# The Accuracy Assessment of Lithospheric Density Models
## 5 Error Analysis  
Large errors are expected in the CRUST1.0 and LITHO1.0 models used for gravimetric forward modeling in this study. As already mentioned in the preceding section, this is particularly evident from pronounced positive sub-lithospheric mantle geoid anomalies (Figure 2_f_) that are also still partially exhibited in their long-wavelength pattern (Figure 3). These positive anomalies correspond with the largest cratonic lithospheric thickness (the Laurentian Shield in North America, the Amazonian Shield and Sao Francisco Craton in South America, the West African Craton, the East European and Siberian Cratons, the Baltic Shield in Eurasia, and the West Australian Craton). As seen in Equation (47), the lithospheric thickness uncertainties propagate almost linearly to the sub-lithospheric mantle geoid uncertainties. We can, therefore, readily estimate the geoid errors for particular lithospheric thickness uncertainties. According to the LITHO1.0 model, the lithospheric mantle density varies roughly from 3000 to 3450 kg\(\cdot\)m\({}^{-3}\). From these density variations, we can assume that \(\delta\rho^{LM}\) is mostly within \(\pm\)200 kg\(\cdot\)m\({}^{-3}\). The boundary between the lowermost lithosphere and the uppermost asthenosphere (i.e., the LAB) is rheological, conventionally taken at the 1300 \({}^{\circ}\)C isotherm, above which the mantle behaves in a rigid fashion and below which it behaves in a ductile fashion [100]. Studies suggest the existence of a compositional or chemical density contrast 0-20 kg\(\cdot\)m\({}^{-3}\)[101], except probably the cratonic mantle. In addition to a possibly chemical density contrast, a strong thermal density contrast of 30-60 kg\(\cdot\)m\({}^{-3}\) occurs when the asthenosphere is locally uplifted by rifting. We, therefore, assume that the density variations \(\Delta\rho^{\rm L/A}\) at the boundary between the lithosphere and the asthenosphere are mostly within \(\pm\)30 kg\(\cdot\)m\({}^{-3}\). For \(\delta\rho^{\rm L/M}+\Delta\rho^{\rm L/A}=\pm\)230 kg\(\cdot\)m\({}^{-3}\), the errors in the lithospheric thickness estimates of \(\varepsilon_{L}\approx\pm\)10 km cause errors in the sub-lithospheric mantle geoid of roughly \(\varepsilon_{N^{\rm SM}}\approx\pm\)0.1 km. The lithospheric thickness models vary significantly. [PERSON] et al. [70], for instance, found large differences between their LITHO1.0 model and that prepared by [PERSON] and [PERSON] [102]. They also explained that these large differences are due to applying different methods, assumptions, and input data. To get a rough idea about the magnitude of these errors, we compared the lithospheric thickness models SLNAAFSA [103], SL2013 sv [104], LITHO1.0 [70], CAM2016 [105, 106], and 3D2015-07 Sv [107], and used their differences to estimate (sub-lithospheric mantle) geoid errors. We note here that the SLNAAFSA model was prepared by [PERSON] et al. [103] by merging regional updates from North America [108], Africa [109], and South America [110] into the global SL2013 sv model. The lithospheric thickness models are shown in Figure 4, with their statistical summary given in Table 3. The statistics of differences between individual lithospheric thickness models are summarized in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Lithospheric Thickness Model** & **Min [km]** & **Max [km]** & **Mean [km]** & **STD [km]** \\ \hline SLNAAFSA & 38 & 364 & 115 & 57 \\ SL2013 sv & 40 & 350 & 112 & 52 \\ LITHO1.0 & 7 & 271 & 114 & 55 \\ CAM2016 & 38 & 241 & 111 & 46 \\
3D2015-07 Sv & 36 & 703 & 110 & 51 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics of the lithospheric thickness models SLNAAFSA, SL2013 sv, LITHO1.0, CAM2016, and 3D2015-07 Sv. Figure 4: Lithospheric thickness models: (**a**) SLNAAFSA, (**b**) SL2013 sv, (**c**) LITHO1.0, (**d**) CAM2016, and (**e**) 3D2015-07 Sv. As seen in Table 4, differences between lithospheric thickness models exceed several hundreds of meters.