# The Accuracy Assessment of Lithospheric Density Models
## 3 Model Uncertainties
### Errors Due to Lithospheric Mantle Density Uncertainties  
The lithospheric mantle density information is used to compute the Moho density contrast \(\Delta\rho^{\text{c}/\text{m}}\) in Equation (35), the lithospheric mantle density variations \(\delta\rho^{LM}\) in Equation (38), and the LAB density contrast \(\Delta\rho^{\text{L}/\Lambda}\) in Equation (42). This involves thecomputation of the Moho potential \(V^{M,\Delta\rho^{c/m}}\) in Equation (32), the lithospheric-mantle gravitational potential \(V^{LM}\) in Equation (39), and the LAB potential \(V^{LAB}\) in Equation (41). The error propagation for the lithospheric mantle density uncertainties is then established in the following form:  
\[\varepsilon_{N^{\text{SM}}}=-\frac{1}{\gamma_{0}}\left(\frac{ \partial V^{M,\Delta\rho^{c/m} \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Gravitational Potential** & **Min [m\({}^{2}\)-s\({}^{-2}\)]** & **Max [m\({}^{2}\)-s\({}^{-2}\)]** & **Mean [m\({}^{2}\)-s\({}^{-2}\)]** & **STD [m\({}^{2}\)-s\({}^{-2}\)]** \\ \hline \(V^{T}\) & \(2226\) & \(8494\) & \(3589\) & \(1114\) \\ \(V^{I}\) & \(-3472\) & \(-312\) & \(-731\) & \(729\) \\ \(V^{B}\) & \(-28.533\) & \(-16.402\) & \(-22.386\) & \(3185\) \\ \(V^{S}\) & \(-3862\) & \(-1937\) & \(-2719\) & \(444\) \\ \(V^{C}\) & \(11,529\) & \(25,075\) & \(15,661\) & \(2741\) \\ \(V^{M,\Delta{\sigma^{I/m}}}\) & \(-69,885\) & \(-46,423\) & \(-55,734\) & \(5832\) \\ \(V^{LM}\) & \(-262,661\) & \(-17,4276\) & \(-213,366\) & \(17,795\) \\ \(V^{LAB}\) & \(168,987\) & \(244,558\) & \(203,311\) & \(16,194\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of gravitational potentials used to compute the sub-lithospheric mantle gravity disturbances. For the notation used, see the legend in Figure 1.  
Figure 2: Global maps of (**a**) the geoid \(N\), (**b**) the Bouguer geoid \(N^{B}\), (**c**) the crust-stripped geoid \(N^{CS}\), (**d**) the mantle geoid \(N^{M}\), (**e**) the lithosphere-stripped geoid \(N^{CL}\), and (**f**) the sub-lithospheric mantle geoid \(N^{SM}\). A long-wavelength geoidal geometry (Figure 2a) reflects mainly a mantle density structure [93; 94], while a signature of crustal density and geometry variations (including a topographic surplus of large orogenic formations) is less prominent. After removing the gravitational contributions of topography and lithospheric density and geometry (i.e., LAB) variations, the resulting (sub-lithospheric mantle) geoidal geometry (see Figure 2f) should (optimally) enhance the gravitational signature of the sub-lithospheric mantle. It is a well-known fact that a spatial pattern in dynamic topography models [54; 95; 96; 97; 98] mainly reflects a mantle convection flow, with maxima marking locations of the African and South Pacific superplumes that represent large-scale regions characterized by an elevated topography and shallow ocean-floor depths caused by a low-density upwelling of mantle material from the core-mantle boundary. The corresponding minima are explained by a high-density mantle downwelling flow. Tomographic studies [99] indicate that superplumes coincide with the locations of large low-shear-velocity provinces (LLSVPs) beneath Africa (called Tuzo) and the South Pacific (called Jason). Since the gravitational contributions of lithospheric density and thickness variations have been modeled and consequently removed in our forward modeling procedure, the sub-lithospheric mantle geoid should mainly reflect deep mantle density anomalies. Consequently, the spatial pattern of the sub-lithospheric mantle geoid (especially its long-wavelength spectrum up to degree five of spherical harmonics; see Figure 3) does not closely agree with the spatial pattern of dynamic topography models (cf. [PERSON] and [PERSON] [81]). A comparative study of spatial patterns in the sub-lithospheric mantle geoid and dynamic topography models is thus not meaningful for the assessment of errors in our gravimetric forward modeling.