*نگارنده رابط: تلفن: 61118230-021 دورنگار: 88630479-021 E-mail:ebayram@ut.ac.ir According to accelerograms that do not clip in small distances unlike seismograms, results for local magnitude estimation can be more acceptable than that from seismogram data. The dataset used in this study contains 780 two-component horizontal accelerograms from 390 earthquakes with magnitudes range Mn ≤ 4. To enhance the quality of the data, we employed baseline correction. We processed the uncorrected strong-motion data to make baseline and instrument correction and band-pass filtering. The local magnitude introduced by Richter (1935) is based on the amplitude recorded by the Wood-Anderson torsion seismograph with a natural period of 0.8 sec, a damping constant of h=0.8, and a static magnification, v=2800. Richter chose his reference earthquake with ML=3, such that amplitude was 1 mm on a Wood-Anderson seismograph at an epicentral distance of 100 km. He determined –log A0 attenuation function for southern California region. Log A0 depends on the effects of geometrical spreading and an elastic attenuation and also these effects depend on the characteristics of the crustal structure (Bakun and Joyner, 1984). For large variability of velocity and attenuation, structure of the Earth’s crust does not permit to develop a unique calibration function for local events. Therefore, it is necessary to calibrate it for any region. In this article, we calibrate ML for northwest Iran using synthetic Wood-Anderson seismograms. The area under study extends from 36 to 40 degrees north latitude and from 44 to 50 degrees east longitude. The local magnitude is determined within the period range of greatest engineering interest. So it is a very useful scale for engineering. Many structures have natural periods close to that of a Wood-Anderson instrument, and the extent of earthquake damage is closely related to ML. Nowadays, the lack of W-A Seismograph prevents the calculation of such magnitude in the original form. Kanamori and Jennings (1978) proposed an alternative method of calculation. The accelerograph records are used as acceleration input to an oscillator with characteristics of the Wood-Anderson instrument to produce a synthetic seismogram. Measurements of peak amplitudes on Wood-Anderson instruments were studied to determine a distance correction curve for use in determining the local magnitude ML. We also use the approach suggested by Hutton and Boore (1987) to invert for the empirical distance-correction function in the local magnitude scales. The distance – correction function can be expressed as: -log Aij = n log )rij / 100( +K )rij -100+ (3.0 - MLi + Sj , where the n and k are parameters related to the geometrical spreading and an elastic attenuation. Aij is the horizontal maximum amplitude of the ith event observed at the jth station component, rij is the hypocentral distance from the ith event to the jth station component, MLi is the local magnitude of the ith event, and Sj is the correction factor for the jth station component. The n=1, is appropriate for body-wave propagation in homogeneous media, but the earth is not perfectly elastic and seismic waves attenuate or decrease in amplitude as they propagate. The geometrical spreading and an elastic attenuation can also reduce wave amplitudes. The above Equation can be cast into a standard matrix formation: Gm=d, which represents a typical linear inversion problem in geophysics that can be solved using least-squares or generalized inversion methods. First we used generalized inverse method to calculate the attenuation relationship but we found a negative an elastic attenuation coefficient which is not correct physically. Negative value of k indicates that the assumption of a simple shape for the attenuation curve, with a constant geometrical spreading for different distances is not correct. At the closest ranges, the direct arrival dominates the waveform; but at larger ranges, the rays reflected from boundaries and all of the energy is reflected upward, so postcritical reflections become more important. The range at which the Moho reflection becomes postcritical is indicated by the abrupt increase in amplitude of that ray (Burger et al., 1987). So we performed the trilinear form of attenuation on the data (Atkinson and Mereu, 1992) to avoid the negative values of k. We used Monte Carlo technique to evaluate distance correction curves for north-westIran, and testing all possible combination that minimizes the average residual errors. Results show that we have 3 values for geometrical spreading. Apparent geometric spreading depends on the geometry of spreading in a layered crust, which is a function of distance, but anelasticity is independent of distance. These three values for geometrical spreadings are: R ≤ 85 km, n1 = 0.73; 85 >R≤ 120 km, n2 = -0.46; R>120 km, n3 = 0.22; k =0.00037 The distances less than 85 km related to direct waves. Note that distance ranges between 85 and 120 km is the distance where the Moho reflection becomes postcritical and is indicated by the abrupt increase in amplitude. The focal depth, crustal thickness, and the crustal velocity gradient have important influences on the range at which the amplitude increases. The result of ground motion in north-west Iran demonstrates that crustal structure can influence the strong motion attenuation relations. The uniform distribution of the residuals about their baselines (Fig. 4) show that the trilinear distance attenuation relation developed in this study provide more reliable estimates of ML values than those from linear relation. ML values using the linear distance attenuation are overestimated at distance larger than about 85 km (Fig. 3). We used trilinear method to estimate the local magnitude, but distance attenuation is independent from crustal structure. The attenuation along the energy ray path and the site geology conditions play roles of great importance in the recorded amplitudes. In the process of magnitude calculation, such effects are reduced if a proper attenuation function and magnitude station corrections are applied, so we applied the station correction on the amplitudes and performed a linear regression analysis on the data to obtain n and k.The results represent a logical response. No trend is evident on the distribution of residual in the corrected linear method, thus the attenuation function determined in this study does not depend on geology variation or hypocentral distances, as it works well for the north-west Iran region. The distance – correction and local magnitude function can be expressed as: -Log A0 = (1.52±0.0057) log(r/100) + (0.00137±3.20E-07) (r-100) + 3, ML = log A + (1.52 ± 0.0057) log(r/100) + (0.0013 ± 3.20E-07) (r-100) +3, The parameter k can be related to the inelastic attenuation coefficient Q using the Bakun and Joyner (1984) formula γ = ln 10k = πf/QVS, where VS is the average crustal S-wave velocity. Taking an average S wave of VS = 3.4 km /s, the k ≈ 0.00137 value obtained in the present study introduces a value of γ = k ln (10) = 0.00317 and Q(1 Hz) = 280. Nuttli (1980) found that a γ value of 0.0045 km -1 (between 0.003 and 0.006) corresponds to an apparent Q of 200 (between 152 and 303) for Sg. The γ and Q value agree with the result given by Nuttli. He showed that the attenuation of 1-sec period crustal phases in Iran is relatively high. The high attenuation value is due to the tectonic complexity and the widespread young volcanics in the region. This result should be treated with caution, because the maximum amplitude data do not necessarily correspond to a single seismic phase .