ارزیابی مولفه های زاویه انحراف قائم حاصل از تلفیق مدل ژئوپتانسیلی جهانی و مدل رقومی زمین در ایران

در حال حاضر بالاترین قدرت تفکیک مکانی مدل‌های ژئوپتانسیلی جهانی حدود 5 دقیقه می‌باشد، در حالی که مدل‌های توپوگرافی با قدرت تفکیک مکانی حدود 3 ثانیه و بالاتر در دسترس است. یکی از روش‌هایی که برای افزایش دقت مدل‌های ژئوپتانسیلی جهانی در تولید تابعک‌های مختلف میدان ثقل مورد استفاده قرار می‌گیرد، تلفیق این مدل‌ها با مدل‌های توپوگرافی با قدرت تفکیک مکانی بالاتر از مدل ژئوپتانسیلی است. در این مقاله هدف ارزیابی مولفه‌های زاویه انحراف قائم حاصل از تلفیق مدل ژئوپتانسیلی جهانی و مدل توپوگرافی با قدرت تفکیک مکانی بالا در ایران می‌باشد. تحقیق حاضر، از مدل egm2008 با قدرت تقکیک مکانی حدود 5 دقیقه به عنوان مدل ژئوپتانسیلی جهانی، از مدل srtm با قدرت تفکیک مکانی 3 ثانیه به عنوان مدل توپوگرافی و از مدل dtm2006 برحسب هارمونیک‌های کروی تا درجه 2190 به عنوان سطح هموار مرجع برای تولید مدل توپوگرافی باقیمانده (rtm) استفاده نموده است. روش تحقیق به این صورت است که ابتدا با استفاده از مدل جهانی، مولفه‌های زاویه انحراف قائم در 10 ایستگاه لاپلاس ایران محاسبه شده و سپس با استفاده از مدل توپوگرافی باقیمانده تصحیحی برای این مولفه‌ها بدست می‌آید. در پایان مولفه‌های زاویه انحراف قائم محاسبه شده توسط مدل جهانی به تنهایی و تلفیق مدل جهانی و مدل توپوگرافی باقیمانده با مولفه‌های زاویه انحراف قائم حاصل از مشاهدات نجومی و ژئودتیکی در 10 ایستگاه لاپلاس مقایسه می‌شوند. نتایج این مقایسه‌ها حاکی از آن است که تلفیق مدل جهانی egm2008 و rtm باعث بهبود حدود 15% در مولفه شمالی-جنوبی(𝜉)  و 1.4% بهبود در مولفه شرقیغربی(𝜂)در منطقه تست ایران می‌گردد.همچنین ارزیابی‌ها نشان می‌دهند که خطای نسبی در محاسبه مولفه𝜉 با استفاده از تلفیق مدل egm2008 و rtm حدود 6% و در محاسبه مولفه 𝜂 حدود 37% است.

Assessment of vertical deflection derived from a combination of Global Geopotential Model and Digital Terrain Model in Iran

IntroductionComponents of verticaldeflection, i.e., NorthSouth component  and EastWest component ,are used for accurate determination of geoid or quasigeoid. Moreover, vertical deflection components area useful source for determination of variations in subsurface density and geophysical interpretations. Generally, there are two definitions for verticaldeflection. According to Helmert definition, vertical deflection at any given pointis the angle between the actualgravity vector (actual plumb line) and a line that is normal to the reference ellipsoid(a straight line perpendicular to the surface of reference ellipsoid). Another definition of vertical deflection is proposed by Molodensky. According this definition, vertical deflection at any given point is the angle between actualgravity vector and normal gravity vector (normal plumb line). Some relations have been introduced to convert Molodensky vertical deflection to Helmert vertical deflection. Helmert vertical deflection is estimated using astrogeodetic observations (combination of astronomical and geodetic observations).Presently, global geopotential models (GGMs) have been expanded to the degree of2190, which is equivalenttoabout 5min spatial resolution. Vertical deflectionat any point on the Earth can be calculated using the GGM. The resulting vertical deflection is consistent with Molodensky definition.Unfortunately, accuracy of GGMs is not sufficient for estimation of verticaldeflection.In other words, since GGMs are expanded up to a limited degree due to their resolution, omission error(or truncation error) occurs in computation of the earth’s various gravity field functionals, such as the geoidal height and verticaldeflection. Combining GGM with a digital terrain model (DTM) is a method used to reduce omission error.It should be noted that DTM has a higher spatial resolution as compared to GGM.In this method, the omitted signals of GGM can be modeled using residual terrain model (RTM) derived from subtracting high resolution DTM from a reference smooth surface. The reference smooth surface is obtained from eitherapplying average operator to DTM or expanding global topography into spherical harmonics. Fortunately, DTMs with spatial resolution of 3seconds or more,and reference smooth surface based on 2190 degree spherical harmonics are publicly available.The present study seeks to assess vertical deflectionderived from a combination of GGM and DTM in Iran. Previously, Jekeli(1999) has studied EGM96 geopotential model with the aim of computingvertical deflection in the USA. Hirt(2010) and Hirt et al. (2010a) have assessed vertical deflection in Europe and the Alps using a combination of EGM2008 and RTM models.In Iran, GO_CONS_GCF_2_TIM_R4, a GOCEonly model, and EGM2008 geopotential model have been used toobtain vertical deflection and the results have been evaluated byKiamehr and ChavoshiNezhad(2014). Materials & MethodsTo implement the present study,a EGM2008 model with a spatial resolution of about 5min is selected asGGM and a SRTM model with 3sec spatial resolution is considered as DTM. To obtain RTM, DTM2006 model based on2190 degree spherical harmonicsis selected as the reference smooth surface.To compute the residual topography effect, prism method was used in an ellipsoidalmulticylindrical equalarea map projection system. First, we compute vertical deflectionusing EGM2008 model. It is also calculated using a combination of EGM2008 model and RTM(EGM2008/RTM method). In the next step, vertical deflection derived from the first method (EGM2008 model) and the second one (combination of EGM2008 model and RTM) are compared with vertical deflectionderived from astrogeodetic observations in 10 available Laplace stations in Iran. Results & DiscussionResults indicate that there is a 1.2sec difference between NorthSouth component of vertical deflection (i.e.) obtained from EGM2008 model and astrogeodetic observations.With RTM, this will reach 1 sec, which shows a 15% improvement. Moreover, there is a5.7secdifference between EastWest component of vertical deflection () obtained from EGM2008 model and astrogeodetic observations, while this value will reach 5.6sec using RTM. Improvement in EastWest component () is1.4%, which is smaller than the improvement of NorthSouth component (). Based on the computations, we found that values of  and  in the Laplace stations canreach 17sec (RMS=7sec) and 15sec (RMS=8sec), respectively. Therefore, it is concluded that the relative error ofNorthSouth component ()computation using EGM2008/RTM method is about 6% and the relative error ofEastWest component ()computation is about 37%. ConclusionThe present research has studied the RTM effect on the improvement of GGM used for the determination of vertical deflectionin Iran. To performthe study, EGM2008 model with around 5min spatial resolution was selected as GGM. RTM is also derived from subtracting the DTM2006 model (based on2190 degree spherical harmonics)from the 3sec spatial resolutionSRTM model. Numerical findings indicate that a combination of RTM and GGM can improve the results of vertical deflectioncomputation, as compared to the results obtained from GGMonly approach. The improvement in NorthSouth component of vertical deflection () is about15%and EastWest component of the vertical deflection () undergoes about 1.4% improvement. In general, EGM2008 model and its combination with RTM have been more successful in the computation of  component as compared to computationin the geographical region of Iran. There is no clear explanation for this difference, but it can be due to errors in theastronomical or geodetic observations oflongitude in Laplace stations.