# The Accuracy Assessment of Lithospheric Density Models
## 1 Introduction  
Gravimetric forward and inverse modeling techniques are essential numerical tools applied in physical geodesy and gravimetric geophysics. In physical geodesy applications, these methods are used to compute topographic and terrain gravity corrections in gravimetric geoid modeling [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11] and compile isostatic gravity maps [12]. In gravimetric geophysics, these methods are used to compile Bouguer and mantle gravity maps [13; 14; 15; 16; 17; 18]. Furthermore, numerous techniques have been developed and applied for a gravimetric interpretation of the Earth's inner structure [19; 20; 21]. Whereas gravimetric inverse modeling is applied to determine an unknown density structure or density interface from observed gravity data, gravimetric forward modeling is used to compute gravitational field quantities generated by a known density structure or density interface. Several different methods have been developed for local and regional gravimetric forward modeling based on solving Newton's volume integral in the spatial domain by applying numerical,  
spectral domain utilize a spherical harmonic analysis and synthesis of gravity and density structure models [33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. The validation of the accuracy and numerical efficiency of newly developed methods for gravimetric forward and inverse modeling is often performed by comparing results with solutions obtained from existing (and typically well-established) numerical methods and procedures. Alternatively, simple or more refined synthetic density models (designed for various configurations of different geometrical density bodies) have been more recently used for testing and validation of spatial methods developed for local and regional gravimetric forward modeling and inversion by adopting a planar approximation. For global (or large-scale regional) applications, synthetic density models should mimic more realistically the Earth's actual shape and inner density structure. Such synthetic density models have already been used to validate numerical techniques involved in gravimetric geoid modeling [43; 44; 45], studies of the sediment bedrock morphology [46], the lithospheric and mantle density structure [16; 47], the crustal thickness [16; 18; 48; 49; 50; 51; 52], the dynamic and residual topography [53; 54; 55], or the oceanic lithosphere [56]. To construct a global synthetic density model that closely resembles the Earth's shape and inner structure, available global topographic and density structure models could be used for this purpose, together with additional models that provide information about the Earth's inner structure (such as crust and lithospheric thickness models). Moreover, constraints have to be applied so that the mass of the Earth's synthetic model is equal to the total mass of the Earth (excluding the atmosphere), and the gravitational field generated by the Earth's synthetic model closely agrees with the Earth's gravitational field (in terms of geoidal geometry, gravity, and gravity gradient). A number of seismic velocities and mass density models have been developed based on the analysis of tomographic data while incorporating geophysical, geochemical, and geothermal constraints [57; 58; 59; 60; 61; 62; 63; 64]. For an overview of these models, see also Trabant [65]. A practical application of global 1D density models [58; 64] is limited by the absence of lateral density information. To address this issue, existing 2D or 3D crust and lithospheric models [66; 67; 68; 69; 70; 71; 72; 73] can be used to refine 1D reference density models. Since many parts of the world are not yet sufficiently covered by tomographic surveys, the refinement of 1D reference density models by incorporating 2D or 3D global lithospheric and mantle density models is not simple. Moreover, the direct relation between seismic velocities and mass densities does not exist because a density distribution depends on many other factors (such as temperature, mineral composition, and pressure).