Master of the Obscure—Automated Geostatistical Classification in Presence of Complex Geophysical Processes

The topic of this paper is the retrieval of hidden or secondary information on complex spatial variables from geophysical data. Typical situations of obscured geological or geophysical information are the following: (1) Noise may disturb the signal for a variable for which measurements have been collected. (2) The variable of interest may be obscured by other geophysical processes. (3) The information of interest may formally be captured in a secondary variable, whereas data may have been collected for a primary variable only, that is related to the geophysical process of interest. Examples discussed here include mapping of marine-geologic provinces from bathymetric data, identification of sea-ice properties from snow-depth data, analysis of snow surface data in an Alpine environment and association of deformation types in fast-moving glaciers from airborne video material or satellite imagery. Data types include geophysical profile or trackline data, image data, grid or matrix-type data, and more generally, any two-dimensional or three-dimensional discrete or discretizable data sets. The framework for a solution is geostatistical characterization and classification, which typically involves the following steps: (1) calculation of vario functions (which may be of higher order or residual type, or combinations of both), (2) derivation of classification parameters from vario functions, and (3) characterization, classification or segmentation, depending on the applied problem. In some situations, spatial surface roughness is utilized as an auxiliary variable, for instance, roughness of the seafloor may be derived from bathymetric data and be indicative of geological provinces. The objective of this paper is to present components of the geostatistical classification method in a summarizing and synoptical manner, motivated by applied examples and integrating principal and generalized concepts, such as hyperparameters and parameters that relate to the same physical processes and work for data in oversampled and undersampled situations, parameters that facilitate comparison among different data types, data sets and across scales, variograms and vario functions of higher order, and deterministic and connectionist classification algorithms.