# The Accuracy Assessment of Lithospheric Density Models
## 5 Error Analysis
If we consider that the average uncertainties in the lithospheric thickness \(\varepsilon_{L}\) are about \(\pm\)40 km (the average of the root-mean-square (RMS) of differences in Table 4), the sub-lithospheric mantle geoid errors \(\varepsilon_{N\otimes\mathrm{M}}\) could reach or even exceed \(\pm\)0.4 km. Tomographic images of the lithosphere have limited accuracy and resolution. Moreover, the conversion between seismic wave velocities and rock densities is not unique [58; 111]. [PERSON] and [PERSON] [112], for instance, mentioned that a lithospheric mantle composition and seismic anisotropy are more complex than a deep mantle structure, making it harder to convert seismic anomalies to density anomalies or buoyancy (cf. also [PERSON] et al. [113]). We, therefore, also expect large (sub-lithospheric mantle) geoid modeling errors due to lithospheric mantle density uncertainties. According to Equation (51), the sub-lithospheric mantle geoid error \(\varepsilon_{N\otimes\mathrm{M}}\) depends on the accuracy of anomalous lithospheric mantle density \(\delta\rho^{L/M}\) and additional errors \(\varepsilon_{\Delta\rho^{L/\Lambda}}\) and \(\varepsilon_{\Delta\rho^{c/\mathrm{m}}}\) in adopted values of the LAB density contrast \(\Delta\rho^{\mathrm{L/\Lambda}}\) and the Moho density contrast \(\Delta\rho^{\mathrm{c/m}}\). Large density variations occur within the lithospheric mantle, although in comparison to the crust, fewer constraints exist on the composition of the lithospheric mantle. Petrological models for the origin of basalt are used to compile models of the oceanic lithospheric mantle. An undepleted peridotitic source that partially melts to produce the mid-ocean ridge basalt leaves behind a depleted residue (a harzburgite), the thickness of which depends on the degree of a partial melt. As the oceanic lithosphere cools, the undepleted mantle becomes part of the lithospheric column, and its thickness increases with the ocean floor age. The composition of the continental lithospheric mantle depends on a tectonic province and its age. [PERSON] [114] proposed that the lithospheric mantle might be cold and buoyant in the thickest cratonic portions of very fast seismic velocity (see also [PERSON] et al. [115]). These conditions require the presence of a depleted layer overlying an undepleted upper mantle layer. Based on the LITHO1.0 lithospheric mantle density variations (roughly within \(\pm\)200 kg\(\cdot\)m\({}^{-3}\)) and the previously summarized studies, we can anticipate that lithospheric mantle density uncertainties \(\varepsilon_{\delta\rho^{L/\Lambda}}\) are mostly within \(\pm\)100 kg\(\cdot\)m\({}^{-3}\). We further assume that uncertainties in the average LAB density contrast \(\varepsilon_{\Delta\rho^{L/\Lambda}}\) are roughly \(\pm\)15 kg\(\cdot\)m\({}^{-3}\). Results from seismic and gravimetric studies revealed that the Moho density contrast varies substantially. [PERSON] [116] demonstrated that the in situ density contrast between the crystalline crust and the lithospheric upper mantle differs substantially between the Cratonic and the Phanerozoic crusts within the European part of the Eurasian tectonic plate: approximately 500 kg\(\cdot\)m\({}^{-3}\) for the crust beneath Western Europe, between 300 and 350 kg\(\cdot\)m\({}^{-3}\) for most of the Precambrian crust, and by as little as 150-250 kg\(\cdot\)m\({}^{-3}\) for some parts of the Baltic and the Ukrainian Shields. [PERSON] and [PERSON] [117] provided the average values of 678 \(\pm\) 78 and 334 \(\pm\) 108 kg\(\cdot\)m\({}^{-3}\) of the Moho density contrast for the continental and oceanic areas, respectively. According to these studies, we speculate that the errors of Moho density contrast \(\varepsilon_{\Delta\rho^{c/\mathrm{m}}}\) could be roughly \(\pm\)50 kg\(\cdot\)m\({}^{-3}\).