# PhD thesis: Otimização Computacional do Método da Camada Equivalente

## Abstract

We have developed an iterative scheme for processing gravity data using a fast equivalent-layer technique. This scheme estimates a 2D mass distribution on a fictitious layer located below the observation surface and with finite horizontal dimensions composed by a set of point masses, one directly beneath each gravity station. Our method starts from an initial approximation to a mass distribution that is proportional to the measured vertical component of gravity attraction. Iteratively, our approach updates the mass distribution by adding mass corrections that is proportional to the gravity residual. At each iteration, the computation of the residual is accomplished by the forward modelling of the vertical component of the gravity attraction produced by the set of point masses. Our method is grounded on the Gauss's theorem and on the positive correlation between the vertical component of the gravity attraction and the masses on the equivalent layer. Mathematically, the algorithm can be formulated as an iteratively least-squares method. However, in practice, it requires neither matrix multiplications nor the solution of linear systems, leading to a computational efficiency that allows a rapid processing of large data sets. The time spent on forward modelling accounts for the much of the total computation time; but this modelling demands a low computational effort. We numerically prove the stability of our method by comparing our solution with the one obtained via the classical equivalent-layer technique with the zeroth-order Tikhonov regularization. After estimating the mass distribution, we obtain a desired processed data by multiplying the matrix of Green's functions associated with the desired processed by the estimated mass distribution. We have applied the proposed method to interpolate, to calculate the horizontal components and to continue the gravity data upward (or downward). Furthermore, we calculate the six components of Full Tensor Gradiometry (FTG) by the product of the Green matrix associated with each component to the estimated mass distribution on the layer. We test our method with synthetic data and real data from the Vinton salt dome, LA, USA, confirm the potential of our approach in processing large gravity data set over on undulating surface.