Simultaneous potential field data interpolation, border padding, and denoising via projection onto convex sets algorithm

摘要

Gravity and magnetic measurement data often contain gaps and significant noise interference and must therefore be interpolated and border-padded prior to processing and transformation in the wavenumber domain. The primary cause of much processing and transformation instability is high-frequency noise interference. Conventional processing methods generally perform interpolation, border-padding, and denoising independently; in this study, we apply a unified approach to implement these three tasks and propose an iterative method for applying them based on the projection onto a convex sets method. The proposed iterative method first fills the vacancies and border of the original potential field data with zeros and determines a final cutoff wavenumber for the iteration by applying fractal model fits of the radial average power spectrum of the zero-padding data. The iteration steps are then performed by applying a simple ideal low-pass filter in the wavenumber domain until the predetermined iteration number is attained. Numerical examples involving synthetic gravity and real aeromagnetic data demonstrate that the proposed iterative method is simple in principle, easy to carry out, and has a high interpolation and denoising accuracy with smooth and distortion-free interfaces between the interpolation and border-padding results. The proposed method has evident advantages in terms of precision and speed relative to classical interpolation-based border padding, denoising, and combined methods. (C) 2020 Elsevier B.V. All rights reserved.