Principal component analysis for filtering and leveling of geophysical data

• We investigate the application of multivariate statistical methods for filtering.
• We propose computationally efficient algorithms to calculate multivariate statistics.
• Moving window approach and PCA are used to derive the generic PCA-based filter.
• Spatial PCA-based filters are constructed and applied for airborne data leveling.

In this study, we investigate the use of multivariate statistical methods for geophysical data filtering. For this purpose, a measured scalar field is vectorized using a moving window technique and mean vector and covariance matrix are calculated by employing memory-efficient numerical algorithms. These multivariate statistics are then used to conduct principal component analysis (PCA). Namely, covariance matrix is decomposed into a set of eigenvalues and eigenvectors. By selecting a subset of eigenvectors, a PCA-based filter is realized. We demonstrate how properties of the filter are determined by the chosen subset of the eigenvectors, which in turn depend on spectrospatial properties of the field. In particular, we presented approaches to construct low-pass and spatial directional PCA-based filters. As an application, we aim at suppressing leveling errors commonly occurring in airborne data sets. The devised PCA filter was analyzed using a real aeromagnetic data set and synthetic leveling errors. The scenarios of statistically dependent and independent leveling errors were studied. Finally, we successfully applied it to real aero-electromagnetic data leveling.