The Concept of Processing, Analysis and Visualization of Geophysical Data Based on Elements of Tensor Calculus

Abstract

One of the main approaches to processing, analysis and visualization of geophysical data is the use of geographic information systems and technologies, which is due to their geospatial reference. At the same time, the complexity of presenting geophysical data is associated with their complex structure, which involves many components that have the same geospatial reference. Vivid examples of data of such a structure and format are gravitational and geomagnetic fields, which in the general case are specified by three and four-component vectors with multidirectional coordinate axes. At the same time, today there are no solutions that allow visualizing these data in a complex without decomposing them into individual scalar values, which, in turn, can be presented in the form of one or many spatial layers. In this regard, the work proposes a concept that uses elements of tensor calculus for processing, storing and visualizing information of this format. In particular, a mechanism for tensor representation of field components has been formalized with the possibility of combining it with other data of the same format, on the one hand, and convolution when combined with data of a lower rank. Using the example of a hybrid relational-hierarchical data model, a mechanism for storing information on tensor fields is proposed, which provides for the possibility of describing and subsequently applying transformation instructions when transitioning between different coordinate systems. The paper discusses the use of this approach in the transition from the Cartesian to the spherical coordinate system when representing the parameters of the geomagnetic field. For complex visualization of tensor field parameters, an approach based on the use of tensor glyphs is proposed. The latter are superellipses with axes corresponding to the rank of the tensor. In this case, the attribute values themselves are proposed to be visualized relative to the corresponding axes of the graphic primitive in such a way that the data distribution can be specified by varying the gradient of the corresponding monochrome representation of the parameter along the corresponding axis. The performance of the proposed concept was investigated during a comparative analysis of the tensor approach with known solutions based on the scalar decomposition of the corresponding complex values with their subsequent representation in the form of one or many spatial layers. The analysis showed that the use of the proposed approach will significantly increase the visibility of the generated geospatial image without the need for complex overlapping of spatial layers.