The nature of short-term mantle rheology for timescales between the seismic frequency band and a few hundred years remains relatively unknown. We have made use of two pieces of information, which have emerged as a consequence of the recent acquisition of data from the LAGEOS satellite, to place some contraints on the rheological parameters of short-term mantle rheology. The first is the secular variation of the gravitational harmonic J ̇. The second is the amount of dispersion of the tidal Love number for the 18.6 y tide, which has been inferred to be ∼ 20%. Two types of rheology have been considered. The first is a frequency-dependent Q rheology. An analytical expression for the transformed shear modulus has been developed from the truncated retardation spectrum explicitly for this purpose. The second anelastic rheology we have used is a standard linear solid, where the parameters of importance are the relaxation strength Δ and the short-term viscosity ν2. Rheological parameters of the frequency-dependent Q model previously proposed by Lambeck and Nakiboglu to explain the dispersion of the tidal Love number for a 18.6 y period are found to produce too much dispersion for the Chandler wobble and to yield seismic Q's between O(103) and O(104) for fundamental toroidal modes, which are not compatible with the data. We have used instead a three-layer model consisting of an elastic lithosphere, a mantle with a standard-linear solid rheology whose Debye peak lies beyond the long time cutoff of the retardation spectrum, and an inviscid core. For relaxation strength of Δ around 1 and short-term viscosity ν2 < 1021 P unacceptably large rates of J ̇ would result from earthquake excitation. A sharp decrease of the tidal dispersion takes place for ν2 ≅ 5 × 1020 P and Δ = 1.0. For smaller values of relaxation strength, Δ = 0.15 the maximum tidal dispersion is only 9% and decreases gradually as ν2 is increased beyond 5 × 1020 P. We have found that the maximum dispersion caused by the Maxwell rheology is small, around 5%, even for asthenospheric viscosities of O(1018P). These results suggest that the datum of 18.6 y tidal dispersion can be utilized eventually to place constraints on potential candidates of short term mantle rheology.
Bibliographical noteFunding Information:
This research has been supported by NASA grant NAG 5-400, NSF grant EAR-8214094 and Minstero della Pubblica Instruzione of Italy. We thank Jim Merriam for useful communication.