Abstract
Field derivatives are essential tools for interpretation of gravity and magnetic data. Several qualitative methods employ high-order derivatives or combine them with functions that equalize amplitude to produce sharper anomaly maps, but often suffer from noise amplification. We propose a finite-difference formula based on upward continuation that provides a robust approximation of the vertical derivative of potential fields. Unlike previous approaches, the formula involves only upward-continued data, which makes it less sensitive to noise, but approximates the vertical derivative at the original data altitude. We show through experiments with synthetic and field magnetic data that the proposed approximation improves the computation of edge-detection enhancement filters and performs better than separately applying finite differences and upward continuation.
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Acknowledgements
The contribution of our reviewers was crucial to render this work more clear and interesting to the readership. SO thanks Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), under Grant 316376/2021-3.
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Both authors have contributed to the conceptualization of this research and computer implementation of the methods. SO worked on the mathematical theory and manuscript preparation. LP carried out the data selection and discussion.
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Oliveira, S.P., Pham, L.T. A Stable Finite Difference Method Based on Upward Continuation to Evaluate Vertical Derivatives of Potential Field Data. Pure Appl. Geophys. 179, 4555–4566 (2022). https://doi.org/10.1007/s00024-022-03164-z
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DOI: https://doi.org/10.1007/s00024-022-03164-z