Fast iterative equivalent-layer technique for gravity data processing: A method grounded on excess mass constraint

Abstract

We have developed a new 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 mass distribution that is proportional to the observed gravity data. Iteratively, our approach updates the mass distribution by adding mass corrections that are proportional to the gravity residuals. At each iteration, the computation of the residual is accomplished by the forward modeling of the vertical component of the gravitational attraction produced by all point masses setting up the equivalent layer. Our method is grounded on the excess of mass and on the positive correlation between the observed gravity data and the masses on the equivalent layer. Mathematically, the algorithm is formulated as an iterative least-squares method that requires neither matrix multiplications nor the solution of linear systems, leading to the processing of large data sets. The time spent on the forward modeling accounts for much of the total computation time, but this modeling demands a small computational effort. We numerically prove the stability of our method by comparing our solution with the one obtained via the classic 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 the Green’s functions associated with the desired processing by the estimated mass distribution. We have applied the proposed method to interpolate, calculate the horizontal components, and continue gravity data upward (or downward). Testing on field data from the Vinton salt dome, Louisiana, USA, confirms the potential of our approach in processing large gravity data set over on undulating surface.