Peer-reviewed geodynamic literature establishes that modern formulations of isostasy can be accurately defined as the static equilibrium of the crust that minimizes deviatoric stresses.
The relation between gravity and topography in central Australia cannot be described by a conventional isostatic response function, whether it assumes local or regional compensation or whether the crust behaves as an elastic or viscoelastic medium. In particular, the response function exhibits considerable anisotropy. Hence a theory for isostatic response has been developed for a crust in mechanical equilibrium of surface loads, buoyancy, and in‐plane forces and subject to erosion, sedimentation, and stress relaxation. The observed north‐south response function exhibits extreme isostatic overcompensation at some wavelengths, and this can be fully explained by the Viscoelastic plate model with in‐plane compression. The observed east‐west response function is consistent with models of regional or local isostatic compensation. The response function implies an effective flexural rigidity of (5–10)×1022 N m, an effective Maxwell relaxation time of 25–50 m.y., an in‐plane compression of 125–150 MPa, and an erosion time constant of about 200 m.y. These parameters assume that the model evolved over a period of about 700 m.y. and are wholly consistent with the evolutionary model developed from geological observations.
Isostasy explains why observed gravity anomalies are generally much weaker than what is expected from topography alone, and why planetary crusts can support high topography without breaking up. On Earth, it is used to subtract from gravity anomalies the contribution of nearly compensated surface topography. On icy moons and dwarf planets, it constrains the compensation depth which is identified with the thickness of the rigid layer above a soft layer or a global subsurface ocean. Classical isostasy, however, is not self-consistent, neglects internal stresses and geoid contributions to topographical support, and yields ambiguous predictions of geoid anomalies. Isostasy should instead be defined either by minimizing deviatoric elastic stresses within the silicate crust or icy shell, or by studying the dynamic response of the body in the long-time limit. In this paper, I implement the first option by formulating Airy isostatic equilibrium as the linear response of an elastic shell to a combination of surface and internal loads. Isostatic ratios are defined in terms of deviatoric Love numbers which quantify deviations with respect to a fluid state. The Love number approach separates the physics of isostasy from the technicalities of elastic-gravitational spherical deformations, and provides flexibility in the choice of the interior structure. Since elastic isostasy is invariant under a global rescaling of the shell shear modulus, it can be defined in the fluid shell limit, which is simpler and reveals the deep connection with the asymptotic state of dynamic isostasy. If the shell is homogeneous, minimum stress isostasy is dual to a variant of elastic isostasy called zero deflection isostasy, which is less physical but simpler to compute. Each isostatic model is combined with general boundary conditions applied at the surface and bottom of the shell, resulting in one-parameter isostatic families. At long wavelength, the thin shell limit is a good approximation, in which case the influence of boundary conditions disappears as all isostatic families members yield the same isostatic ratios. At short wavelength, topography is supported by shallow stresses so that Airy isostasy becomes similar to either pure top loading or pure bottom loading. The isostatic ratios of incompressible bodies with three homogeneous layers are given in analytical form in the text and in complementary software.
In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper I gave a general formulation of Airy isostasy as an elastic loading problem solved with Love numbers, and applied it to the case of minimum stress isostasy. In this sequel, the same framework is used to study Airy isostasy as the long-time evolution of a viscoelastic shell submitted to surface and internal loads. Isostatic ratios are defined in terms of time-dependent deviatoric Love numbers. Dynamic isostasy depends on the loading history, two examples of which are the constant load applied on the surface in the far past and the constant shape maintained by addition or removal of material at the compensation depth. The former model results in a shape decreasing exponentially with time and has no elastic analogue, whereas the latter (stationary) model is equivalent to a form of elastic isostasy. Viscoelastic and viscous approaches are completely equivalent. If both load and shape vary slowly with time, isostatic ratios look like those of the stationary model. Isostatic models thus belong to two independent groups: the elastic/stationary approaches and the time-dependent approaches. If the shell is homogeneous, all models predict a similar compensation of large-scale gravity perturbations. If the shell rheology depends on depth, stationary models predict more compensation at long wavelengths, whereas time-dependent models result in negligible compensation. Mathematica and Fortran codes are available for computing the isostatic ratios of an incompressible body with three homogeneous layers.
Everything we examined (3)
This check searched the claim as stated. It did not run a separate search for evidence against it.