Exemplo de bom condicionamento inconveniente causado numericamente na inversão gravimétrica para a estimação das densidades de uma camada

Abstract

A well-conditioned sensitivity matrix can be inconvenient for estimating densities of a layer? We found an example of this inconvenience numerically caused in the gravimetric inversion when the horizontal dimensions of the elementary sources that make up the interpretive model are very small. Amazingly in this case a gravity inversion to obtain the equivalent layer is not effective and does not fit the data. We found that in this case the well-conditioning of the sensitivity matrix occurs simultaneously with low singular values. This feature of the sensitivity matrix leads to severe loss of resolution and leads to biased estimates and very smooth. It happens that part of the resolution would be mathematically possible to be obtained is lost due to this phenomenon numerical computational degradation of the sensitivity matrix . We present a procedure for repayment of the resolution for mapping the density distribution of a layer, which enables new perspectives on gravimetric applications, including environmental studies. We skirted the numerical problem with a semi-heuristic approach which extends the horizontal dimensions of the elementary sources and subsequently corrects the estimates. We obtained with this new procedure in synthetic tests the distribution of the density contrast outlining lateral contacts between regions of different density contrasts, which would only be possible to recover elemental sources larger. We apply this methodology to the dataset of the Thomas Farm landfill site landfill.