Total meltwater volume since the Last Glacial Maximum and viscosity structure of Earth's mantle inferred from relative sea level changes at Barbados and Bonaparte Gulf and GIA-induced J₂

Inference of globally averaged eustatic sea level (ESL) rise since the Last Glacial Maximum (LGM) highly depends on the interpretation of relative sea level (RSL) observations at Barbados and Bonaparte Gulf, Australia, which are sensitive to the viscosity structure of Earth's mantle. Here we examine the RSL changes at the LGM for Barbados and Bonaparte Gulf (RSL^{Bar, Bon}_L ), differential RSL for both sites (ΔRSL^{Bar, Bon}_L ) and rate of change of degree-two harmonics of Earth's geopotential due to glacial isostatic adjustment (GIA) process (GIA-induced J˙₂) to infer the ESL component and viscosity structure of Earth's mantle. Differential RSL, ΔRSL^{Bar, Bon}_L and GIA-induced J˙₂ are dominantly sensitive to the lower-mantle viscosity, and nearly insensitive to the upper-mantle rheological structure and GIA ice models with an ESL component of about (120-130) m. The comparison between the predicted and observationally derived ΔRSL^{Bar, Bon}_L indicates the lower-mantle viscosity higher than ~2 × 10²² Pa s, and the observationally derived GIA-induced J˙₂ of -(6.0-6.5) × 10^-11 yr^-1 indicates two permissible solutions for the lower mantle, ~10²² and (5-10) × 10²² Pa s. That is, the effective lower-mantle viscosity inferred from these two observational constraints is (5-10) × 1022 Pa s. The LGM RSL changes at both sites, RSL^Bar_L and RSL^Bon_L, are also sensitive to the ESL component and upper-mantle viscosity as well as the lower-mantle viscosity. The permissible upper-mantle viscosity increases with decreasing ESL component due to the sensitivity of the LGM sea level at Bonaparte Gulf (RSL^Bon _L ) to the upper-mantle viscosity, and inferred upper-mantle viscosity for adopted lithospheric thicknesses of 65 and 100 km is (1-3) × 10²⁰ Pa s for ESL~130m and (4-10) × 10²⁰ Pa s for ESL~125 m. The former solution of (1-3) × 10²⁰ Pa s is consistent with the inferences from the postglacial differential RSL changes in the Australian region and also inversion study of far-field sea-level data. The inference of the viscosity structure based on these four observational constraints is, however, relatively insensitive to the viscosity structure of D" layer.