Three-dimensional geological Earth models typically comprise wireframe surfaces of connected triangles that represent geological contacts. In contrast, Earth models used by most current 3D geophysical numerical modeling and inversion methods are built on rectilinear meshes. This is because the mathematics for computing data responses are simpler on rectilinear meshes. In such a model, the relevant physical properties are uniform within each brick-like cell but possibly different from one cell to the next, producing a pixellated representation of the Earth. In principle, arbitrary spatial variations can be represented if a sufficiently fine discretization is used. However, no matter how fine the discretization of the rectilinear mesh, such a mesh is always incompatible with geological models comprising wireframe surfaces. Also, because the computational resources required by 3D numerical modeling and inversion methods increase dramatically as the discretization of a model is refined, it is never really possible to achieve as fine a discretization as one would like. This exacerbates the mismatch between models that comprise wireframe surfaces and those built on rectilinear meshes. To address this incompatibility, we are using unstructured tetrahedral meshes to specify 3D geophysical Earth models. We hope that working with unstructured meshes will facilitate the construction of common Earth models consistent with both the geological and geophysical data available.