Cálculo do sinal gravimétrico de um prisma com variação vertical de contraste de densidade para qualquer posição no espaço 3D - QUARESMA, André Luiz Lobato (2018)
We have developed an effective and computationally efficient alternative to the calculation, at any position of the space, of the vertical component of the gravimetric anomaly produced by a rectangular prism in which the density increases with the depth according to a parabolic law. It is found in literature analytical/algorithmic solution for this calculation that cannot be evaluated if the height of the observation point is lower than the height of the top of the prism. To run through this limitation, we evaluated this anomaly as the sum of the anomaly produced by two prisms vertically stacked, that being overlapped have the same size of the original prism, and they are positioned one above and another below of the observation point. However, this double evaluation is computationally expansive. To make the solution more computationally efficient, we considered valid the equality approach between the gravimetric signal produced by the prism above the observation point and the signal of a compensation prism located below of the observation point, which has the same mass of the prism above. We have deduced the closed expression of the compensation prism size, and this solution is not computationally expansive. So, at the end we evaluated only the gravimetric anomaly of one prism, the prism that rest after the compensation. However, this parity between the gravimetric signal of the top prism and the compensation prism is only numerically valid for observations positions from a certain horizontal distance of the original prism. We performed synthetic tests for the calculation of the gravimetric anomaly of one prism positioning the observations in different positions of the three-dimensional space around the prism, evaluating the solutions we propose and those presented in the literature. We also performed the synthetic simulation of the gravimetric anomaly of a sedimentary basin with terrestrial observations accompanying the topography of the basin and, thus, many points have lower heights than some portions of the basin.