Inference of mantle viscosity for depth resolutions of GIA observations

Inference of the mantle viscosity from observations for glacial isostatic adjustment (GIA) process has usually been conducted through the analyses based on the simple three-layer viscosity model characterized by lithospheric thickness, upper- and lower-mantle viscosities. Here, we examine the viscosity structures for the simple three-layer viscosity model and also for the two-layer lower-mantle viscosity model defined by viscosities of η_670,D (670-D km depth) and η_D,2891 (D-2891 km depth) with D-values of 1191, 1691 and 2191 km. The upper-mantle rheological parameters for the two-layer lower-mantle viscosity model are the same as those for the simple three-layer one. For the simple three-layer viscosity model, rate of change of degree-two zonal harmonics of geopotential due to GIA process (GIA-induced J˙₂) of -(6.0-6.5) × 10-11 yr^-1 provides two permissible viscosity solutions for the lower mantle, (7-20) × 10²¹ and (5-9) × 10²² Pa s, and the analyses with observational constraints of the J₂ and Last Glacial Maximum (LGM) sea levels at Barbados and Bonaparte Gulf indicate (5-9) × 10²² Pa s for the lower mantle. However, the analyses for the J˙₂ based on the two-layer lower-mantle viscosity model only require a viscosity layer higher than (5-10) × 10²¹ Pa s for a depth above the core-mantle boundary (CMB), in which the value of (5-10) × 10²¹ Pa s corresponds to the solution of (7-20) × 10²¹ Pa s for the simple three-layer one. Moreover, the analyses with the J˙₂ and LGM sea level constraints for the two-layer lower-mantle viscosity model indicate two viscosity solutions: η_670,1191 > 3 × 10²¹ and η_1191,2891 ~ (5-10) × 10²² Pa s, and η670,1691 > 1022 and η1691,2891 ~ (5-10) × 1022 Pa s. The inferred upper-mantle viscosity for such solutions is (1-4) × 1020 Pa s similar to the estimate for the simple three-layer viscosity model. That is, these analyses require a high viscosity layer of (5-10) × 1022 Pa s at least in the deep mantle, and suggest that the GIA-based lower-mantle viscosity structure should be treated carefully in discussing the mantle dynamics related to the viscosity jump at ~670 km depth. We also preliminarily put additional constraints on these viscosity solutions by examining typical relative sea level (RSL) changes used to infer the lower-mantle viscosity. The viscosity solution inferred from the far-field RSL changes in the Australian region is consistent with those for the J˙₂ and LGM sea levels, and the analyses for RSL changes at Southport and Bermuda in the intermediate region for the North American ice sheets suggest the solution of η_670,D > 10²², η_D,2891 ~ (5-10) × 10²² Pa s (D = 1191 or 1691 km) and upper-mantle viscosity higher than 6 × 10²⁰ Pa s.