Isostatic compensation on a continental scale: local versus regional mechanisms

Summary. Using the techniques of linear and quadratic programming, it can be shown that the isostatic response function for the continental United States, computed by Lewis & Dorman (1970), is incompatible with any local compensation model that involves only negative density contrasts beneath topographic loads. We interpret the need for positive densities as indicating that compensation is regional rather than local. The regional compensation model that we investigate treats the outer shell of the Earth as a thin elastic plate, floating on the surface of a liquid. The response of such a model can be inverted to yield the absolute density gradient in the plate, provided the flexural rigidity of the plate and the density contrast between mantle and topography are specified.
If only positive density gradients are allowed, such a regional model fits the United States response data provided the flexural rigidity of the plate lies between 10²¹ and 10²² N m. The fit of the model is insensitive to the mantle/ load density contrast, but certain bounds on the density structure can be established if the model is assumed correct. In particular, the maximum density increase within the plate at depths greater than 34 kin must not exceed 470 kg m⁻³; this can be regarded as an upper bound on the density contrast at the Mohorovicic discontinuity.
The permitted values of the flexural rigidity correspond to plate thicknesses in the range 5–10 km, yet deformations at depths greater than 20 km are indicated by other geophysical data. We conclude that the plate cannot be perfectly elastic; its effective elastic moduli must be much smaller than the seismically determined values. Estimates of the stress-differences produced in the earth by topographic loads, that use the elastic plate model, together with seismically determined elastic parameters, will be too large by a factor of four or more.