In near-surface geophysics, ground-based mapping surveys are routinely employed in a variety of applications including those from archaeology, civil engineering, hydrology, and soil science. The resulting geophysical anomaly maps of, for example, magnetic or electrical parameters are usually interpreted to laterally delineate subsurface structures such as those related to the remains of past human activities, subsurface utilities and other installations, hydrological properties, or different soil types. To ease the interpretation of such data sets, we propose a multi-scale processing, analysis, and visualization strategy. Our approach relies on a discrete redundant wavelet transform (RWT) implemented using cubic-spline filters and the à trous algorithm, which allows to efficiently compute a multi-scale decomposition of 2D data using a series of 1D convolutions. The basic idea of the approach is presented using a synthetic test image, while our archaeo-geophysical case study from North-East Germany demonstrates its potential to analyze and process rather typical geophysical anomaly maps including magnetic and topographic data. Our vertical-gradient magnetic data show amplitude variations over several orders of magnitude, complex anomaly patterns at various spatial scales, and typical noise patterns, while our topographic data show a distinct hill structure superimposed by a microtopographic stripe pattern and random noise. Our results demonstrate that the RWT approach is capable to successfully separate these components and that selected wavelet planes can be scaled and combined so that the reconstructed images allow for a detailed, multi-scale structural interpretation also using integrated visualizations of magnetic and topographic data. Because our analysis approach is straightforward to implement without laborious parameter testing and tuning, computationally efficient, and easily adaptable to other geophysical data sets, we believe that it can help to rapidly analyze and interpret different geophysical mapping data collected to address a variety of near-surface applications from engineering practice and research.
Fast algorithms using minimal data structures for common topological relationships in large, irregularly spaced topographic data sets