A review of spectral analysis of magnetic data for depth estimation

Spectral analysis has been used for studying a variety of geologic structures and processes, such as estimation of the depth to the crystalline basement or estimation of the Curie temperature isotherm from magnetic anomalies. However, the analysis is not standard because it refers to different theoretical frameworks, such as statistical ensembles of homogeneous sources and uncorrelated or fractal randomly distributed sources. We have aimed to unify the approaches by reformulating all of the common spectral expressions in the form of a product between a depth-dependent exponential factor and a factor, which we call the spectral correction factor, that incorporates all of the a priori assumptions for each method. This type of organization might be useful for practitioners to quickly select the most appropriate method for a given study area. We also establish a new formula for extending the Spector and Grant method to the centroid depth estimation. Practical constraints on the depth estimation and intrinsic assumptions/limitations of the different approaches are examined by generating synthetic data of homogeneous ensemble sources as well as random and fractal models. We address the statistical uncertainty of depth estimates using ordinary error propagation on the spectral slope. Critical parameters, such as the window size, are also analyzed in terms of the type of method used and the geologic complexity. We find that the window size is smaller for the centroid/modified centroid methods and larger for the spectral peak, defractal, and nonlinear parameter depth estimation methods. In any case, the window size can be large in tectonically stable regions and relatively small over volcanically, tectonically, and geothermally active areas. Finally, we estimate and discuss the depth to the magnetic top and bottom in the Adriatic Sea region (eastern Italy) in the context of the heat flow, Moho depth, and gravity data of the region.