Semi-Empirical Oceanic Depth–Age Relationship Inferred from Bathymetric Curve

Abstract

In this paper, we report on a preliminary investigation into a semi-empirical method for derivation of depth–age relationship for oceanic lithosphere. The global 30-arcsecond bathymetry data from the General Bathymetric Charts of the Oceans (GEBCO) were corrected for (1) sediment thickness using the Total Sediment Thickness of the World’s Oceans and Marginal Seas and (2) isostasy. The corrected bathymetry was processed to obtain the empirical bathymetric curve, the solution computed with 50 m elevation bin. Subsequently, the data-based curve was approximated with the optimal polynomial model. By combining the model with a formula for derivative of area with respect to age, we obtained the approximate differential equation for depth–age relationship. We solved the equation numerically. The solution was compared with (1) depth–age relationships derived empirically using the combination of the corrected GEBCO bathymetry with digital isochrons of the oceans, (2) Parsons Sclater Model (PSM) and (3) Global Depth Heatflow model (GDH1). In the new depth–age curve, three sections with specific relationships of ocean depth versus age of the crust are identified: (1) moderate increase in depth from 2500 to 5900 m for lithospheric ages 0–118 Ma, (2) more pronounced increase in depth from 5900 to 6700 m for the lithosphere 118–147 Ma old, (3) stabilization of ocean depth at 6700–6760 m for the lithosphere older than 147 Ma. The fit to empirical data as well as PSM and GDH1 models is good for the first section, but rather imperfect for the other two. Reasons for mismatches are complex and probably different for dissimilar sections of the curve.