Magnitude–intensity and intensity–attenuation relationships for atlas region and Algerian earthquakes

This paper presents the results of an investigation of the magnitude–intensity and intensity–attenuation relationships for earthquakes in the Atlas block and Algeria using macroseismic data. This work is based on a selected sample of isoseismal maps from 32 events which were recently revised. Surface-wave magnitudes, M_s, are recalculated using the Prague formula and range from 4·2 to 7·45. Because the Atlas mountains block is in a collision zone, earthquakes occur in general within a layer 15 km deep. Expressions of general form for the magnitude–intensity and intensity–attenuation correlations are adopted and are, respectively, and where R² = d² + h², d the source distance in km, h the focal depth in km, M_s the revised surface-wave magnitude, M_sc the predicted surface-wave magnitude, I_i the intensity at isoseismal i, I the predicted intensity, σ the standard deviation and P is zero for 50-percentile values and one for 84-percentile, and the coefficients A's and B's are determined by regression analysis. The results of this study show that the intensity–attenuation models are adequate to predict quite well the die-out of intensity with distance in the Atlas zone and coastal Algeria; it is also found that magnitude can be predicted accurately by calibrating isoseismal radii against revised instrumental surface-wave magnitude. Such magnitude–intensity relationships may be used to evaluate the magnitude of historical earthquakes in the region under survey, with no instrumental data, for which isoseismal radii and intensities are available.     

Revision of magnitudes of large shallow earthquakes, 1897–1912

In previous research, trace amplitudes of surface wave maxima recorded by undamped Milne seismographs were used to determine the surface-wave magnitudes M_s of large shallow earthquakes which occurred prior to 1912. For this purpose, the effective gain of these instruments was calibrated by using the surface-wave magnitudes M_s(GR) which were calculated from the unpublished worksheets for Seismicity of the Earth of Gutenberg and Richter. In this paper, the real quality of M_s(GR) is critically re-evaluated by using independent sets of data. It is found that M_s(GR) for the period 1904–1909 is considerably overestimated. The average excess from the real M_s is 0.5 units for 1904–1906, 0.4 for 1907, 0.3 for 1908–1909 and 0.0 for 1910–1912. This overestimation is so systematic and large that the previous results are all redetermined. The average effective gain of Milne instruments is revised to be 21.9; previously, the gain depended on M_s. This revision results in systematic reduction in the previously assigned magnitudes. The revised values of M_s for 264 shallow earthquakes, with M_s=6.8 and over in the period 1897–1912 inclusive, are listed. The present revision is large enough to preclude the possibility of the high activity of large shallow earthquakes around the turn of the century. The present results have a direct effect on all the magnitude catalogues of shallow earthquakes which occurred prior to 1909.     

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.     

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.     

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.     

Homogenization of Earthquake Catalog for Northeast India and Adjoining Region

A catalog for northeast India and the adjoining region for the period 1897–2009 with 4,497 earthquakes events is compiled for homogenization to moment magnitude M _w,GCMT in the magnitude range 3–8.7. Relations for conversion of m _b and M _s magnitudes to M _w,GCMT are derived using three different methods, namely, linear standard regression, inverted standard regression (ISR) and orthogonal standard regression (OSR), for different magnitude ranges based on events data for the catalog period 1976–2006. The OSR relations for M _s to M _w,GCMT conversion derived in this paper have significantly lower errors in regression parameters compared to the relations reported in other studies. Since the number of events with magnitude ≥7 for this region is scanty, we, therefore, considered whole India region to obtain the regression relationships between M _w,GCMT and M _s,ISC. A relationship between M _w,GCMT and M _w,NEIC is also obtained based on 17 events for the range 5.2 ≤ magnitude ≤ 6.6. A unified homogeneous catalog prepared using the conversion relations derived in this paper can serve as a reference catalog for seismic hazard assessment studies in northeast India and the adjoining region.     

Probabilistic Seismic Hazard Assessment for Iraq Using Complete Earthquake Catalogue Files

Probabilistic seismic hazard analysis (PSHA) has been carried out for Iraq. The earthquake catalogue used in the present study covers an area between latitude 29°–38.5° N and longitude 39°–50° E containing more than a thousand events for the period 1905–2000. The entire Iraq region has been divided into thirteen seismogenic sources based on their seismic characteristics, geological setting and tectonic framework. The completeness of the seismicity catalogue has been checked using the method proposed by Stepp (1972). The analysis of completeness shows that the earthquake catalogue is not complete below M_s=4.8 for all of Iraq and seismic source zones S1, S4, S5, and S8, while it varies for the other seismic zones. A statistical treatment of completeness of the data file was carried out in each of the magnitude classes. The Frequency Magnitude Distributions (FMD) for the study area including all seismic source zones were established and the minimum magnitude of complete reporting (M_c) were then estimated. For the entire Iraq the M_c was estimated to be about M_s=4.0 while S11 shows the lowest M_c to be about M_s=3.5 and the highest M_c of about M_s=4.2 was observed for S4. The earthquake activity parameters (activity rate , b value, maximum regional magnitude m_max) as well as the mean return period (R) with a certain lower magnitude m_min m along with their probability of occurrence have been determined for all thirteen seismic source zones of Iraq. The maximum regional magnitude m_max was estimated as 7.87 ± 0.86 for entire Iraq. The return period for magnitude 6.0 is largest for source zone S3 which is estimated to be 705 years while the smallest value is estimated as 9.9 years for all of Iraq.The large variation of the b parameter and the hazard level from zone to zone reflects crustal heterogeneity and the high seismotectonic complexity. The seismic hazard near the source boundaries is directly and strongly affected by the change in the delineation of these boundaries. The forces, through which the geological structure along the plate boundary in Eastern and Northeastern Iraq are evolved, are still active causing stress-strain accumulation, deformation and in turn producing higher probabilities of earthquake activity. Thus, relatively large destructive earthquakes are expected in this region. The study is intended to serve as a reference for more advanced approaches and to pave the path for the probabilistic assessment of seismic hazard in this region.     

Theoretical and Observed Depth Correction for M s

—?Modal summation technique is used to generate 5000, three-component theoretical seismograms of Love and Rayleigh waves, assuming modified PREM (PREM-C) and AK135F global earth models. The focal depth h and the geometrical fault parameters are randomly chosen so as to uniformly cover possible source mechanisms and obtain uniform distribution of log h in the interval 1?h?h?M _s of the form:¶ΔM _s (h)=0 forh< 20km, ΔM _s (h)=0.314log(h)-0.409 for 20≠h< 60km, ΔM _s (h)=1.351log(h)-2.253 for 60≠h< 100km, ΔM _s (h)=0.400log(h)-0.350 for 100≠h< 600km .¶After applying the above correction, the relationship between the surface wave magnitude and the scalar seismic moment for the observational data set significantly improves, and becomes independent of the source depth. In relation to CTBT, no depth correction is needed for M _S when the m _b ???M _S discriminant is computed, because the proposed correction is zero for earthquakes with foci above 20?km.     

Spectral magnitude and seismic radiated energy computed from CDSN records

We have employed 10 digital records and computed the spectral magnitude and the seismic radiated energy for 18 large earthquakes (M _s≥6) occurred in Eur-asian belt during 1986–1989. The nine digital stations (CD-SN) distribute all over China and one in Germany. The spectral magnitudes of various period have different stability among stations. The stability is better for maximum spectral magnitudemi and seismic radiated energyE, their differences among stations are smaller, especially for the stations where the ray path main penetrates the low mantle. But the stability of corner period is usually not good. The relation between seismic radiated energy and seismic moment magnitudeM _w is lg (E)=1.5Mw+c, wherec is a constant. The maximum spectral magnitudemi=M _w+0.1, it is consistant with theoretical prediction. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 418–426, 1993. This work supported by the Deutsche Forschungsgemeinschaft, Bonn, F. R. Germany. The support is grateful acknowledge.     

CalculationoflongperiodresponsespectratoearthquakegroundmotionfromseismogramsofType513seismographs

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Regional coda magnitudes of underground nuclear explosions

The concept of determining magnitudes, M_τ, of regional events (Δ < 1000 km) by means of coda-duration measurements is re-examined by using short-period vertical-component seismograms from Nevada Test Site explosions. The duration is specified as the time interval between the expected arrival of the S-wave and the time when coda waves fall and stay below 80 μm peak-to-peak ground displacement. The suggested procedure requires that for M_τ = 4.0 the coda duration at a distance of 100 km is 120 s. The adaptivity of the method is examined in terms of the single-station magnitude scatter, and with respect to the potential accuracy of the yield estimation of the explosions.The derived magnitude formula for underground nuclear explosions in granite is of the form: M_τ =0.18+0.001Δ+1.79 log τ+C_s, where C_s is a station correction coefficient for non-WWNSS stations.     

M L Determination for Local and Regional Events Using a Sparse Network in Southwestern Germany

A method for the determination of consistent local magnitude M _L values (Richter scale, or M _WA) for earthquakes with epicentral distances ranging from 10 km through 1000 km is demonstrated. The raw data consists of nearly 1300 amplitude readings from a network of six digital seismographs in Baden–Württemberg (Southwestern Germany) during 26 months starting in 1995, later extended by another 1000 amplitude readings until 1999. Relying on most of the basics introduced by C.F. Richter a three-parameter attenuation curve (distance correction, magnitude-distance relation) for Baden–Württemberg and adjacent areas is presented. Station corrections are evaluated and the attenuation curve is calibrated with respect to other agencies for distances greater than 650 km. Reasonable parametrisations are discussed and meaningful error bars are attributed. Finally, a seventh station is incorporated by means of its station correction alone, without needing to update the attenuation curve.     

Study of calibration function for surface wave magnitude of DK1 seismographs

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Determining the time and space domains for estimating b value in seismic zoning

To take the seismic zone that includes the great shock with M _s≥8.2 as the statistical unit of estimating b value can often lead to more large variance, because the seismogenic zone of the great shock with M _s≥8.2 are larger than that delineated in general seismic zone. Two-level statistical units are considered in this paper. The seismic province is the first level unit that is suitable for group of earthquakes including the great shock of M _s≥8.5. A seismic province can be divided into several seismic zones. They can be taken as the second level unit for group of quakes in which the super magnitude of the greatest shock do not exceed 8. Because of the nonstationarity in time of seismic activity, the unbalancedness of data and differential of seismic temporal series feature in different areas need to be considered when we select the time period for estimating b value. According to local conditions, the time period is selected at one’s discretion in order to reflect seismicity level of this statistical unit in future 100 years. Contribution No. 98A02039, Institute of Geophysics, China Seismological Bureau, China.     

Yield Estimation from Surface-wave Amplitudes

— Surface-wave amplitudes from explosion sources show less variation for a given event han body wave amplitudes, so it is natural to expect that yield estimates derived from surface waves will be more accurate than yield estimates derived from body waves. However, yield estimation from surface waves is complicated by the presence of tectonic strain release, which acts like one or more earthquake sources superimposed on top of the explosion. Moment-tensor inversion can be used to remove the tectonic component of the surface waves, however moment-tensor inversion for shallow sources is inherently non-unique so the explosion isotropic moment cannot be determined with the necessary accuracy by this means. Explosions on an island or near a mountain slope can exhibit anomalous surface waves similar to those caused by tectonic strain release. These complications cause yield estimates derived from surface waves to be less accurate than yield estimates from body waves recorded on a well-calibrated network with good coverage. Surface-wave amplitudes can be expressed as a surface-wave magnitude M _s , which is defined as the logarithm of the amplitude plus a distance correction, or as a path corrected spectral magnitude, log $M^{\prime}_0$ , which is derived from the surface-wave spectrum. We derive relations for M _s vs. yield and log $M^{\prime}_0$ vs. yield for a large data set and estimate the accuracy of these estimates.     

The ground motion excited by the Olyutorskii earthquake of April 20, 2006 and by its aftershocks based on digital recordings

We studied broadband digital records of the M _W = 7.6 Olyutorskii earthquake of April 20, 2006 and its aftershocks at local and regional distances. We have made a detailed analysis of data on peak ground motion velocities and accelerations due to aftershocks based on records of two digital seismic stations, Tilichiki (TLC) and Kamenskoe (KAM). The first step in this analysis was to find the station correction for soil effects at TLC station using coda spectra. The correction was applied to the data to convert them to the reference bedrock beneath the Kamenskoe station. The second step involved multiple linear regression to derive average relationshis of peak amplitude to local magnitude M_L and distance R for the Koryak Upland conditions. The data scatter about the average relationshis is comparatively low (0.22–0.25 log units). The acceleration amplitudes for M _L = 5, R = 25 km are lower by factors of 2–3 compared with those for eastern Kamchatka, the western US, or Japan. A likely cause of this anomaly could be lower stress drops for the aftershocks.     

Magnitudes of large shallow earthquakes from 1904 to 1980

In order to obtain a uniform magnitude catalogue, surface-wave magnitudes M_s and broad-band body-wave magnitudes m_B have been determined for large shallow earthquakes from 1904 to 1980. In making the catalogue homogeneous, the author consistently adheres to the original definitions of M_s and m_B given by Gutenberg (1945) and Gutenberg and Richter (1956). The determinations of M_s and m_B are all based on the amplitude and period data listed in Gutenberg and Richter's unpublished notes, bulletins from stations worldwide, and other basic information. m_B is measured on broad-band instruments in periods of ～8 s. Consistency of the magnitude determinations from these different sources is carefully checked in detail. More than 900 shallow shocks of magnitude 7 and over are catalogued. The meaning of the magnitude scales in various catalogues is examined in terms of M_s and m_B. Most of the magnitudes listed by Gutenberg and Richter (1954) in their “Seismicity of the Earth” are basically M_s for large shocks shallower than 40 km, but are basically m_B for large shocks at depths of 40–60 km. The surface-wave magnitudes given by “Earthquake Data Reports” are higher than M_s by 0.2 unit whether the combined horizontal amplitude or the vertical amplitude is used. m_B and the currently used 1 s body-wave magnitude are measured at different periods and should not be directly compared.     

Sources of Error and the Statistical Formulation of M S: m b Seismic Event Screening Analysis

The Comprehensive Nuclear-Test-Ban Treaty (CTBT), a global ban on nuclear explosions, is currently in a ratification phase. Under the CTBT, an International Monitoring System (IMS) of seismic, hydroacoustic, infrasonic and radionuclide sensors is operational, and the data from the IMS is analysed by the International Data Centre (IDC). The IDC provides CTBT signatories basic seismic event parameters and a screening analysis indicating whether an event exhibits explosion characteristics (for example, shallow depth). An important component of the screening analysis is a statistical test of the null hypothesis H ₀: explosion characteristics using empirical measurements of seismic energy (magnitudes). The established magnitude used for event size is the body-wave magnitude (denoted m _b) computed from the initial segment of a seismic waveform. IDC screening analysis is applied to events with m _b greater than 3.5. The Rayleigh wave magnitude (denoted M _S) is a measure of later arriving surface wave energy. Magnitudes are measurements of seismic energy that include adjustments (physical correction model) for path and distance effects between event and station. Relative to m _b, earthquakes generally have a larger M _S magnitude than explosions. This article proposes a hypothesis test (screening analysis) using M _S and m _b that expressly accounts for physical correction model inadequacy in the standard error of the test statistic. With this hypothesis test formulation, the 2009 Democratic Peoples Republic of Korea announced nuclear weapon test fails to reject the null hypothesis H ₀: explosion characteristics.     

Magnitude scale for the Central American tsunamis

Based on the tsunami data in the Central American region, the regional characteristic of tsunami magnitude scales is discussed in relation to earthquake magnitudes during the period from 1900 to 1993. Tsunami magnitudes on the Imamura-Iida scale of the 1985 Mexico and 1992 Nicaragua tsunamis are determined to bem=2.5, judging from the tsunami height-distance diagram. The magnitude values of the Central American tsunamis are relatively small compared to earthquakes with similar size in other regions. However, there are a few large tsunamis generated by low-frequency earthquakes such as the 1992 Nicaragua earthquake. Inundation heights of these unusual tsunamis are about 10 times higher than those of normal tsunamis for the same earthquake magnitude (M _s =6.9–7.2). The Central American tsunamis having magnitudem>1 have been observed by the Japanese tide stations, but the effect of directivity toward Japan is very small compared to that of the South American tsunamis.     

Use of the mantle magnitudeM m for the reassessment of the moment of historical earthquakes

The mantle magnitudeM _m is used on a dataset of more than 180 wavetrains from 44 large shallow historical earthquakes to reassess their moments, which in many cases had been previously estimated only on the basis of the earthquake's rupture area. We provide 27 new or revised values ofM _o, based on the spectral amplitudes of surface waves recorded at a number of stations, principally Uppsala and Pasadena. Among them, and most significantly, we document a large low-frequency component to the source of the 1923 Kanto earthquake: the low-frequency seismic moment is 2.9×10²⁸ dyn-cm, in accord with geodetic observations. On the other hand, we revise downwards the seismic moment of the 1906 Ecuador event, which did not exceed 6×10²⁸ dyn-cm.Finally, the study of the 1960 Chilean and 1964 Alaskan earthquakes whose exceptionally large moments are properly retrieved throughM _m measurements, serves proof that this approach performs flawlessly even for the very greatest earthquakes, and is therefore successful in its goal to avoid the saturation effects plaguing any magnitude scale measured at a fixed period.