Producing Gravity Acceleration at Sea Surface in Persian Gulf Using Ellipsoidal Splines

In this paper, a method is proposed for producing gravity acceleration at sea surface in the Persian Gulf. This method is based on the Geoid height from satellite altimetry, high resolution Geopotential models, and ellipsoidal splines. First, the definition of the ellipsoidal spline functions is presented in a Hilbert space, which is consisted of infinitely often differentiable functions. In order to define the elipsoidal spline functions, the norm of the differential operators, including the Beltrami and Helmholtz in both the simple and iterated form, are minimized. In this respect, the reproducing kernels and the Green functions play an important role. The derived formulae are used to produce gravity acceleration at sea surface.  To perform this method, the Geoid height, derived from satellite altimetry, is transformed into potential residual by Bruns formula. Then, the actual potential is derived by adding the Geoid’s potential to the potential residuals. To obtain potential difference values,  the effect of the reference field is subtracted from the actual potential values. By using ellipsoidal splines, the potential difference values are interpolated, which represent an analytical formula.  By using the gradient of the analytical formula, we arrive at the gravity difference values. The removed effect of the reference field is added to the gravity difference values to obtain the gravity accelerations by adding the gravity values of a Geopotential model up to the degree and order 360, plus the centrifugal force. In the final step, the obtained gravity accelerations are moved to the sea surface using free air correction. A comparison between ellipsoidal and spherical splines is also presented.