Ocean singularity analysis and global heat flow prediction reveal anomalous bathymetry and heat flow

The investigations of physical attributes of oceans, including parameters such as heat flow and bathymetry, have garnered substantial attention and are particularly valuable for examining Earth's thermal structures and dynamic processes. Nevertheless, classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres. Furthermore, a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking. In this study, we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry. Notably, power-law models offer distinct advantages over traditional plate cooling models, showcasing robust self-similarity, scale invariance, or scaling properties, and providing a better fit to observed data. The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model. In addition, we applied the similarity method to predict a higher resolution (0.1° × 0.1°) global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis. Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures. Finally, combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow, which deviate from traditional plate cooling models. The anomalous regions of subsidence and heat flow show different degrees of anisotropy, providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.