (EMSC, ATH). The duration magnitude M_D used by most seismic networks confirms that its use requires accurate station calibrations and should be restricted only to events with low seismic moments.     

Attenuation,source parameters and site effects in the Irpinia–Basilicata region (southern Apennines,Italy)

We derive S-wave attenuation characteristics, earthquake source parameters and site amplification functions at seismic stations used for earthquake early warning in the Irpinia–Basilicata region, using non-parametric spectral inversion of seismograms from 49 local events with M _L = 1.5–3.1. We obtain relatively low Q values (Q ₀ = 28 at a frequency of 1 Hz) in conjunction with a strong frequency-dependence (close to linear). The source spectra can be satisfactorily modeled using the omega-square model, with stress drops ranging between 0.01–2 MPa, and in the narrow magnitude range available for analysis, the source spectra seem to scale self-similarly. The local magnitude M _L shows a linear correlation with moment magnitude M _W, however with a systematic underestimation by about 0.5-magnitude units. The results obtained in this work provide important insights into the ground-motion characteristics that are required for appropriate seismic hazard assessment and are of practical relevance for a suite of applications, such as the calibration of ground-motion prediction equations or the correction for site amplification in earthquake early warning and rapid calculation of shake-maps for seismic emergency management.     

Q and high-frequency strong motion spectra

Empirical scaling equations for Fourier amplitude spectra of strong ground motion are used to describe A₀ and τ in the assumed (high-frequency) shape of strong motion amplitudes: FS(_φ) = A₀e-^πτφ. The res of computed A₀ and τ with other related estimates of spectral amplitudes; (2) smooth decay of strong motion spectral amplitudes up to φ = 25 Hz, without an abrupt low-pass filtering of high frequecies; and (3) good agreement with other estimates of the regionally specific attenuation of high-frequncy seismic waves.As the recorded strong earthquake shaking in the western United States typically samples only the shallow (10 km) and local (100km) characteristics of wave attenuation, the processed strong motion accelerograms can be used as the most direct means of describing the nature of the high-frequency attenuation of the entire strong motion signal for use in earthquake engineering applications. Seismological body wave, Lg and coda wave estimates of Q sample different volumes of the crust surrounding the station, and involve different paths of the waves. These differences must be carefully documented and understood before the results can be used in earthquake engineering characterization of strong motion amplitudes.     

Empirical model for estimating Fourier amplitude spectra of ground acceleration in Taiwan region

A collection of ground‐motion recordings (1070 acceleration records) of moderate (5.1⩽M_L⩽6.5) earthquakes obtained during the execution of the Taiwan Strong Motion Instrumentation Program (TSMIP) since 1991 was used to study source scaling model and attenuation relations for a wide range of earthquake magnitudes and distances and to verify the models developed recently for the Taiwan region. The results of the analysis reveal that the acceleration spectra of the most significant part of the records, starting from S‐wave arrival, can be modelled accurately using the Brune's ω‐squared source model with magnitude‐dependent stress parameter Δσ, that should be determined using the recently proposed regional relationships between magnitude (M_L) and seismic moment (M₀) and between M₀ and Δσ. The anelastic attenuation Q of spectral amplitudes with distance may be described as Q=225 ƒ^1.1 both for deep (depth more than 35 km) and shallow earthquakes. The source scaling and attenuation models allow a satisfactory prediction of the peak ground acceleration for magnitudes 5.1⩽M⩽6.5 and distances up to about 200 km in the Taiwan region, and may be useful for seismic hazard assessment. Copyright © 2000 John Wiley & Sons, Ltd.     

A local-magnitude scale for Mt. Vesuvius from synthetic Wood-Anderson seismograms

The Local-Magnitude scale actually in use at Vesuvius Observatory is basedon the measure of seismogram coda duration, and calibrated with data fromIrpinia aftershocks. A recent study on local seismic attenuation at Mt.Vesuvius reveals coda shapes highly different from those from Irpiniaaftershocks, and a very low quality factor, if compared to the average Qof the region, indicating the necessity of the revision of the Magnitudescale, in order to better compare the seismic energy associated to the localseismicity of Mt. Vesuvius to that of other active volcanoes. Being theseismic attenuation parameters known in the area, we could correct theseismic amplitudes for the path effect to obtain precise estimates of theamplitude level of the displacement spectrum. Hence we estimated theMoment-Magnitude, M _W, for a set of well recorded micro-earthquakes.To use the Richter formulaM _L =log₁₀ A _max –log A₀(R)we estimated the log Amplitude-Distance correction curve, - log A₀(R),numerically synthesizing an S-wave-packet and letting it propagate in aearth medium with the same attenuation properties of those measured at Mt.Vesuvius. Then we synthesized the Wood-Anderson equivalent seismogram forthe same data set and used the distance correction in order to calculate theWood-Anderson Magnitude.This Magnitude scale was normalized in order to fit the Richter formulavalid for Southern California at a distance of 10 km, and resultsto be M _WA =log A + 1.34log(R) –1.10. The comparison of the Wood-Anderson scale with the Duration-Magnitude scalein routine use at Vesuvius Observatory indicates that care must be takenwhen the estimate of the Duration-Magnitude is carried out for smallearthquakes recorded at a site characterized by a high level of seismicnoise.     

High frequency fall-off of source spectra using Q -free spectra estimation

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传统与现代震级标度

首先阐述并比较传统震级(M_L、m_b、m_B、M_S及M_JMA)所用数据、计算方法及适用范围,系统梳理两种现代震级标度M_e和M_W的理论基础及计算方法。然后根据使用数据及适用场景不同,介绍M_WW、M_WC、M_Wb、M_wp及M_dt等矩震级测定方法;同时,随着越来越丰富的GPS观测数据,基于高频GPS观测也越来越多地被用于地震震级快速测定工作。最后对这些震级测定方法的时效性进行对比分析,讨论不同震级标度的适用场景及其稳定性。     

Macroseismic estimates of magnitude in Italy

A multi-parametric study of empirical relationships between macroseismic data and magnitude is presented for the Italian region by the analysis of a new extended data set concerning 146 earthquakes. The available magnitude determinations include all of the most intense earthquakes which occurred in Italy in the last century and have been obtained by an accurate revision of original instrumental data. Intensity data have been revised and upgraded on the basis of the most recent studies: only local intensities directly documented have been used. Macroseismic determinations ofM _s ,m _B andM _wa magnitudes have been performed. The empirical relationships between maximum felt intensity (I _max ) and magnitude have been determined by the use of a distribution-free approach and a linear regression analysis. This last parameterization allows for the explanation of more than 60% of the variation in magnitude. In order to improve these results, the linear dependence between magnitude,I _max and average distances (in logarithm) corresponding to fixed attenuation values has been explored. The comparison between instrumental magnitudes and corresponding macroseismic estimates obtained from empirical relationships shows that the respective uncertainties are comparable.     

Comparison between different earthquake magnitudes determined by China Seismograph Network

By linear regression and orthogonal regression methods, comparisons are made between different magnitudes (lo-cal magnitude ML, surface wave magnitudes MS and MS7, long-period body wave magnitude mB and short-period body wave magnitude mb) determined by Institute of Geophysics, China Earthquake Administration, on the basis of observation data collected by China Seismograph Network between 1983 and 2004. Empirical relations between different magnitudes have been obtained. The result shows that: 1 As different magnitude scales reflect radiated energy by seismic waves within different periods, earthquake magnitudes can be described more objectively by using different scales for earthquakes of different magnitudes. When the epicentral distance is less than 1 000 km, local magnitude ML can be a preferable scale; In case M<4.5, there is little difference between the magnitude scales; In case 4.5MS, i.e., MS underestimates magnitudes of such events, therefore, mB can be a better choice; In case M>6.0, MS>mB>mb, both mB and mb underestimate the magnitudes, so MS is a preferable scale for deter-mining magnitudes of such events (6.08.5, a saturation phenomenon appears in MS, which cannot give an accurate reflection of the magnitudes of such large events; 2 In China, when the epicentral distance is less than 1 000 km, there is almost no difference between ML and MS, and thus there is no need to convert be-tween the two magnitudes in practice; 3 Although MS and MS7 are both surface wave magnitudes, MS is in general greater than MS7 by 0.2~0.3 magnitude, because different instruments and calculation formulae are used; 4 mB is almost equal to mb for earthquakes around mB4.0, but mB is larger than mb for those of mB≥4.5, because the periods of seismic waves used for measuring mB and mb are different though the calculation formulae are the same.     

Spectral parameters of ground motion in different regions: comparison of empirical models

Fourier-amplitude spectrum is one of the most important parameters describing earthquake ground motion, and it is widely used for strong ground motion prediction and seismic hazard estimation. The relationships between Fourier-acceleration spectra, earthquake magnitude and distance were analysed for different seismic regions (the Caucasus and Taiwan island) on the basis of ground motion recordings of small to moderate (3.5≤M_L≤6.5) earthquakes. It has been found that the acceleration spectra of the most significant part of the records, starting from S-wave arrival, can be modelled accurately by the Brune's “ω-squared” point-source model. Parameters of the model are found to be region-dependent. Peak ground accelerations and response spectra for condition of rock sites were calculated using stochastic simulation technique and obtained models of source spectra. The modelled ground-motion parameters are compared with those predicted by recent empirical attenuation relationship for California.     

The October 4th, 1983 — Magnitude 4 earthquake in Phlegraean Fields: Macroseismic survey

On Oct. 4th, 1983 the area of Phlegraean Fields, near Naples (Southern Italy) was shaked by an earthquake of magnitude (M _L) 4.0 that caused some damage in the town of Pozzuoli and its surroundings. This seismic event was the largest one recorded during the recent (1982–84) inflation episode occurred in the Phlegraean volcanic area, and a detailed macroseismic reconstruction of the event was carried out.Failing macroseismic data on other earthquakes occurred in Phlegraean Fields, the attenuation law of the intensity as a function of the distance as obtained for the Oct. 4th earthquake was compared with those obtained for other volcanic areas in central Italy —i.e., Tolfa, Monte Amiata — in order to check the reliability of the results obtained for Phlegraean Fields.The Blake's model of the earthquake of Oct. 4th, 1983 does not agree with the experimental data because isoseismals contain areas larger than those shown by the model. This result has been interpreted as an effect of energy focusing due to a reflecting layer 6–8 km deep.     

Relationship of ML and magnitudes determined by regional seismological stations in South-Eastern and Central Europe

We show how by comparing M_L^SM (computed from strong motion accelerograms within 150 km from the epicenter) and M_STA (reported by different seismological stations in Yugoslavia, Italy, Albania, Greece, Austria and Czechoslovakia) it is possible to calibrate amplitude-distance attentuation equations used in M_STA definitions. This, more accurate, magnitude determination for regional networks is essential for: (1) better and more accurate integration of the engineering estimates of siesmic risk; and (2) for more accurate and quick estimation of strong motion amplitudes in epicentral region of destructive earthquakes.     

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.     

Regional characteristics of coda attenuation after the lancang-Gengma earthquake

In the light of the single scattering model of coda originating from local earthquakes, and based on the aftershock coda registered respectively at the 4 short period stations installed near the foci shortly after theM7.6 Lancang andM7.2 Gengma earthquakes, this paper has tentatively calculated the rate of amplitude attenuation and theQ _c-value of the coda in the Lancang and Gengma areas using a newly-founded synthetic determination method. Result of the study shows the rate of coda amplitude attenuation demonstrates remarkable regional differences respectively in the southern and northern areas. The southern area presents a faster attenuation (Q _c=114), whereas the northern area shows a slower attenuation (Q _c=231). The paper also discusses the reasons causing such differences. Result of the study also suggests a fairly good linear relation between the coda source factorA _o(f) and the seismic moment and the magnitude. Using the earthquake scaling law, the following formulas can be derived: lgM ₀=lgA ₀(f)+17.6,M _D=0.67lgA ₀(f)+1.21 and logM ₀=1.5M _D+15.79. In addition, the rates of amplitude attenuationβ _s andβ _m are respectively calculated using the single scattering and multiple scattering models, and the ratioβ _s/β_m=1.20−1.50 is found for the results respectively from the two models. Finally, the mean free pathL of the S-wave scattering in the southern and northern areas are determined to be 54 km and 122 km respectively by the relations which can distinguish between the inherentQ _i and scatteringQ _s, testify to this areas having lowQ-values correspond to stronger scatterings. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 71–82, 1992. This study is partly supported by the Seismological Science Foundation of the State Seismological Bureau of China, and the present English version of the paper is translated from its Chinese original by Wenyi Xia, Seismological Bureau of Yunnan Province.