Using 48016 synthetic maximum Wood-Anderson amplitudes read from waveforms of 2650 events recorded by stations of Iranian Seismological Center (IRSC, irsc. ut. ac. ir), Iranian National Seismograph Network (INSN, www. iiees. ac. ir) and temporary seismic networks belong to Institute for Advanced Studies in Basic Sciences (IASBS, iasbs. ac. ir), the empirical attenuation curve ( 0  log A ) for local Magnitude of Iran has been calculated as follows: 0 log (1. 556 0. 06) log (0. 001637 0. 0009) ( 100) 3 100 R A R              where R is hypocentral distance in km and 0 A is maximum displacement amplitude of shear wave in millimeter. The empirical attenuation relationship is valid for hypocentral distances equal or smaller than 800 km. ML amplitude is the maximum amplitude observed on a Wood-Anderson (W-A) seismogram. We manually picked the maximum amplitudes on the shear window of synthetic W-A seismograms having S/N of larger than 5. We calculated synthetic W-A seismograms by removing the instrument response of each record and convolving the resulting signal with the response of the standard W-A torsion seismograph. We assumed a static magnification of 2080 for the W-A instrument. The selected ML amplitudes are belonging to events at hypocentral distance of 10 to 800 km. Except for the Makran and South Caspian Basin regions, the ray coverage of the ML amplitude covers properly the whole Iranian Plateau. To reduce the scatter of Magnitude residues and ensure a reliable calculation of the attenuation curve, the selected events belong to 45 precisely relocated seismic clusters with location uncertainties of 5 km or less. The cluster approach produces redundancy in amplitudes arriving from a cluster to a given station. The redundancy will facilitate easy recognition and removal of possible outliers and thus provide a reliable estimate for the Magnitude station correction. The Magnitude station corrections attempts to absorb the regional attenuation difference relative to that dictated by average attenuation relationship derived in this work. The calculated attenuation curve shows a larger geometrical spreading for hypocentral distances closer than 100 km, representing a super-spherical geometrical spreading, and a smaller value for intrinsic attenuation for distances farther than 200 km once compared with the currently used ML relationship of Hutton and Boore (1987). Excluding amplitudes with hypocentral distances smaller than 60 km results in a geometrical spreading coefficient close to spherical spreading, emphasizing the importance of near distances data on accurate estimation of the geometrical spreading value. The difference in the attenuation parameters between our results and those of Hutton and Boore (1987) relationship clearly indicates the crustal disparity of Iranian Plateau and southern California. This necessitates using the new attenuation relationship for Iran. We calculated the local Magnitude empirical attenuation relationship by inverting the amplitude data set for the geometrical spreadin]g and intrinsic attenuation. We did not consider Magnitude station corrections in our inversion to avoid any tradeoff between the station corrections and attenuation parameters. We have shown that the Magnitude residuals calculated by our local Magnitude empirical relationship do not vary systemically versus hypocentral distance or Magnitude. Due to the cluster-wise approach in selection of our events and partially because of the precise location of the selected events, the standard deviation of Magnitude residues is about 0. 19, significantly smaller than those reported by others. We calculated the station corrections by averaging the Magnitude residual in each station. The station corrections vary between-0. 44 to 0. 32. Generally, stations located in Zagros, Alborz and north west of Iran have negative station correction representing amplitude amplification in these regions relative to central Iran and north east of Iran. The new attenuation relationship provides better estimates for the attenuation parameters and especially provides precise Magnitudes at close hypocentral distances. By time, the expansion of Iranian seismic networks reduces the average distance spacing of Iranian seismic stations and thus usage of better local Magnitude formula such as ours becomes more important.

Magnitude has played a particular role in the realistic description of global seismicity. Most studies in earthquake seismology use Magnitude data as a guide to the strength of an earthquake. So biases in Magnitude estimates, caused by any effect, directly affect the result of any study in which Magnitude data is used. In this study, efficiency of using different formulae and depth-distance calibration terms are examined. Applications of the MsR-P formula and new depth-distance terms to the ISC dataset, show that the estimated Ms and mb values are independent of distance, and provide unbiased estimates of Ms and mb in comparison with commonly-used Prague formula and Gutenberg-Richter terms. Comparison of standard deviation of Ms values for single events using the MsR-P and MsPrague formulae show that the MsR-P standard deviations are consistently smaller than those of Prague formula. Also standard deviations of estimated mb values using the new depth-distance terms are smaller than standard deviations of estimated values using Gutenberg-Richter terms. Estimated Ms and mb values using MsR-P formula and the new depth-distance terms reduce overlap in Ms:mb criterion for underground explosions and earthquakes. The study reported here confirms the need to modify the formula for Ms calculation and depth-distance correction terms for mb calculation, which are used by global agencies such as ISC and NEIC.

In the 16th and 17th centuries the classical Greek notions of (discrete) numberand (continuous) Magnitude (preserved in medieval Latin translations of Euclid’sElements) underwent a major transformation that turned them into continuous but measurableMagnitudes. This article studies the changes introduced in the classical notionsof number and Magnitude by three influential Renaissance editions of Euclid’s Elements.Besides providing evidence of earlier discussions preparing notions and argumentseventually introduced in Simon Stevin’s Arithmétique of 1585, these editionsdocument the role abacus algebra and Renaissance views on the history of mathematicsplayed in bridging the gulf between discrete numbers and continuous Magnitudes.

To record local earthquakes, the telemetric-digital seismic network of the tabriz comprising of eight three component seismic stations was installed in the north-west of Iran. This array started operation at the end of 1995. Investigation of archived data in the Tabriz seismic network between 1999 to September 2004 shows that Magnitude values in the database have not been determined using a single formula or a specific method. Comparison of Magnitude values in the database with those values that have been published in the ISC/NEIC bulletin shows that Magnitude values calculated in the Tabriz network are underestimated for events occurred in greater distances. By using Magnitude values in the database and corresponding mb ISC/NEIC (mb ISC or mbNEIC) values, a scale as M=log (v/4π)+2.6log (Δ)-2.2 is derived for determination of the Magnitude in distance range of 170 to 1000 km, where v is peak-to-peak amplitude in micrometer/second and Δ is epicentral distance in kilometers. This formula gives a better estimate for the Magnitude of events in comparison with the formula that is presently used in the Tabriz seismic network.

The availability of a large amount of the data recorded by the Iranian Seismic Telemetry Network (ISTN) has motivated this study to develop relations for the routine determination of ML scale for Central Alborz region of northern Iran. The ML is commonly used in engineering because it is determined within the frequency range (0.5-3 sec) of interest in most of such applications. For any comprehensive seismic hazard analysis, one needs a calibrated Magnitude relationship as well as an earthquake catalog for the study region. It is a well-known fact that the regional geology has a great influence on Magnitude relations. Therefore, for each seismic region a specific Magnitude relation has to be developed. The ML scale is based on the arithmetic mean of horizontal components of the synthesized Wood–Anderson seismograms. We used both nonparametric and parametric methods for inversion. We used a large dataset of 3886 events including 62031 waveforms which recorded by Tehran, Semnan and Sari seismic networks during 02/03/1997 to 13/03/2011. These seismic networks comprise of 19 three-component stations. We calculated the associated synthesized Wood-Anderson seismogram for each SS-1 waveform which records the velocity. Based on Richter’s method, we used amplitudes which are arithmetic means of those of horizontal components.Richter’s ML formula first developed for southern California and Savage and Anderson introduced a nonparametric least-squares inversion method which has been used by others. In this method, the amplitudes recorded at arbitrary distances are linearly interpolated to yield values for the attenuation curve at some fixed distances. In this study, we used both methods.The resulting equations are -logA0=0.9819log (r/100)+0.0028 (r-100)+3.0 and-logA0=1.076log (r)+0.0029 (r)+0.5580 from parametric and non-parametric methods, respectively. Where r is hypocentral in kilometer and A0 is amplitude in millimeter. The two methods yielded very similar results. Unlike the parametric method, the nonparametric one does not impose any a priori assumption of the shape of the attenuation curve on the data and has the potential to detect hinges in the attenuation curve that are caused by structural boundaries such as Moho or geological variations affects on the attenuation curve. Thus the result obtained by nonparametric method was chosen as the final result.Bakun and Joyner (1984) give the following formula for the Q/f ratio: taking an average S-wave crustal velocity of VS=3.3 km/sec, the k value obtained by the non-parametric method, 0.0029, would imply a Q/f ratio of 150 in Central Alborz, Iran.

Image hashing allows compression, enhancement or other signal processing operations on digital images that are usually acceptable manipulations. Cryptographic hash functions are very sensitive to even single bit changes in image. Image hashing is a sum of important quality features in quantized form. In this paper, we propose a novel image hashing algorithm for authentication, which is more robust against various kinds of attacks. In the proposed approach, a short hash code is obtained using a minimum Magnitude Center Symmetric Local Binary Pattern (CSLBP). The desirable discrimination power of image hash is maintained by modified Local Binary Pattern (LBP) based edge weight factor generated from gradient image. The proposed hashing method extracts texture features using the CSLBP. The discrimination power of hashing is increased by weight factor during the CSLBP histogram construction. The generated histogram is compressed to 1/4 of the original histogram by a minimum Magnitude of CSLBP. The proposed method, has a two-fold advantage; first, it has small length, and second, it has an acceptable discrimination power. The experimental results are demonstrated by the hamming distance and the TPR, FPR, and ROC curves. Therefore, the proposed method successfully does a fair classification of content preserving and content changing images.

Determining seismic parameters especially estimating Magnitude with enough precision has an important role in the explanation of the seismicity of a region. However, the method of Magnitude determination based on an empirical relation, relates to the released energy in each earthquake. Magnitude scale is widely used because it is the proper method for estimating the size of the earthquake. In this study, to evaluate the reported Magnitude value for Kojor-Baladeh earthquake which occurred on 28th May 2004, the value of Magnitude was determined by using recorded seismograms in seismic stations then compared with that value reported by IGUT. The result of the investigation shows that the reported Magnitude, about 0.6 Magnitude unit was underestimated. This study shows that the main factor in this underestimation is the software which is used to process recorded data. Many researchers have shown that it is better to estimate local Magnitude by using measurements on horizontal components. This study also showed that in the Kojor-Baladeh earthquake the resultant horizontal amplitude of Lg wave on horizontal components is about twice the amplitude on vertical component.