On the practical implementation of the enhanced horizontal derivative filter for potential field data

Saulo Pomponet OLIVEIRA; Alessandra de Barros e Silva BONGIOLO; Luan Thanh PHAM; Luís Gustavo DE CASTRO; Vinicius Theobaldo JORGE

doi:10.31577/congeo.2023.53.4.1

Saulo Pomponet OLIVEIRA Federal University of Paraná, Department of Mathematics, Curitiba, Brazil
Alessandra de Barros e Silva BONGIOLO Federal University of Paraná, Graduate Program in Geology, Curitiba, Brazil
Luan Thanh PHAM University of Science, Vietnam National University, Hanoi, Vietnam
Luís Gustavo DE CASTRO Federal University of Paraná, Graduate Program in Geology, Curitiba, Brazil
Vinicius Theobaldo JORGE Federal University of Paraná, Graduate Program in Geology, Curitiba, Brazil

DOI: https://doi.org/10.31577/congeo.2023.53.4.1

Keywords: gravimetry, magnetometry, enhanced horizontal derivative

Abstract

The enhanced horizontal derivative (EHD) is an enhancement filter whose maxima provide estimated locations of the sources' boundaries. This filter is defined as the total horizontal derivative (THDR) of a weighted sum of vertical derivatives of increasing order. We consider some aspects of the practical implementation of the EHD filter, especially its robustness. A slightly different version of EHD, which we refer to as mEHD, is obtained when we switch the order of THDR and the weighted sum; that is, when we consider the weighted sum of total horizontal derivatives of the successive vertical derivatives. It turns out that mEHD can be more stable and provide a clearer enhanced map than the original filter, as demonstrated with examples of synthetic data and aeromagnetic data from Southern Brazil. Moreover, we address the choice of the weighting coefficients of the vertical derivatives, emphasizing that the standard choice of unitary weights may not be the most appropriate one. The enhanced horizontal derivative (EHD) is an enhancement filter whose maxima provide estimated locations of the sources' boundaries. This filter is defined as the total horizontal derivative (THDR) of a weighted sum of vertical derivatives of increasing order. We consider some aspects of the practical implementation of the EHD filter, especially its robustness. A slightly different version of EHD, which we refer to as mEHD, is obtained when we switch the order of THDR and the weighted sum; that is, when we consider the weighted sum of total horizontal derivatives of the successive vertical derivatives. It turns out that mEHD can be more stable and provide a clearer enhanced map than the original filter, as demonstrated with examples of synthetic data and aeromagnetic data from Southern Brazil.