An authentic model of a large part of the Earth’s crust and mantle must obey the same equations as the prototype does, and the independent variables in these equations must have the same values in model and prototype. It follows that all the equations must be expressed in dimensionless form. The equations that govern slow deformations express the conditions of continuity and equilibrium, the mechanical properties of the materials, the applied forces, and the initial and boundary conditions.

Dimensionless elastic and plastic property diagrams, based on estimated and simplified characteristics of the Earth, show that no ordinary material will fit both the elastic and plastic requirements for a model of reasonable size. A plastic material was chosen for tests involving the formation of a geologic basin.

Since the force that determines the equilibrium arrangement of the Earth’s components is a radially-inward gravity force, the pull of the Earth’s gravity must be nullified in a proper model and a radial model-gravity substituted. The former may be accomplished by submerging the model in a liquid, but no feasible means of producing the latter was discovered. Hence, deformations of a thick sphere were studied in a submerged model and the gravity fill-in of a depression was measured in an otherwise flat model. Surface strains could be added qualitatively.

The results showed that moderate strains were widely distributed when an elliptical basin was caused by the contraction of a deep interior region. There were no areas where large strains were concentrated. Because of gravity fill-in the amount of strain is not necessarily related to the final depth of a basin.

Since the initial condition, the boundaries and their displacements, and the long-time properties of the Earth all must be estimated, a model can not determine what mechanism produced a known topographic feature. Rather, it will show whether or not a hypothesis is reasonable, and it will suggest mechanisms that otherwise might be overlooked.

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