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Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
Title: 
Author(s): 

Issue Info: 
  • Year: 

    0
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    -
Measures: 
  • Citations: 

    0
  • Views: 

    1163
  • Downloads: 

    0
Keywords: 
Abstract: 

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Title: 
Author(s): 

Issue Info: 
  • Year: 

    0
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    -
Measures: 
  • Citations: 

    0
  • Views: 

    621
  • Downloads: 

    0
Keywords: 
Abstract: 

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Title: 
Author(s): 

Issue Info: 
  • Year: 

    0
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    -
Measures: 
  • Citations: 

    0
  • Views: 

    484
  • Downloads: 

    0
Keywords: 
Abstract: 

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Title: 
Author(s): 

Issue Info: 
  • Year: 

    0
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    -
Measures: 
  • Citations: 

    0
  • Views: 

    502
  • Downloads: 

    0
Keywords: 
Abstract: 

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    1-20
Measures: 
  • Citations: 

    0
  • Views: 

    658
  • Downloads: 

    0
Abstract: 

The present article addresses a new approach form using tidal analysis of long and short observations of tidal heights by tidal tools of Mike 21 software. Predicted or observed tides must be available as open boundaries in a hydrodynamic model to simulate tidal currents. Mike 21 is a powerful software in simulating of marine and oceanic parameters. Hydrodynamic models use tidal data as a main input in the open boundaries of 2D/3D simulation. The accuracy of the simulation results from tides and tidal currents as well as sediment transportation and other related marine parameters, is quite dependent on accurate input data in the open boundaries of the hydrodynamic model. Large and meso-scale simulations usually use sophisticated global tidal models. These tidal models are prepared by assimilating of satellite altimeter data and tide gage data. The accuracy of such a tidal input seems to be quite sufficient. In shallower part of ocean, like estuaries and coastal areas, these data are not so accurate; therefore direct tide observations are important. On the other hand, long-term tide observations are limited due to technical and economical constraints. In this study, the appropriate solution to tidal analysis and predictions was introduced in the Mike 21 software to produce acceptable and accurate tidal height data. Mike 21 is provided with two different tidal analysis and prediction modules. The IOS and Admiralty methods of tidal analysis and prediction are known for the corresponding high quality functions. Using the software, the tidal analysis of sample data was discussed in order to produce the accurate tidal data. In this article, hourly tidal observations for a year which belonged to three stations in the Oman Sea and Persian Gulf were analyzed. All tidal analyses were performed for one year, 30, 15 and 10 days periods using Canadian IOS and Admiralty method software. The predicted tidal data were compared with respect to observed data for evaluating of computations. Residuals normally will describe such discrepancies, if there are no abnormal fluctuations of tides. These abnormal inconsistencies might be produced by storm surges and other non-tidal effects. The presented results were statistically analyzed. Two different statistical indices, Root Mean Square Error and Reduction in Variance, were used to evaluate predicted tide data. Consequently, the tool for appropriate analysis and predicting of tidal data of the different periods was introduced. It is shown that for long term tide observations, the IOS method is the proper solution for tidal analysis and prediction, while the Admiralty method is fitted for short term analysis and prediction of tides.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    21-38
Measures: 
  • Citations: 

    0
  • Views: 

    1169
  • Downloads: 

    0
Abstract: 

application of interpolation is in semi-Lagrangian methods. In semi-Lagrangian methods, the departure points of the particles arriving at the regular grid are calculated and the scalar quantity is interpolated at the departure points. A common problem is the creation of spurious fluctuations in interpolation values in areas with strong gradients if polynomial interpolation of higher than first degree is used. In order to remove spurious fluctuation, it is necessary to use monotone interpolation. The concept of monotone interpolation requires that the value of the interpolation of the function at the interval between two neighboring grid points should not be greater or less than the maximum and minimum of the function at that interval, respectively. That is, no relative extrema should be produced in the interval. The most famous method for monotone interpolation results from changing the derivatives used in cubic Hermit polynomial with respect to the slop of the function within the interpolation interval. By changing the derivatives, one can adjust the curvature of the interpolator between the beginning and the end of the interpolated interval. The main idea of the change in derivatives is that the derivatives in each interval should not exceed by roughly three times the slop of the function on that interval. In this paper, the curvature of the cubic Hermit polynomial is adjusted between the maximum value still giving monotonicity and the minimum value, corresponding to linear interpolation between the two points. The Hermit functions need derivatives of the function on the grid points for interpolation. For this reason, the cubic Hermit was chosen for implementation of the monotonicity procedure. The monotone piecewise cubic interpolants are easy to use, of sufficient accuracy and have been widely used. This interpolation is of second order accuracy near strict local extrema due to the application of the monotonicity constraint. It is generally the case that most monotonicity-preserving methods sacrifice accuracy in order to obtain monotonicity. Numerical experiments with this method show that the maximum curvature still giving monotonicity may bring the cubic Hermit function close to the relative maximum and minimum in the interval. The (weakly monotone) interpolant with minimum curvature between the two neighboring points may decrease the accuracy of the interpolation as the curve connecting the two points tends to a line. The best choice for curvature in terms of both accuracy and monotonicity is intermediate between the discussed maximum and minimum values. For an important example of practical application in meteorology, the presented method is used in transforming meteorological data in horizontal and vertical directions. An error analysis suggests that interpolation in the vertical direction for transferring data from pressure to the hybrid σ-θ , exhibits a large sensitivity to the amount of curvature used in the implementation. Maintaining maximum curvature in the interpolation function reduces the distance between vertical surfaces such that the crossing of vertical surfaces will result in error.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    39-52
Measures: 
  • Citations: 

    0
  • Views: 

    626
  • Downloads: 

    0
Abstract: 

The Caspian Sea, the world’ s largest inland enclosed water body, consists of three basins namely northern, middle and southern. This study investigates physical oceanography properties and long waves in the southern Caspian Sea. To deal with this, we used ADCP, CTD, weather data, sea level and satellite imageries. The data were collected by National Institute of Oceanography and Atmospheric Sciences (ADCP and CTD), Port and Maritime Organization (sea level), and Meteorological Organization (wind data). The results show that the temperature plays pivotal role in the structure of water in this basin. The place of thermocline and pycnocline are about at the same depth and the thickness of mixed layer in the summer and fall are about 25 and 15 meters, respectively. The analyses of ADCP data show that thermocline disappears from February to March and after two months, the thermocline starts to develop. In most of cases, the magnitude of meridianal velocity is stronger than zonal speed based on ADCP data. Spectral density of time variations of velocities of current and wind show that there are many peaks from a few hours to many days. We consider some periods such as 30, 40, 48 and 60 hours as Kelvin waves based on our background information about these waves. Sea level data and satellite images (Aviso sensor) confirm the results in terms of periods and wavelengths. Due to barotropic and baroclinic modes of Kelvin waves, wavelengths, angular frequencies and group speeds are calculated separately. According to these results, baroclinic mode is more important than barotropic mode in this basin. Based on the governing equations of shallow water, the sea level gradient equation was written and time series of sea surface level changes were plotted. The results show that the long wave amplitudes are from 10 to 15 cm according to satellite and observation data. In this basin, the reduced gravity varies from 0. 006 to 0. 008 m/s2 in different seasons and the thickness of the denser water column is considered about 150-200 m. The Rossby radius of deformation and group velocity are 20 km and 1. 2 m/s, respectively. Due to different periods of Kelvin waves, the wavelengths vary from 129 to 259 km. The satellite images confirm Kelvin waves because there are some anomalies in sea level similar to that produced by Kelvin waves with similar periods and wavelengths. Based on results, it is recommended that more detailed observational data should be collected in the deep parts of the southern and middle basins of the Caspian Sea.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    53-69
Measures: 
  • Citations: 

    0
  • Views: 

    494
  • Downloads: 

    0
Abstract: 

To obtain the distribution of the Love wave group velocities in northwest Iran and its surrounding areas for 7, 10, 20 and 25 second periods, the waveform of 241 local and regional events used in a dispersion curve tomography of the Love waves. The evnets occurred within NW Iran and surrounding areas between 2005 and 2015 and were recorded by 39 permanent and temporary medium and broad band seismic stations belonging to national and international seismic networks. In order to reduce the effect of non-uniform distribution of events, we selected the more uniform list of events out of an initial number of 1734 non-uniform distributed events. We applied the Frequency-Time Analysis method to each event-station path for estimation of Love wave group velocities, then we used a tomographic method to compute the distribution of local group velocities throughout the region. From the analysis of the surface wave tomography, we concluded that crustal structure in the South Caspian Basin and the Kura Depression is almost the same, but it is significantly different from that of the northwest Iran. In the presence of thick and low shear velocity sediments in the South Caspian Basin, we observed low velocity anomalies at periods less than 10 seconds that are surrounded by relatively higher velocities along Alborz, Talesh and Lesser Caucasus. In the “ Eastern Anatolian Accretionary Complex” where volcanic activities are much higher than in rest of the region, less group velocities were observed for periods less than 25 seconds. The main reason for this observation can be related to the presence of partial melting zones inside the crust as a result of intensive volcanic activities in this region. In Zagros, for the periods of 7 and 10 seconds, a relatively high velocity anomaly along the “ Sanandaj-Sirjan” metamorphic zone was observed, which was trapped by two low velocities along the “ Zagros Folding and Thrust Belt” in one side and “ Urmieh-Dokhtar Magmatic Arc” in another side. The active and broken crust, reverse, active and shallow thrust faults and high seismicity of Zagros Folding and Thrust Belt is characterized by low group velocities in our results for periods of less than 25 seconds. In most areas of central Iran and Urmieh-Dokhtar Magmatic Arc, local sedimentary basins are characterized by low velocities for periods of 7 and 10 seconds. Our results indicate that crustal structure in the northwest of Iran is almost uniform and has the minimum changes, but it is completely different from the crustal structure in the South Caspian Basin, eastern Turkey, and the Zagros mountains.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    87-106
Measures: 
  • Citations: 

    0
  • Views: 

    624
  • Downloads: 

    0
Abstract: 

The empirical attenuation relationship for spectral amplitudes was calculated to study the attenuation of shear waves of shallow events at close hypocentral distances inside Tarom-Rudbar region, western Alborz. 3122 waveforms (170 shallow events) recorded by 40 seismic passive stations of two local temporary seismic networks were included in this analysis. The selected events have moment magnitudes between 1. 8 and 4. 2 and epicentral distances of 10 km to 70 km. All events have location accuracy better than 2 km in epicenter and less than 5 km in depth. The good location quality of the events allows us to estimate accurately geometrical spreading of shear waves at close hypocentral distances. By selecting the small events, we can safely treat them as point sources and thus use hypocentral distance as our distance metric. Additionally, for smaller events, we automatically avoid the non-linearity of amplitude of seismic waves with magnitude and its possible trade-off with geometrical spreading. Due to a rather low dependence of geometrical spreading on magnitude (v. NGA-WEST2 models), our approach of using weak-motion data may provide a means to reliable assessment of the geometrical spreading coefficient which can then be used to partially regionalize NGA-WEST2 GMPEs for regions with low rate of seismicity or lack of enough strong motion records. The shape of the attenuation curve at different frequencies was obtained using non-parametric fit to the data with Robust Lowess algorithm showing a mono-linear curve in the associated distance. Assuming mono-linear attenuation model and using regression, the value of geometrical spreading coefficient in the equation derived from the spectral method was obtained as 1. 6 in frequencies higher than 2 Hz. Spectral amplitude attenuation curves show an obvious super-spherical geometrical spreading at close hypocentral distances. We show that the geometrical spreading is strongly super-spherical in close agreement with those used in some of the NGAWEST2 GMPEs. The observed super-spherical geometrical spreading of seismic waves could drastically change the level of seismic hazard in close hypocentral distances by localizing strong motion to short hypocentral distances. The calculation of geometrical spreading coefficient using data from more frequent small events recorded by dense local networks can be used to partially regionalize the geometric term of GMPEs in regions with small rate of seismicity. The residuals were averaged on a station-by-station basis to determine station corrections. The calculated station corrections for the study area shows sharp contrast between the northern and southern hills of western Alborz. The stations in the northern hill, mostly in Gilan plain, show higher amplification (positive station corrections) relative to those in the southern hill. The strong amplification of seismic waves has a strong implication for preparation of seismic hazard maps of the densely populated Gilan province.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    89-70
Measures: 
  • Citations: 

    0
  • Views: 

    691
  • Downloads: 

    0
Abstract: 

Soil moisture influences the partitioning of rainfall into evapotranspiration, infiltration and runoff, hence it is an important factor for determining the magnitude of flood events. The Soil Moisture Active and Passive (SMAP) mission is a microwave all-weather sensor with cloud penetration capability it can be harnessed for inundation mapping. On the other hand, Global Precipitation Measurement (GPM) is the first satellite that has been designed to measure light rain and snowfall, in addition to heavy tropical rainfall. The Integrated Multi-satellitE Retrievals for GPM (IMERG) products, with 0. 1° × 0. 1° spatial resolution and 30 min temporal resolution, are available in the form of near-real-time data, i. e., IMERG Early and Late, and in the form of post-real-time research data, i. e., IMERG Final, after monthly rain gauge analysis is received and taken into account. In this study, daily rainfall estimates from IMERG Early, Late, and Final runs (IMERG-E, IMERG-L and IMERG-F) are compared with daily precipitation measured by 22 synoptic rain-gauges over the northwest and western regions of Iran. Assessment is implemented for a period from April 2016 to February 2017. The assessment technique is using a contingency table that reflects the frequency of “ Yes” and “ No” of the satellite estimation. We have used two threshold values of 0. 1 mm/day to define rain/no rain and 5. 0 mm/day as moderate or higher rainfall events. The scatter plots of daily precipitation values, IMERG-E, IMERG-L and IMERG-F data against rain-gauge observations, indicate underestimation according to Bias for moderate or higher rainfall; this is more so when the precipitation threshold is increased. However, the IMERG-F shows better performance (i. e., closer to one-to-one line) in estimating moderate or higher rain. For the first threshold, all the three runs show approximately same performances; but some differences are seen at the second threshold. At this threshold, POD for IMERG-F is about 0. 27 and for the two other products is about 0. 14, which means larger fraction of the observed “ Yes” events was correctly estimated by IMERG-F than IMERG-E and IMERG-L. At the second part of this work, the synergistic use of satellite-based precipitation and soil moisture observations was dedicated to mapping of flood monitoring in the northwest of Iran on 14 April 2017. In this study, a value-added product was used that over-samples the SMAP volumetric soil moisture data with a spatial resolution of 40 km and posts it on a 9 km grid, SPL2SMP_E. The SMAP data maps show a pattern that is consistent with the precipitation maps; i. e., following the rainfall on 14 April, there is an increase in the saturated area and after that it begins to decay. So together, SMAP and GPM can provide information on the surface water fluxes, an important quantity for assessing and monitoring the Earth’ s fresh water resources. Therefore, integrated GPM and SMAP data can serve as a key tool for application users and emergency management to assess the extent and potential impact of flooding events among other hydrometeorological phenomena.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    107-121
Measures: 
  • Citations: 

    0
  • Views: 

    506
  • Downloads: 

    0
Abstract: 

The prediction of the minimum temperature is one of the main approaches to manage and reduce the risk damage caused by frostbite. For this purpose, using daily statistics of minimum, maximum and dew point temperatures during the period of 2005 to 2009, the minimum temperature of the next day was predicted for four stations (Rasht, Kerman, Shiraz and Hamedan) with different climate types by applying the Linacre regression model and the Multi-Layer Perceptron artificial neural network (MLP) in the whole year, the cold period (from October to late March) and the warm period (from April to late September). For this aim, the Matlab-2015 and IBM SPSS-20 software were used and statistical criteria RMSE, NRMSE and R2 were applied to evaluate the performance of the models. The results of this study, in all three periods, demonstrated that the best estimate of the Linacre regression model was obtained with root mean square error of 1. 70 and 2. 44° C for the whole year, 2. 01 and 2. 32° C for the cold period and 1. 51 and 2. 24° C for the warm period for Rasht and Shiraz stations with the PH-CW and SA-C-W, respectively. The best results from MLP neural networks with Levenberg-Marquardt algorithm, logic sigmoid transfer function in the hidden layer, the linear transfer function in the output layer and two inputs (dew point and maximum temperature), like the Linacre regression model, were obtained with RMSE of 1. 57 and 1. 93° C for the whole year and 1. 61 and 1. 8 for the cold period for Rasht and Shiraz stations, respectively. The RMSE of the best results from MLP neural networks in the warm period was 1. 21 and 1. 44° C for Rasht and Hamedan stations, respectively. To evaluate the role of relative humidity on model results, this parameter was added as a third input to the multi-layer Perceptron network. The improved RMSE for the whole year was 17. 4, 12. 9, 49. 4 and 18. 3 percent and for the cold period of the year was 3. 4, 2. 86, 9. 48 and 15. 83 percent at Kerman, Shiraz, Hamedan and Rasht stations, respectively. These values for the warm period were 6, 13. 33, 2. 86 and 18. 63 percent for the above mentioned stations. These improved errors indicate that only at Hamedan station, the cold period of the year produces more improvement in error reduction than the warm period of the year by adding relative humidity as the third input to the neural network model. In other stations, adding relative humidity in the warm year has led to a reduction in the error rate. In general, it can be said that selected MLP networks had better performance than the Linacre regression model in predicting the minimum daily temperature.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    122-144
Measures: 
  • Citations: 

    0
  • Views: 

    875
  • Downloads: 

    0
Abstract: 

Calculating the focal mechanism of earthquakes, helps us to investigate the direction of rupture propagation, the style of faulting, stress field and the seismicity potential of an area. Focal mechanisms classically are determined by using the polarity of P-wave first motion. This method depends on the number of P wave polarities per event and the data set dispersion distribution Significant improvement of long period instruments caused advantages in using waveform inversion method for determining focal mechanism of earthquakes. In this method outspread outlier data can be used. Extensive availability of small earthquakes makes them useful in determining focal mechanisms. The current study accomplished to determine focal mechanisms of 4204 events with magnitude 2≤ Mn ≤ 5. The earthquakes were recorded in 41 stations of Iranian Seismological Center (IRSC) in the Alborz region. The focal mechanisms were prepared by using the polarity of P wave first motion and S/P amplitude ratios. In this study, waveforms of three-component seismograms were filtered with bandpass filter in a 0/1– 10 Hz frequency range. Seismograms with velocity components were integrated to the corresponding displacement components. P-wave first motion polarities are revised by reviewing the waveforms carefully. For calculating the S/P ratios, P wave, S wave and background noise amplitudes were measured by selecting 2 second time windows from waveforms. Maximum amount of S/P ratio is near the nodal planes and the minimum amount is far from the nodal planes. Using P wave polarities and ratios, the final focal mechanisms were obtained. With the progressive improvement of IRSC networks since 2012, more P wave first motion polarities can be recorded and the number of the calculated S/P ratios for each event has increased. In this study, data set of 1997 to May 2015 was investigated. Because of weak qualities of small earthquakes waveforms, small events were omitted and a focal mechanism catalogue containd strike, dip and rake angels for earthquakes with Mn greater than 3. 5 was produced. The method also was tested with 12 synthetic earthquakes in the Alborz rigion. Most of the focal mechanisms at north of the region have thrust-faulting components and at south they are strike-slip. Along the left side of the Talaghan fault, most of the focal mechanisms are left-lateral strike-slip which shows the left-lateral motion along the Mosha fault. The Indes fault has north west-south east strike. Along the south east side of this fault, the focal mechanisms of 18/6/2007 event and its aftershocks show the inverse faulting. The results of this study are compatible with most of the previous studies in this region.

Yearly Impact: مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    12
  • Issue: 

    3
  • Pages: 

    145-154
Measures: 
  • Citations: 

    0
  • Views: 

    1196
  • Downloads: 

    0
Abstract: 

Plate tectonics provides a general framework for understanding the worldwide distribution of seismicity, volcanism, and mountain building. These phenomena are largely associated with plate interactions at plate margins. The basic mechanism responsible for plate tectonics must provide the energy for the earthquakes, volcanism, and mountain building. The only source of energy with sufficient magnitude is the heat from the interior of the Earth (~30 milliwatts per square meter). This heat is the result of the radioactive decay of the uranium isotopes 238U and 235U, the thorium isotope 232Th, and the potassium isotope 40K as well as the cooling of the Earth (~30 milliwatts per square meter). An accurate estimate of the heat lost from the interior of the Earth can be obtained from measurements of the surface heat flow. By figuring out the temperature distribution in different depths of the Earth, it is possible to plot the heat flow diagram for those areas. Investigation of geothermal gradient is useful in estimating the maturity and transformation of hydrocarbon organic materials and estimating the relative age of hydrocarbonization of the source rocks. The importance of temperature and heat flow distribution calculation can be more obvious when we relate them to other physical parameters such as density, seismic velocity, chemical composition and melt fraction and use these parameters to more accurate modeling of anomalies and sub-surface layers. Primary understanding of geothermal gradient can be very applicable in oil and gas exploration and production; particularly in designing the combination of drilling mud, cement, rubber tools inside the well, using of digitization tools and electronic devices in the well and designing the drilling pipes. The basic relation for conductive heat transport is Fourier’ s law, which states that the heat flux at a point in a medium is directly proportional to the temperature gradient at that point. Using Fourier’ s law, it is possible to compute temperature and heat flow distribution in a one-layer section, with boundary conditions such as given surface heat flow and surface temperature. In this paper, we use Fourier’ s law and present a new formula which calculates the temperature and heat flow distribution for a depth section with desired number of layers which each layer has its own heat production and thermal conductivity. The boundary conditions for this calculation are the given temperature of the uppermost and lowermost layer and a steady state vertical heat conduction with no lateral heat variation. This is not far-fetched, because there are two boundaries with defined temperature in the Earth: LAB and surface of the Earth. So, we can determine the temperature and heat flow distribution for a lithospheric section with various number of layers with different thermal conductivity and heat production. For verification, this formula was written in MATLAB programming software and the distribution of heat flow and temperature for the synthetic models were calculated.

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