مجله ژئوفیزیک ایران
سال هشتم شماره 2 (پیاپی 21، تابستان 1393)

Gravity anomaly data are usually interpreted on the initial acquired surface. In some situations, it is useful to move the data to another surface for interpretation or comparison with another data set. Moving the data to another surface is called upward or downward continuation.The regional-residual gravity anomaly separation is one of the most important steps inprocessing and interpretation of potential field data. The regional and residual gravityanomalies have long and short wavelengths, respectively. On the other hand, upwardcontinuation is a mathematical transform that reduces the short-wavelength or shallow anomalies. Therefore, the upward continuation can be used to separate regional-residualgravity anomalies. In other words, upward continuation can be considered as a low-passfilter that attenuates the short-wavelength anomalies more than long-wavelength ones.Selection of the optimum height for upward continuation is very important. Bychoosing the upward height less than optimum value, remains the residual anomalies inthe result of upward continuation and choosing the upward height more than optimumvalue, reduces the amplitude of the regional anomalies in the data Qualitative comparingof results from the upward continuation with the main data for various heights of upwardcontinuation is a common method for detection of the optimum value of height.A good height to separate regional from residual gravity anomalies will have amaximum cross-correlation between the regional and the upward-continued data. Apossible method for estimating the optimum height for the synthetic model data can bederived using the cross-correlation between the regional anomaly at the observation leveland the upward continuation of the observed anomaly at different heights. We usedsynthetic model data as two regional bodies at the 1500-meter depth with various lateralboundaries and three local bodies at the 200-meter depth and various lateral boundaries.Because we do not know the real regional anomaly, we present a practical methodbased on the cross-correlations between the upward continuations at two successiveheights to derive an optimum upward continuation height for the regional-residual gravityseparatation. We calculate the cross-correlation versus height over a range, from zero to aheight where a change in the cross-correlation values has clearly passed a maximumdeflection from the chord joining the end point heights. The height of the maximumdeflection of these cross-correlation values yields the optimum height for the upwardcontinuation.We tested the efficiency of the method on synthetic data. Our results showed that themaximum cross-correlation between regional and the upward-continued data coincide onthe maximum deflection of the upward continuations at two successive heights.Furthermore, the method was applied to the real gravity anomaly in the HormozghanProvince in the south of Iran to prospect a chromite ore bodies. As we expected, theBouguer anomaly included both regional and residual anomalies related to the chromiteore body and other shallow sources, respectively. Therefore, we cannot distinguish thelocation of the mineral deposit. When we separate regional and residual gravity anomaliesby an upward continuation at the optimum height, we can see that the obtained residualanomaly clearly shows the location of mineral deposit.

Magnetotelluric (MT) method is an important passive surface geophysical method whichuses the Earth’s natural electromagnetic fields to investigate the electrical resistivitystructure of the subsurface. In thermal areas, the electrical resistivity is substantially of adifferent form and generally lower than in areas with colder subsurface temperatures. Theselected MT profile in the region crosses over the hydrothermally altered zones anddifferent geological structures. Reflection and refraction of EM signals at both horizontaland vertical interfaces separates the media of different electrical parameters.Electromagnetic methods have been developed and employed to recognize the geologicalfeatures and particularly fault zones in many regions. To achieve a higher lateral resolution and also greater depth penetration, the MT method is one of the most effective electromagnetic techniques to imagine the subsurface structures electrically. For subsurface mapping purposes, the long period natural-field MT method proved to be veryuseful. The MT method, due to a high penetration depth, is one of the most effectiveelectromagnetic methods to recognize deep geothermal systems.In this study, the geothermal reservoirs were conducted using Magnetotelluric (MT) data. Mahallat in Markazi Province was chosen as the case study area and the MT surveywas carried out at 17 sites with a 500-meter distance between stations using GMS05 (Metronix, Germany) systems. Three magnetometers and two pairs of non-polarizable electrodes were connected to this five-channel data logger. The experimental setup included four electrodes distributed at a distance of 100 m in north–south (Ex) and east–west (Ey) directions.Measurements of the horizontal components of the natural electromagnetic field wereused to construct the full complex impedance tensor, Z, as a function of frequency. Usingthe effective impedance, determinant apparent resistivities and phases were computed and used for the inversion. The MT data were processed using a code from Smirnov (2003) aiming at a robust single site estimate of electromagnetic transfer functions. As the area of the study was populated and close to electric noise sources and travertine mines, the recorded data did not have a good quality to justify the low coherency between the electric and magnetic channels. Since it was assumed that the earth structure was largely 2D for the purpose of a 2D inversion, the 3D structure would appear in the data as noise.We performed a 1D inversion of the determinant data using a code from Pedersen (2004)for all sites. The 2D modeling was applied to the data to explain the data if their responses fitted the measured data within their errors. Generally, the better the fit between measured and predicted data, the better the model resolution. The 2D inversion of the TE-,TM-, TE+TM and DET-mode data using a code from Siripunvaraporn and Egbert (2000) were performed. The data were calculated as apparent resistivities and phases. Apparent resistivity and phase data exhibited fairly different characteristics in the TE- and TMmodes.The determinant provides a useful average of the impedance for all current directions. Since the quality of the determinant data was acceptable, 2D modeling of the determinant data would be expected to provide a more reasonable approximation of thetrue subsurface structure. Therefore, we used the model obtained from the DET-modedata as an interpretation model. The resistivity model obtained from the DET-mode isconsistent with the geological model of the Mahallat region down to two kilometers.From surface down to about 400 m depth, there is a conductive layer (<30 ohm-m)showing a variable thickness along the profile, which is hydrogeologically interpreted asthe penetrated zone for water. The surface was covered by clay and sand making it a good condition for keeping water. The conductive zone located in the middle part of the profile was interpreted as a geothermal reservoir that its estimated depth ranged from 800 m down to 2000 m. The conductive zone was hidden under the Quaternary alluviums and travertine stones along the profile.

Investigating the trend and fluctuations of the sea surface temperature (SST) data arecritically important for understanding the interactions between the oceans, the atmosphere and the land in various spatial and temporal timescales. Such analysis of the SST timeseries is also essential for the detection and modeling of climate change. The increase in the global SST is one of the primary physical impacts of climate change. Some recent investigations have shown that the fluctuations in SST data over the Persian Gulf and the western parts of the Indian Ocean regulates Iran's precipitation particularly over the southern districts. The present study was, therefore, motivated to analyze the trends in the SST data over the northwestern parts of the Indian Ocean waters containing 30 nodes of 2by 2 (longitude and latitude) grids for the period 1950-2009. These grids were spread over various parts of the Persian Gulf and Arabian Sea, the water bodied between 18 to 30 North and between 45 to 72 East. The monthly SST data was gratefully extracted from the database of the physical sciences division of the National Oceanic and Atmospheric Administration (NOAA). According to their geographical positions, these 30 grids were classified into three groups, namely, the Persian Gulf, coastal areas (i.e., the grids off the coasts by 2) and the Arabian Sea regions. Since the SST time-series generally have a normal distribution, a linear regression analysis was applied to detect the trend in the constructed time series for the classified regions in annual and seasonal timescales. The analysis was conducted by each grid individually as well as by averaging the SST data over each of the three mentioned zones. The seasonal time series were constructed by averaging monthly data so that winter, spring, summer and autumn consisted of the months Jan-March, April-June, July-Sep and Oct-Dec, respectively. The 60 years of the study period were also divided into three consecutive 20 years to assess the consistency in trend-line slope over time. The parametric statistical tests were used to investigate whether the detected trends are significant The study revealed that during the 60 years of the study period, the SST of these 30 grids has inclusively increased by about 0.61°C. It is in general agreement with Deser et al. (2010) that reported the magnitude of the global SST trend during the 1900-2008 period as approximately 0.4–1.0°C per century in the tropics and subtropics and 1.2– 1.6°C per century at higher latitudes. The amount of such increase for the Persian Gulf, coastal areas and the Arabian Sea was 0.5°C, 0.65°C and 0.63°C, respectively. Comparing with other seasons, for the large regions of the three classified zones the increasing trend was the greatest and the least for autumn and winter, respectively. While the spring and summer’s SST were increased by about 0.5°C during the last six decades, the corresponding increases for winter and autumn were found to be 0.60°C and 0.85°C, respectively. The autumnal upward trend was significantly greater than other seasons for the Persian Gulf and the coastal regions. However, the upward trend is statistically identical during autumn and winter over the Arabian Sea areas. With the exception of the spring, the slopes of the trend-lines were different between the Persian Gulf, coastal areas and the Arabian Sea during the other seasons.When the considered 60 year period was divided into three consecutive 20 yearperiods, the trend exhibited a variety of differences between these new shorter data sets. While the spring and wintertime SSTs did not exhibit any significant trend during either 1950-1969 or 1970-1989 periods, the upward trend was significant for the period 1990- 2009. In contrast to winter and spring, most of the considered SST time series (excluding the Persian Gulf data) were significantly warmed up during 1950-1969. No significant trend was observed for the period 1970-1989 on a seasonal scale. In spite of the fact that the Persian Gulf SSTs did not exhibit any significant positive trend during the summers or autumns for either 1950-1969 or 1970-1989 periods, the trend abruptly increased during the 1990-2009 period for these two seasons.

The aeromagnetic data of Iran was surveyed by Aeroservice Company (Houston, Texas) under auspicious of Geological Survey of Iran during 1974-1977. The survey was done with a two-engine airplane using a cesium vapor magnetometer with a sensitivity of 0.02 gama. The data was collected along flight lines with average line spacing of 7.5 km over 62 flight blocks mostly with a constant barometric flight height. A barometric elevation range of 1000-3600 m was used (Yousefi and Feridberg, 1977) which translated to about a 500-1000 m height from the Earth surface. Saleh (2006) used the raw data of the 62 blocks and produced an aeromagnetic composite map of Iran. The raw data had already been corrected for daily variations of the geomagnetic field. To produce a composite grid of the aeromagnetic map of Iran from the original ratherraw data, Saleh (006) first implemented the detailed leveling and micro-leveling proceduresfor each block. The fully leveled blocks were stitched initially to eight geol gically coherentlarger blocks and finally the larger blocks were stitched. The final 1 km by 1 km grid of theaeromagnetic map of Iran was produced from the combined data set using a bidirectionalinterpolation scheme. Magnetic anomalies in Iran latitudes do not correlate directly with their corresponding causative magnetic bodies because the direction of the geomagnetic field and magnetization are not normal to the Earth surface. The asymmetry between the magnetic anomalies and their causative magnetic bodies increases from north to south of Iran. The deviation could reach to tens of kilometers for aeromagnetic anomalies located in the south of Iran. For geological interpretation purposes, it is very desirable to derive aeromagnetic anomalies that are positioned over their causative magnetic bodies, quite similar to that expected from gravity anomalies, or an induced magnetic body located in the North Pole. Baranov and Naudy (1964) introduced a procedure called reduction-to-the-pole (the standard RTP method) which converts magnetic anomalies in mid-latitudes to that produced by the magnetic bodies having vertical magnetization, and lying at the north geomagnetic pole. The standard RTP is only valid for regions in which the direction of the geomagnetic field is almost constant. Therefore, the standard RTP method is not applicable to produce an RTP map of the aeromagnetic field of Iran. The RTP methods which allow for variations of geomagnetic field are called differential reduction-to-pole methods (DRTP). In this study, the revised aeromagnetic map of Iran (Saleh, 2008) was reduced to the pole considering the variations of inclination and declination of the geomagnetic field over Iran.The new aeromagnetic map was produced using the differential reduction to the pole (DRTP) method developed by Arkani-Hamed (1988). The DRTP operator shifts aeromagnetic anomalies in different geographical latitudes to the top of their causativesources, thus facilitating an easier geological interpretation of the magnetic anomalies. Wefirst applied the DRTP method to the synthetic magnetic anomalies of three identical spheres lying in north, centre and south of Iran assuming induced magnetization for the spheres. We found that the DRTP method did not show any instability; thus it is appropriate to use in Iran. The DRTP aeromagnetic map of Iran showed significantly a better correlation between the magnetic anomalies and the boundaries of the main tectono-stratigraphic units of Iran (e.g. Alborz, Jazmurain Depression), volcanoes (e.g. Sabalan Mountain) and major active faults (e.g. Tabriz and Doruneh faults).

Magnetic survey is one of the most important geophysical methods extensively used inmineral explorations. Therefore, the interpretation and modeling of this data is very important before doing any drilling exploration. Modeling this data makes it possible to choose the best position for drilling. In this study, the magnetic data of Morvarid Zanjandeposit has been modeled and a 3D model of the magnetic susceptibility has been achieved. The results were compared with the real model created with drilling explorationdata. There are many inversion algorithms for modeling the magnetic data. However, a principal difficulty with the inversion of the potential data is the inherent nonuniqueness. By Gauss’ theorem, if the field distribution is known only on a bounding surface, there are infinitely many equivalent source distributions inside the boundary that can produce the known field. A second source for nonuniqueness is the fact that the magnetic observations are finite in number and are inaccurate. If there exists one model that reproduces the data, there will be other models that will reproduce the data to the samedegree of accuracy. Faced with this extreme nonuniqueness, authors have mainly taken two approaches in the inversion of magnetic data. The first one is the parametric inversion in which the parameters of a few geometrically simple bodies are sought in a nonlinear inversion and the values are found by solving an overdetermined problem. This methodology is suited for anomalies known to be generated by simple causative bodies, but it requires a great deal of a priori knowledge about the source expressed in the form of an initial parameterization, an initial guess for the parameter values, and limits on the susceptibility allowed.In the second approach to inverting magnetic data, the earth is divided into a large number of cells of fixed size but of unknown susceptibility. Nonuniqueness of the solution is recognized and the algorithm produces a single model by minimizing an objective function of the model subject to fitting the data. Based on the second approach, Li and Oldenburg (1996) formed a multicomponent objective function that had the flexibility to generate different types of models. The objective function incorporates an optional reference model so that the constructed model is close to that. It penalizes roughness in three spatial directions, and it has a depth weighting designed to distribute the susceptibility with depth. Because there is no depth resolution inherent in the magnetic field data, the recovered model is occurred near the surface and takes away from its original position. The depth weighting function helps to locate the recovered model in its real position. Li and Oldenburg (1996, 2000) proposed relations for the depth weighting function. Additional 3-D weighting functions in the objective function can be used to incorporate further information about the model. The user can incorporate other information about the inversion model. The information might be available from othergeophysical surveys, geological data, or the interpreter’s qualitative or quantitative understanding of the geologic structure and its relation to the magnetic susceptibility.In principle, this algorithm can be applied to large-scale data. Numerically, however,the computational complexity increases rapidly with the increasing size of the problemand the solution of a large-scale inversion of magnetic data is faced with two majorobstacles. The first one is the large amount of computer memory required for storing thesensitivity matrix. And the second obstacle is the large amount of CPU time required forthe application of the dense sensitivity matrix to vectors. These two factors directly limitthe size of practically solvable problems. To encounter these obstacles, Li and Oldenburg(2003) used the fast wavelet transform along with thresholding the small waveletcoefficients to form a sparse representation of the sensitivity matrix. The reduced size ofthe resultant matrix allows the solution of large problems that are otherwise intractable.The compressed matrix is used to carry out fast forward modeling by performing matrixvector multiplications in the wavelet domain.The algorithm used in this study is based on the mentioned multicomponent objectivefunction and the fast wavelet transform is used to make a sparse representation of thesensitivity matrix to reduce the time and computer memory required for inversion.

One of the most important parameters in the interpretation of gravity data is the depth to the center or top of the buried body. In this study, the interpretation of gravity anomalies of spherical and cylindrical models is examined using the modified Hilbert transform. The Hilbert transform of a real function f(x) is defined as: 0 H (x) 1 [IF()cos(x) RF()sin(x)]d, where RF(ω) and FI(ω) are the real and imaginary component of the Fourier transform of f(x).The Hilbert transform defined by Eq.(1) is a mathematical operation which shifts thephase of a function by 90° without changing its amplitude.Modified Hilbert transform is identical in amplitude with the conventional Hilbert transform but differs in phase as it yields a phase shift of 270°. Modified Hilbert transform, MH(x), can be obtained from Hilbert transform H(x) by replacing x with –x in Eq.(1) (Shriniivas 2000; Sundararajan et al 2000), i.e, MH(x)  [IF() cos(x)  RF()sin(x)]d. The general gravity effect caused by simple models such as horizontal circular cylinderand sphere, centered at x=0 and buried at a depth z is given by (Abdelrahman et al 2001): 2 2 (), ()q g x Az x z where q is shape factor and depends on the nature of the source, and is 3/2, for a sphere and 1, for a horizontal cylinder. And A is amplitude factor given by: 4GR3, for a sphere and 2GR2 for a horizontal cylinder, where ρ is the density contrast, G is the universal gravitational contrast and R is the radius.The application of the method is examined using noise free and noise corrupted syntheticgravity data created for spherical and cylindrical models with a density contrast of 1 and1.5g/cm3 respectively. The gravity anomaly g(x), modified Hilbert transform MH(x),along a profile at an interval of 1m are computed for both data sets. The procedure hasbeen tested for several models at different dephts and radii, for three of which the results are presented here. It is observed that the depth to the origin of the gravity anomaly can be computed as a function of the intersection point of gravity anomaly g(x) and its modified Hilbert transform MH(x).The effect of random noise on the models shows that even by including up to 16%random noise, interpretational values do not differ significantly from thoes of the noisefree case. Hence the effect of noise is negligible on the procedure.To illustrate the applicability of the method two field examples from “Abade” in Farsprovince and “Havasan” in Ilam province, Iran, are also included. A Scintrex CG3gravimeter with a sensitivity of 5 microGal was used for micro-gravity observations inthe selected areas. Station altitudes were measured with a total station model Leica Tc407 with an accuracy of 1-5mm in horizontal and vertical coordinates. The residualgravity grids of were obtained obtained using Geosoft software.To demonstrate the reliability of the proposed method, the Euler de-convolution methodis used to detect the depth of the real gravity anomalies. The results from theinterpretation of real data by modified Hilbert transform method are compared to the ones obtained from the Euler de-convolution method and the known depth values from drilling information.

The magnetic method is a common tool in mining exploration, engineering geology andoil exploration. Depth estimation of potential field anomalies is an important step in the interpretation of the potential field data. There are various methods for depth estimation,which act in a space or wavenumber domain. Euler deconvolution is an automatic andconventional space-domain based method for depth estimation. The success of this approach depends on the choice of the two parameters, i.e. structural index and windowlength. Nowadays, wavelet transform is frequently used in geophysical data processingand interpretation. Cooper (2006) used the continuous wavelet transform of the derivative of the potential field data to estimate the depth of the potential source. This method is a qualitative approach and gives an estimate of the source depth by calculation of the similarity between the potential field data and the wavelet at different depths.The Spector and Grant method is a common approach which acts on the wavenumberdomain. Their method is based on the correlation between the wavenumber and anomalydepth. In this method, the depth of the anomaly can be estimated from the slope of thecurve fitted to the logarithm of the potential field data power spectrum. In the Spector and Grant method the power spectrum of the potential field data is calculated by a standard Fourier transform. Fourier analysis has provided important visions into the interpretation of both local and regional effect. However, there is an intrinsic disadvantage in Fourier transform the kernel of Fourier transform is a sinusoidal function extended on the whole potential filed data interval, so that it uses global oscillations to analyze local ones. Due to its global approach, the Fourier power spectral density is inherently nonlocalized in space.In this study, we used the continuous wavelet transform of the potential field data tocompute the power spectral density of data. From a mathematical point of view, thecontinuous wavelet transform analysis does not use a global-space sinusoidal function buta space-wavenumber localized function called space-wavenumber wavelet. Unlike theFourier analysis, the wavelet transform uses different wavelets and the success of theanalysis often depends on the appropriate choice of the analyzing wavelet. We used theMorlet wavelet, due to its similarity with the potential filed data. The Morlet powerspectral density is smoother than that of standard Fourier analysis and it can separate thetwo lateral and vertical anomalies.The efficiency of this method is evaluated by applying it to both synthetic and realmagnetic data. Synthetic models are considered with and without noise. The results of the synthetic example show that the space-wavenumber depth estimation method results in a more desirable estimation than the standard Fourier power spectral density. We use the mentioned methods to estimate the depth of the iron deposit of Ojat Abad located in the south of the Semnan-Damghan road.

The El Niño-Southern Oscillation (ENSO) is strongly connected to the inter-annual tointer-seasonal variations of Sea Surface Temperature (SST) over the Pacific Oceanequators. On the other hand, the Decadal Pacific Oscillation (PDO) is related to neardecadal fluctuations of the Pacific SSTs in the northeastern parts of the ocean. Theinfluence of these oscillations on the global climate is generally more obvious when theENSO or PDO is in its extreme condition. For such circumstances, the SST anomaliesover a per-defined Ocean waters are highly positive or negative (positive or negativephase, respectively).The present study has made an effort to analyze the individual and the coupled effectsof the ENSO or PDO on the occurrence of the autumnal dry or wet periods in southernparts of Iran for the period 1951-2005. Regional maps of precipitation and vector windwere also produced to extend the outcome of the present study for the Middle Easteregion. Total precipitation during the October-December period was collected for 30 raingauge stations spread in various parts of southern Iran. In addition to precipitation,monthly values of the October-December SST anomalies over the Niño 3.4 region werealso extracted from the webpage of the National Oceanic and AtmosphericAdministration (NOAA). These monthly data were then averaged to three monthly(seasonal) records that were used as the ENSO indicator. Years related to the rank 1 to 18 and 37 to 55 (18 years each) were registered as the ENSO negative (El Niño) and positive (La Niña) phases, respectively. A similar procedure was also used to detect 18 years of the negative or positive phase of the PDO. The events that El Niño or La Niña years were coincided with the positive or negative phase of the PDO were then investigated. It was found that out of 18 years of La Nina, for 10 or 7 years, the PDO was in its negative (La- LPDO) or positive phase (La-HPDO), respectively. Similarly, out of 18 years of El Niño, the PDO was in its positive (El-HPDO) or negative (El-LPDO) phase for 8 and 5 years.For each individual station, mean precipitation for the El Niño, La Niña events as well asfor the opposite phases of the PDO were examined. Furthermore, the autumnalprecipitation was also investigated and compared for the La-LPDO, La-HPDO, El-LPDO,El-HPDO events.In addition to the rain-gauge data, the regional maps of precipitation and 850 hPa vectorwind anomalies were also produced using the http://www.esrl.noaa.gov/psd/cgibin/data/composites/printpage.pl webpage. These maps were generated for the oppositephases of ENSO, PDO and for the La-LPDO and El-LPDO periods. The GrADS softwarewas then used to overlay the produced maps of precipitation and the 850-hPa vector wind.The interpretation of these overlaid maps was found to be an efficient approach forunderstanding the impact of the considered tele-connections on the atmosphericcirculation and rain-bearing airflows.The results indicated that, for the southwestern parts of the country, precipitation hasbeen significantly suppressed or enhanced during the La Niña or El Niño event,respectively. This suppression or enhancement, however, was not significant for thesoutheastern districts. Although the above or below normal precipitation in the southernparts of Iran was generally coincided with the PDO positive or negative phase, the effectsof this oscillation on the precipitation variability were found to be significant forsoutheastern rather than southwestern parts of the country. In other words, while theprecipitation variability in the southwestern parts of the country is more sensitive to theENSO status, the PDO is more influential on the precipitation characteristics insoutheastern districts. The more dry or wet event was recognized as the periods that LaNiña or El Niño is, respectively, coincided with the negative or positive phase of the PDO(La-LPDO and El-HiPDO, respectively). For the La-LPDO events, the precipitationdeficiency was estimated as 68% to 100% for the southwestern and 37% to 67% for thesoutheastern districts. On the other hand, the occurrence of the El-HiPDO has enhancedthe autumnal precipitation by about 50% to 90% in the southwest and 30% to 50% in thesoutheast parts of Iran.According to the given results, ocurrence of the El Niño event intensifies the westerlyor southwesterly airflows which carry the Red Sea, Mediterranean Sea and Persian Gulfsmoistures to most parts of the Middle Eastern regions including most parts of Iran, Iraq,eastern coasts of the Mediterranean Sea, the Arabian Peninsula and Afghanistan.Furthermore, intensification of the near-surface easterly, southeasterly or southwesterlycirculation over northwestern parts of the Indian Ocean also pushes substantial amountsof water vapor to the Arabian Peninsula and southern parts of Iran for such spells. Thecharacteristics of atmospheric circulation during the PDO positive phase are mostlysimilar to that of the El Nino, though the latter is more vigorous than the former. Themost/least strengths of these moisture-laden circulations are associated with the El-HiPDO/La-LPDO epochs.

The deflection of vertical components, are the second order spatial derivatives ofthe gravity potential, efficiently counteract signal attenuation at the low andmedium frequencies. Regional gravimetric geoid and quasi-geoid models are now commonly fitted to GPS-leveling data, which simultaneously absorb GPS/leveling and quasi/geoid errors due to their inseparability. We propose that independent vertical deflections are used instead as they are not affected by this inseparability problem. The formulation is set out for geoid slopes and changes in slopes. In this research, 10 Laplace points form the Iranian astro-geodetic networks were utilized for calibration and combination of the EGM2008 and GOCE global geoid models. Several two-, three- and four-parameter- models were used as a correction surface for the combination and evaluation of the geoid models. The standard deviation of the deflection of vertical components before and after fitting in geoid models evaluated with independent data. The results showed a significant improvement in the N-S direction of the GOCE model from 0.095 to 0.003 and in the E-W direction of the EGM2008 model from 0.246 to 0.008. To sum up, the two-parameter models worked best among the other corrective surface models. Also, the EGM2008 model gave slightly better results versus the GOCE model. For any future researches, use of homogenous and high quality zenith-nadir digital camera data is strongly recommended.

Mountain waves are formed on the leeward side when a uniform and steady air flowimpinges a mountain. Unstable air and severe winds on the leeward side are hazardous tothe flight of aircrafts, change the distribution of aerosols, and cause damage to agricultural products. The purpose of this study is to examine the air flow over the entiremountain region using a two-dimensional analytical meso-scale model. The model wasrun for various conditions by changing one of the main factors or the number of mountainridges. These factors included Lyra parameter (c=2 U/N, where the initial state zonal flow U and buoyancy frequency N are both assumed to be constant), Froude number (Fr=c/2hm, where hm is the amplitude of the mountain ridge), height and width of mountains. For simplicity, we made many assumptions. The initial air flow on thewindward side was assumed to be stable, steady and frictionless with no rotation. Also,the horizontal temperature gradient and thereby the vertical wind shear for maintaining athermal wind balance are constant. These conditions cause the non-linear equations tobecome linear. By running the model, the Helmholtz equation is solved using the first andsecond Bessel equations and the horizontal wind which impacts the mountain nearly at aright angle is transformed to the Lyra parameter.Our results showed that all the factors mentioned above could substantially affect thecharacteristics of the air flow over the mountain ridge as well as at the leeward side. Inthis regard, streamlines as well as the horizontal and vertical components of the windwere investigated. For fixed height and width of a single mountain, the maximumamplitude of the streamlines and thereby the maximum upward motions were weakenedby increasing the Lyra parameter, whereas there was no specific change in the horizontalcomponent of the wind. Alternatively, for a fixed mountain height and the Lyraparameter, the maximum amplitude of the streamlines and the maximum horizontal windwere increased in the wide mountain ridge compared to the narrow one. Since streamlines tilted toward the west with height in the leeward side, the maximum upward motions were decreased somewhat. In the next experiment, for a fixed mountain width and the Lyra parameter, all the characteristics of the air flow in the leeward side (the maximum amplitude of streamlines and the maximum values of horizontal and vertical components of wind) were intensified largely when the mountain height was increased.In general, the effect of the mountain height on the characteristics of the air flowimpinging a mountain is the dominant one among the other factors. It can be mainly dueto the increase of streamline gradient in the windward side of the mountain. Extremelylarge surface and upper-level winds (horizontal and vertical components) were seen in allthe experiments. This is because the friction term has been neglected in the equations. In the real atmosphere, friction would moderate these winds quickly.Now consider a mountain associated with two ridges having equal heights. It isobserved that the existence of the second ridge leads to more intensification of thehorizontal and vertical components of the wind in the leeward side of the second ridge.Also, the lee cyclones produced by the wide ridges, especially over the second ridge,were more intense than those by the narrow ridges. The other noticeable point was thatthe more westward vertical tilt of streamlines in the wide ridges were associated withsmaller vertical motions, compared to the narrow ridges. This is because the verticalgradient of streamlines for the narrow ridges is much more than in the wide ridges. Butgenerally, the upward and downward motions became maxima in the downstream andupstream sides of the troughs, respectively.