Stable Computation of the Vertical Gradient of Potential Field Data Based on Incorporating the Smoothing Filters
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The vertical gradient is an essential tool in interpretation algorithms. It is also the primary enhancement technique to improve the resolution of measured gravity and magnetic field data, since it has higher sensitivity to changes in physical properties (density or susceptibility) of the subsurface structures than the measured field. If the field derivatives are not directly measured with the gradiometers, they can be calculated from the collected gravity or magnetic data using numerical methods such as those based on fast Fourier transform technique. The gradients behave similar to high-pass filters and enhance the short-wavelength anomalies which may be associated with either small-shallow sources or high-frequency noise content in data, and their numerical computation is susceptible to suffer from amplification of noise. This behaviour can adversely affect the stability of the derivatives in the presence of even a small level of the noise and consequently limit their application to interpretation methods. Adding a smoothing term to the conventional formulation of calculating the vertical gradient in Fourier domain can improve the stability of numerical differentiation of the field. In this paper, we propose a strategy in which the overall efficiency of the classical algorithm in Fourier domain is improved by incorporating two different smoothing filters. For smoothing term, a simple qualitative procedure based on the upward continuation of the field to a higher altitude is introduced to estimate the related parameters which are called regularization parameter and cut-off wavenumber in the corresponding filters. The efficiency of these new approaches is validated by computing the first- and second-order derivatives of noise-corrupted synthetic data sets and then comparing the results with the true ones. The filtered and unfiltered vertical gradients are incorporated into the extended Euler deconvolution to estimate the depth and structural index of a magnetic sphere, hence, quantitatively evaluating the methods. In the real case, the described algorithms are used to enhance a portion of aeromagnetic data acquired in Mackenzie Corridor, Northern Mainland, Canada.
KeywordsPotential field magnetic data vertical gradient fast Fourier transform enhancement wavenumber extended Euler deconvolution
We would like to thank the Editor, Hans-Jürgen Götze, and the reviewers Giovanni Florio and Roman Pašteka for their thoughtful comments and criticisms which helped us to improve the original manuscript. The Geological Survey of Canada is appreciated to permit to use the aeromagnetic data set. This research was supported by grants from the NSF of China and Hubei Province (Nos. 41604087, 2016CFB122), the China Postdoctoral Science Foundation (No. 2016M590132), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGL170407, CUG160609).
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