Singularity of lithosphere mass density over the mid-ocean ridges and implication on floor depth and heat flow

The relation of heat flow and floor depth across the mid-ocean ridges versus lithosphere age can be described by linear functions of square root of age according to plate thermal conductive Half Space Models (HSM). However, one of the long-standing problems of these classical models is the discrepancies between predicted and observed heat flow and floor depth for very young and very old lithosphere. There have been several recent attempts to overcome this problem: one model incorporates temperature- and pressure-dependent parameters and the second model includes an additional low-conductivity crustal layer or magma rich mantle layer (MRM). Alternatively, in the current paper, the ordinary density of lithosphere in the plate conductive models is substituted with a reduction of lithosphere density towards axis that features the irregularity and nonlinearity of plates across the mid-ocean ridges. A new model is formulated incorporating the new form of density for predicting both peak heat flow and floor depth. Simple solutions of power-law forms derived from the model can significantly improve the predicting results of heat flow and floor depth over the mid-ocean ridges. Several datasets in the literature were reutilized for model validation and comparison. These datasets include both earlier datasets used for original model calibration and the more recently compiled high-quality datasets with both sedimentary and crustal loading corrections. The results indicate that both the heat flow and the slope (first order-derivative) of sea floor approach infinity (undifferentiability or singularities) around the mid-ocean ridges. These singularities are partially due to the boundary condition as it has been already known in the literature and partially to the reduction of density of lithosphere as discovered for the first time in the current research.