Masao Nakada

Water-load definition in the glacio-hydro-isostatic sea-level equation

Abstract Models of glacio-hydro-isostatic rebound and the concomitant sea-level change have been progressively improved over the past three decades. Recently, the procedures used by the group at the Australian National University (ANU) for the hydro-isostatic component of the theory have been questioned (Quat. Sci. Rev. 21 (2002) 409) although the details of the ANU groups procedures have not been published because they are mainly computational in nature rather than representing significant conceptual advances. Because of this criticism, we set out here in detail the procedures that have been used for the treatment of the migration of shorelines as sea levels rise and fall, the effect of retreat and advancing grounded ice on shelves and shallow seas, and the transitions from grounded to floating ice (and vice versa). We conclude that there is no basis for the criticism, that these formulations and their implementation provide a high resolution and complete description of both sea-level change and of the estimates of volumes of ice exchanged with the oceans. The results from this formulation are confirmed by the entirely independent analyses of Milne et al. (Quat. Sci. Rev. 21 (2002) 361) and Mitrovica and Milne (Geophys. J. Int. (2002), submitted for publication) who conclude that our formulation is significantly more accurate than the procedure advocated by Peltier (Science 265 (1994) 195; Rev. Geophys. 36 (1998a) 603, Geophys. Res. Lett. 25 (1998b) 3955).

Late pleistocene and halocene sea-level changes in Japan: implications for tectonic histories and mantle rheology

Abstract It is very important to separate the tectonic and glacial-isostatic components in the observed Holocene and Late Pleistocene sea-level changes in tectonically active areas such as Japan for studying tectonic processes and for constraining mantle rheology. The separation can be achieved by considering the spatial dependence of the relative sea-level on the geometry of the coastline around the site where sea-level is evaluated. In fact, the relative sea-level caused by the last deglaciation at sites in the embayment such as Tokyo and Osaka has a sea-level curve with a high stand at mid-Holocene, and that site situated on the tip of peninsula has a sea-level curve culminating towards the present. The geometric effect also causes the regional difference of the sea-level variations in the late glacial phase. In the Japanese Islands, the regional difference of the predicted relative sea-level is about 5 m at 6000 years ago, 20 m at 10,000 years ago and 30 m at 18,000 years ago. Comparison between observations and predictions indicates that the observations at several sites in Japan are consistent with the predicted sea-level variations. More systematic data is required for the period 18,000 years ago to the present in order to examine tectonic processes and mantle rheology.

Holocene sea-level change and hydro-isostasy along the west coast of Kyushu, Japan

Abstract Mid- to late-Holocene sea-level variations have been obtained at sites along the west coast of Kyushu, Japan. Sea-level observations for this relatively stable area are very important for evaluating the crustal tilting associated with the hydro-isostatic adjustment due to the last deglaciation, and for examining the cause of underwater Jomon sites (submerged archeological sites during the Jomon period of mid-Holocene) typically observed in this region. For these purposes, we conducted systematic boring samplings at sites from Goto Island to Tamana along the latitude of about 33°N. Then we performed diatom assemblage and pyrite-sulfur analyses of these sediment samples and 14 C datings for intertidal shells in order to get the sea-level variations for these sites. Observations at Tsumizu faced to Oomura Bay with tidal range of 0.9 m show a sea-level high-stand of 1 m at about 5500 yr B.P. (years before present) followed by smoothly falling to the present level. Evidences for sea-level oscillation of greater than 50 cm have not been found here. Relative sea-levels at about 5000 yr B.P. are, however, −2 m at Goto Island (125 km west of Tsumizu) and 2 m at Tamana (50 km east of Tsumizu). Thus observations at sites along the traverse from Goto Island to Tamana are indicative of crustal tilting of about ∼3–4 m for the distance of 175 km, which seems to be consistent with the prediction caused by the hydro-isostatic adjustment.

Holocene sea levels in oceanic islands: Implications for the rheological structure of the earth's mantle

Abstract Relative sea levels in oceanic islands that are situated sufficiently far from glaciated regions were studied in relation to the rheological structure of the earths mantle. The local hydro-isostatic adjustment associated with the mantle flow from the oceanic side to an inland side depends on the size of the island, the effective upper-mantle viscosity and the elastic plate thickness. The relative sea level has a significant dependence on the upper mantle rheology for islands with a radius larger than 10 km, but it is almost independent of the upper mantle rheology for islands with a radius less than 10 km. In other words, the observed sea-level changes in such small islands follow the global isostatic adjustment which depends strongly on the lower mantle viscosity. In fact, the relative sea levels in small oceanic islands impose important constraints on the lower-mantle viscosity. On the other hand, the effective upper-mantle viscosity and the elastic plate thickness are determined by analyzing the relative sea levels for islands greater than 10 km. The observed sea-level curves in Japan and New Zealand are consistent with the effective viscosity of the upper mantle, equal to 2 to 6 × 10 21 poises. The effective elastic plate thickness for Japan and New Zealand is estimated to be less than 50 km and greater than 100 km, respectively. The thickness of the lithosphere obtained by sea-level curves in Japan and New Zealand is compatible with the results obtained by seismological studies.

Ice age as a trigger of active Quaternary volcanism and tectonism

Abstract The stress accumulation within the crust, caused by the surface mass redistribution associated with the glaciation-deglaciation cycle during the Quaternary, was numerically evaluated in order to examine the relationship between active Quaternary volcanism and tectonism in island-arc areas and ice age. The vertical gradient of horizontal stress difference in the lithosphere for a meltwater of 130 m in equivalent sea-level reaches a maximum value of 0.8 MPa/km, which is corresponding to the equivalent buoyancy of about 100 kg/m3 for magma-filled cracks, for an earth model with a lithospheric layer of 20–30 km thickness and with a viscosity greater than 1023 Pa s. The changes in stress difference during the stages of deglaciation of 10,000 years amount to 13 MPa for both the top and bottom of the thin lithosphere. Thus, the additional stress difference within the crust may be effective for island-arc areas with thin lithospheric thickness. We, therefore, speculate that the stress accumulation associated with ice age may be an important trigger and/or accelerator on the active Quaternary volcanism and tectonism for the areas along the circum-Pacific.

Electrical conductivity anomalies beneath the Western Sea of Kyushu, Japan

Geomagnetic depth soundings have been made in the area covering Kyushu island and its neigh- boring islands in the western sea of Kyushu to investi- gate the back-arc conductivity structure. The in-phase induction arrows derived from geomagnetic variations are found to point roughly southwestwards at most sites on Kyushu island for the period range 300-7200 sec. This is quite different from some other areas of Japan. The non-uniform thin sheet model calculation indicates that the induction arrows in this area are strongly influ- enced by the surrounding seas. However, the observed arrows have much more intense westward components than indicated by the model calculations. This strongly suggests existence of highly conducting layers (HCLs) beneath the East China Sea. And the existence of HCLs in the upper mantle are confirmed by a two-dimensional finite element modeling. These HCLs may be consid- ered to be a part of mantle upwelling extended to East

Effects of water load on geophysical signals due to glacial rebound and implications for mantle viscosity

We investigate the effects of the ocean function on predictions of the sea-level changes and other geophysical signals due to glacial rebound. To precisely predict these signals, a realistic ocean function including the effects of the palaeotopography, the distribution of ice sheet and meltwater influx is required. The adoption of a precise ocean function is very important in simulating the observables in Hudson Bay for an earth model with a low lower mantle viscosity of ∼1021 Pa s. In this case, the contribution from water loads can be comparable to that from ice loads. In the Fennoscandian region, however, the predictions are less sensitive to the details of the ocean function, because the width of the Gulf of Bothnia is very small compared with that of Hudson Bay. With an assumption that the ice model is represented by ARC3+ANT4b, we have examined the viscosity structure using relative sea-levels, gravity anomaly and solid surface gravity changes in North America and northern Europe. This study suggests a lower mantle viscosity of greater than 1022 Pa s and a upper mantle viscosity of (4 ∼ 10) × 1020 Pa s.

Polar wander caused by the Quaternary glacial cycles and fluid Love number

Abstract Perturbations of the Earth’s rotation caused by the Quaternary glacial cycles provide an important constraint on the viscosity of the deep mantle because they represent a long-wavelength response of the Earth to surface load redistribution. The predicted present-day polar wander speed (PWS) is, however, sensitive to both the lower mantle viscosity ( η lm ), the density jump at 670 km depth, and the lithospheric thickness and viscosity (e.g., Sabadini and Peltier, Geophys. J. R. Astron. Soc. 66 (1981) 553–578; Yuen et al., J. Geophys. Res. 87 (1982) 10745–10762; Peltier and Wu, Geophys. Res. Lett. 10 (1983) 181–184; Wu and Peltier, Geophys, J. R. Astron. Soc. 76 (1984) 753–791; Peltier, J. Geophys. Res. 89 (1984) 11303–11316; Vermeersen et al., J. Geophys. Res. 102 (1997) 27689–27702; Mitrovica and Milne, J. Geophys. Res. 103 (1998) 985–1005; Johnston and Lambeck, Geophys. J. Int. 136 (1999) 537–558; Nakada, Geophys. J. Int. 143 (2000) 230–238). For earth models with η lm 21 Pa s and an elastic lithosphere, the present-day PWS is very sensitive to the M1 mode (buoyancy mode) related to the density jump at 670 km depth [Mitrovica and Milne, J. Geophys. Res. 103 (1998) 985–1005]. The contribution of the M1 mode, however, is less significant for earth models with a viscoelastic lithosphere [Nakada, Geophys. J. Int. 143 (2000) 230–238]. This is due to the fact that this contribution depends on the relative strength of the M1 mode, Δ k 2 T (M1)/ k f T , where Δ k 2 T (M1) is the magnitude of tidal Love number ( k 2 T ) of the M1 mode and k f T is the value of k 2 T in the fluid limit (fluid Love number). The magnitude of k f T for earth models with a viscoelastic lithosphere is larger than that for an elastic lithosphere, and it is smaller for a thicker elastic lithosphere than for a thinner one. Thus, for earth models with a viscoelastic lithosphere, the PWS is mainly sensitive to the lower mantle viscosity regardless of the behavior of the 670 km density discontinuity. This relation also explains why the predicted PWS increases with increasing thickness of an elastic lithosphere. That is, since the value of Δ k 2 T (M1)/ k f T with a thicker elastic lithosphere is larger than that with a thinner elastic lithosphere, the M1 mode will have a higher contribution in the case of a thicker elastic lithosphere.

Crustal tilting derived from Holocene sea‐level observations along the east coast of Hokkaido in Japan and upper mantle rheology

Late Holocene sea-level observations at sites along the east coast of Hokkaido in Japan indicate a gradual decrease of the altitude of relative sea-level eastward toward the tip of Nemuro Peninsula. These observations in seismically active areas can be explained by glaciohydroisostatic adjustment due to the last deglaciation for an Earth model with a thin lithosphere of 30–40 km thickness and with no low viscosity layer, or with a 25 km lithosphere overlying a low viscosity layer less than 50 km, although more data as a function of time are needed to distinguish these models. Thus the vertical crustal displacement associated with the subduction of the Pacific plate seems to has not been cumulated on a time scale of 103–104 years.

Lower crustal erosion induced by mantle diapiric upwelling: Constraints from sedimentary basin formation followed by voluminous basalt volcanism in northwest Kyushu, Japan

Abstract A sequence of geological events, beginning with basement subsidence to form a shallow-water sedimentary basin and subsequent voluminous basalt volcanism and uplift of land, has been observed in the back-arc region of northwestern Kyushu, Japan. The basin consists of a succession of marine and non-marine sediments with a total thickness of 1000–1500 m which range in age from 43 to 10 Ma. The basalt volcanism commenced at 10 Ma and continued until 1 Ma. Uplift started at around 30 Ma and continued after the cessation of the basalt volcanism. These geological phenomena may be explained by the convective coupling between the ductile lower crust and upper mantle induced by mantle diapiric upwelling. Thus, surface subsidence leading to sedimentary basin formation is attributed to lower crustal erosion by mantle diapiric upwelling. For an earth model with lower crustal and upper mantle viscosities of 10 19 –10 20 Pa s, 5 km of lower crust can be eroded 10–20 Myr after the start of convective coupling between the ductile lower crust and upper mantle, compatible with the period estimated by observations. In this process, the melt due to adiabatic mantle diapiric upwelling accumulates beneath the lower crust. The accumulation of low density melt in the space originally occupied by mantle material causes crustal uplift. When the stress state became extensional, as inferred from the extension of Okinawa Trough during the middle to late Miocene [1], the melt filling the eroded lower crustal area may have reached the surface, leading to voluminous basalt volcanism.