برآورد تانسور گراديان گراني بر سطح زمين با استفاده از روش تفاضل محدود و تلفيق داده هاي جاذبي زميني با مدل هاي ژئوپتانسيل جهاني: مطالعه موردي در منطقه فارس ساحلي

On Gravity Gradient Tensor Determination Using Finite-Difference Method and Land-Based Gravity Data: A Case Study of Coastal Fars of Iran

تانسور گراديان گراني، ماتريسي مشتمل بر مشتقات مرتبه ­ي دوم گراني مي­باشد كه كاربردهاي فراواني درعلوم ژئودزي و ژئوفيزيك دارد. تا به امروز تلاش ­هاي زيادي براي اندازه­ گيري و برآورد تانسور گراديان گراني با دقت مناسب صورت گرفته است. اين كميت تانسوري از روش­هاي متنوعي قابل برآورد بوده كه يكي از اين روش­ها استفاده از مشاهدات ثقلي و به كارگيري روش تفاضل محدود است. روش تفاضل محدود با استفاده مستقيم از مفهوم رياضي تانسور گرايان، بدون در نظر گرفتن فرضيات اضافي كه ممكن است از واقعيت مسئله به دور باشد، ميتواند از نقطه نظر تئوري امكان برآورد صحيح تانسور گراديان گراني را فراهم آورد. در اين مطالعه، تانسور گراديان با استفاده از داده­هاي جاذبي زميني و روش تفاضل محدود فرموله و تعيين شده است. در اين مقاله، روابط پيشنهادي به صورت عددي با استفاده از يك مدل جاذبي جهاني زمين مورد آزمايش قرار ميگيرد و سپس از اين روش، جهت برآورد تانسور گراديان گراني در 6350 ايستگاه ثقلي در منطقه ­ي فارس ساحلي در جنوب ايران، استفاده ميگردد. آزمايش هاي عددي اين تحقيق نشان از توانايي روش در برآورد مولفههاي تانسور گراديان گراني با دقت مناسب ميباشد. به عنوان مثال در آزمايش هاي عددي ديده ميشود كه روش پيشنهادي اين تحقيق امكان برآورد مولفههاي قطري تانسور گراديان (به عبارتي مشتقات دوم گراني در جهتهاي شرق، شمال و قائم) را با دقتهايي به ترتيب برابر با 12.46، 34.49 و 454.82 اتووش فرآهم نموده است.

Gravity gradient tensor is a matrix containing the second order derivatives of the Earth’s gravity field, which has numerous applications in geodesy and geophysics. To date, much effort has been done for estimating gravity gradient tensor with reasonable accuracy. This quantity can be estimated via using various methods, and one of these methods is applying finite-difference method to gravity observations. Finite-difference method can estimate gravity gradient tensor directly by using the mathematical concept of gradient, regardless of extra assumptions. This ability of finite-difference method, from theoretical point of view, provides the possibility of accurate estimation of gravity gradient tensor without considering additional assumptions to the problem. This study tends to introduce and evaluate Finite difference method for estimating the gradient tensor and present formulae for determining gravity gradient tensor from land-based gravity observations. In this paper, the proposed equations are numerically tested by means of using a global gravity model of the earth. Global gravity model of the earth (EGM 2008) is a geopotential model of the earth consisting of spherical harmonic coefficients up to degree 2190 and order 2159. There are numerous uses for these high degree potential coefficient models. One of these uses is modeling and estimating gravity gradient tensor. Finally, gravity gradient tensor is estimated by the proposed method for 6350 gravity stations located in Costal Fars region in a northern part of the Persian Gulf, between the latitudes from 26.5 N to 27.27 N and longitudes from 53.41 E to 55.58 E. The target area is about 10000 square kilometers. About 8500 square kilometers of the study area is located in moderate mountainous regions, and about 1500 square kilometers is located in flat coastal areas. The altitudinal distribution and spatial distribution of gravity in study area are shown in figure 1 and 2 respectively. Numerical experiments of this study demonstrate the ability of this method in gravity gradient tensor estimation with acceptable accuracy. For example, numerical experiments showed that the proposed method can estimate diagonal components of gravity gradient tensor (second order derivatives of the Earth’s gravity field in east, north and vertical directions) with the accuracy values of 12.46, 34.49 and 454.82 Eotvos respectively. The spatial distribution of the gravity gradient tensor components obtained from finite difference method in study area are shown in figure 3. Finally, according to the theoretical concepts discussed in this paper, It can be said because the finite difference method using from derivative and difference concepts directly for estimating gravity gradient tensor, it is expected that this method provide accurate estimation of gravity gradient tensor, As this is happen in the simulation conducted. However the accuracy of this method is very dependent on distances between sampling stations and by reducing distance between the stations, the accuracy of proposed method will be increased. The numerical results of this study also showed that the proposed method can provide accurately estimate of gravity gradient tensor components In some stations surrounded by suitable spatial distribution of gravitational observations.