title: Symmetry operators and separation of variables for spin-wave equations in oblate spheroidal coordinates

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: A family of second-order differential operators that characterize the solution of the massless spin s field equations, obtained via separation of variables in oblate spheroidal coordinates and using a null tetrad is found. The first two members of the family also characterize the separable solutions in the Kerr space-time. It is also shown that these operators are symmetry operators of the field equations in empty space-times whenever the space-time admits a second-order Killing–Yano tensor.

text: Symmetry operators and separation of variables for spin-wave equations in oblate spheroidal coordinates A family of second-order differential operators that characterize the solution of the massless spin s field equations, obtained via separation of variables in oblate spheroidal coordinates and using a null tetrad is found. The first two members of the family also characterize the separable solutions in the Kerr space-time. It is also shown that these operators are symmetry operators of the field equations in empty space-times whenever the space-time admits a second-order Killing–Yano tensor.

year: 1990-07

title: Sedimentary facies and unconformity analysis of some Paleocene-Eocene sections, Marlborough and Campbell Island, New Zealand

authors: Andrew, Benjamin Steven

subjects: Marlborough

abstract: Throughout the Late Cretaceous to Eocene, sedimentation in gradually subsiding basins on the passive eastern margin of the micro-continent of Zealandia recorded climatic and paleoceanographic changes in a greenhouse world. One such fundamental change in Southern Ocean circulation is hypothesised to be recorded in a regionally extensive unconformity surface and short-lived lithofacies changes contained within Late Paleocene to Early Eocene sedimentary successions at key sections throughout New Zealand, and investigated here on Campbell Island and in southeastern Marlborough.

On Campbell Island, this oceanographic event is represented by an unconformity between the Late Cretaceous to Late Paleocene Garden Cove Formation and the Early Eocene to Oligocene Tucker Cove Limestone. This unconformity signifies a major lithofacies change from Garden Cove Formation which consists of siliceous mudstone containing fine sand to coarse silt sized siliciclastic grains, pelletal glaucony grains and rare quartz pebbles, to a nannofossil and foraminiferal limestone containing little to no siliciclastic grains comprising the Tucker Cove Limestone. Geochemically this lithofacies change is characterised by a dramatic decrease in terrigenous supply and a shift from siliceous to calcareous productivity, along with a significant concentration of Zr and rare earth elements. Lithofacies at this site are inferred to record possible episodes of ice rafting and eventual unconformity formation by invigorated intermediate depth ocean currents which resulted in winnowing of seafloor sediments and concentration of heavy minerals.

At the distal Mead Stream site in southeastern Marlborough, deposition of bio-siliceous sediments of the Mead Hill Formation and Amuri Limestone was locally disrupted by deposition of the Waipawa Formation, the lateral equivalent of an important hydrocarbon source rock identified in several of New Zealand‟s sedimentary basins. In outcrop, the Waipawa Formation at Mead Stream is characterised by a very distinctive rusty‟ brown fissile appearance, while in thin section, though radiolarians and sponge spicules are common, the overall fine grained nature of the unit makes identification of other components difficult. Geochemical proxies show a significant increase in terrigenous supply in the Waipawa Formation, along with an increase in siliceous productivity concomitant with a decrease in oxygenation at the site. Lithofacies changes through the Late Paleocene at Mead Stream suggest the site lay under a zone of upwelling which resulted in an increase in siliceous productivity during the Late Paleocene.

At the more proximal sites of Muzzle Stream and Kaikoura wharf in southeastern Marlborough, Mead Hill Formation and Amuri Limestone are separated by an unconformity, overlain by Teredo Limestone. The Teredo Limestone is considered to be a lateral equivalent of the Waipawa Formation, but both the base and top of the Teredo Limestone are timetransgressive. This means that at Muzzle Stream the unit is contemporaneous with the Waipawa Formation (Late Paleocene), while at Kaikoura wharf the unit is entirely Early Eocene in age. At these sites, the Teredo Limestone Member of the Amuri Limestone is a calcareous greensand sometimes containing phosphatised limestone clasts and sharks teeth. In thin sections, the unit consists of well sorted, fine to very fine sand sized siliciclastic grains and fine sand sized pelletal and vermicular glaucony set in a calcareous matrix that shows evidence of secondary silicification. Unconformity formation and the subsequent deposition of the overlying Teredo Limestone record a period of invigorated intermediate depth ocean currents that resulted in the transport of siliciclastic grains and glaucony to these bathyal sites. This interpretation is supported by a palinspastic map of the Teredo Limestone that suggests the unit was deposited under different conditions than those responsible for the deposition of the bounding Mead Hill Formation and Amuri Limestone. This map also suggests the Teredo Limestone was deposited as a skin drift‟, here named the Clarence Drift, possibly under the influence of contour currents.

Based on similarities between unconformities and lithofacies changes in Late Paleocene to Early Eocene sedimentary sections and an earlier, well documented event at the Cretaceous/Tertiary boundary in southeastern Marlborough, evidence for a period of enhanced siliceous productivity, invigorated ocean currents and possible episodes of ice rafting is suggested to be consistent with a brief period of Antarctic ice sheet growth during a phase of global cooling in the Late Paleocene.

The possible identification of Antarctic ice sheets, ephemeral though they may have been, not only challenges long held beliefs that the Antarctic continent remained ice free during the early Paleogene greenhouse world but also questions the suggested mechanisms responsible for Antarctic ice sheet growth. The lack of ocean gateways in the Southern Ocean during this time effectively rules out thermal isolation of the Antarctic continent as a driver. Given that this period of ice sheet growth is contemporaneous with a documented period of enhanced global ocean productivity and terrestrial carbon accumulation and related draw down in atmospheric CO2, it is suggested this may represent the driver responsible for brief Antarctic glaciation during this period, though the postulated link requires further investigation.

text: Sedimentary facies and unconformity analysis of some Paleocene-Eocene sections, Marlborough and Campbell Island, New Zealand Throughout the Late Cretaceous to Eocene, sedimentation in gradually subsiding basins on the passive eastern margin of the micro-continent of Zealandia recorded climatic and paleoceanographic changes in a greenhouse world. One such fundamental change in Southern Ocean circulation is hypothesised to be recorded in a regionally extensive unconformity surface and short-lived lithofacies changes contained within Late Paleocene to Early Eocene sedimentary successions at key sections throughout New Zealand, and investigated here on Campbell Island and in southeastern Marlborough.

On Campbell Island, this oceanographic event is represented by an unconformity between the Late Cretaceous to Late Paleocene Garden Cove Formation and the Early Eocene to Oligocene Tucker Cove Limestone. This unconformity signifies a major lithofacies change from Garden Cove Formation which consists of siliceous mudstone containing fine sand to coarse silt sized siliciclastic grains, pelletal glaucony grains and rare quartz pebbles, to a nannofossil and foraminiferal limestone containing little to no siliciclastic grains comprising the Tucker Cove Limestone. Geochemically this lithofacies change is characterised by a dramatic decrease in terrigenous supply and a shift from siliceous to calcareous productivity, along with a significant concentration of Zr and rare earth elements. Lithofacies at this site are inferred to record possible episodes of ice rafting and eventual unconformity formation by invigorated intermediate depth ocean currents which resulted in winnowing of seafloor sediments and concentration of heavy minerals.

At the distal Mead Stream site in southeastern Marlborough, deposition of bio-siliceous sediments of the Mead Hill Formation and Amuri Limestone was locally disrupted by deposition of the Waipawa Formation, the lateral equivalent of an important hydrocarbon source rock identified in several of New Zealand‟s sedimentary basins. In outcrop, the Waipawa Formation at Mead Stream is characterised by a very distinctive rusty‟ brown fissile appearance, while in thin section, though radiolarians and sponge spicules are common, the overall fine grained nature of the unit makes identification of other components difficult. Geochemical proxies show a significant increase in terrigenous supply in the Waipawa Formation, along with an increase in siliceous productivity concomitant with a decrease in oxygenation at the site. Lithofacies changes through the Late Paleocene at Mead Stream suggest the site lay under a zone of upwelling which resulted in an increase in siliceous productivity during the Late Paleocene.

At the more proximal sites of Muzzle Stream and Kaikoura wharf in southeastern Marlborough, Mead Hill Formation and Amuri Limestone are separated by an unconformity, overlain by Teredo Limestone. The Teredo Limestone is considered to be a lateral equivalent of the Waipawa Formation, but both the base and top of the Teredo Limestone are timetransgressive. This means that at Muzzle Stream the unit is contemporaneous with the Waipawa Formation (Late Paleocene), while at Kaikoura wharf the unit is entirely Early Eocene in age. At these sites, the Teredo Limestone Member of the Amuri Limestone is a calcareous greensand sometimes containing phosphatised limestone clasts and sharks teeth. In thin sections, the unit consists of well sorted, fine to very fine sand sized siliciclastic grains and fine sand sized pelletal and vermicular glaucony set in a calcareous matrix that shows evidence of secondary silicification. Unconformity formation and the subsequent deposition of the overlying Teredo Limestone record a period of invigorated intermediate depth ocean currents that resulted in the transport of siliciclastic grains and glaucony to these bathyal sites. This interpretation is supported by a palinspastic map of the Teredo Limestone that suggests the unit was deposited under different conditions than those responsible for the deposition of the bounding Mead Hill Formation and Amuri Limestone. This map also suggests the Teredo Limestone was deposited as a skin drift‟, here named the Clarence Drift, possibly under the influence of contour currents.

Based on similarities between unconformities and lithofacies changes in Late Paleocene to Early Eocene sedimentary sections and an earlier, well documented event at the Cretaceous/Tertiary boundary in southeastern Marlborough, evidence for a period of enhanced siliceous productivity, invigorated ocean currents and possible episodes of ice rafting is suggested to be consistent with a brief period of Antarctic ice sheet growth during a phase of global cooling in the Late Paleocene.

The possible identification of Antarctic ice sheets, ephemeral though they may have been, not only challenges long held beliefs that the Antarctic continent remained ice free during the early Paleogene greenhouse world but also questions the suggested mechanisms responsible for Antarctic ice sheet growth. The lack of ocean gateways in the Southern Ocean during this time effectively rules out thermal isolation of the Antarctic continent as a driver. Given that this period of ice sheet growth is contemporaneous with a documented period of enhanced global ocean productivity and terrestrial carbon accumulation and related draw down in atmospheric CO2, it is suggested this may represent the driver responsible for brief Antarctic glaciation during this period, though the postulated link requires further investigation.

year: 2010

title: The Long Bay Restaurant site, R10/1374: Volume 1, the archaeology (HNZPTA authorities 2015/19 and 2016/81): Report to Heritage New Zealand Pouhere Taonga and Auckland Council

authors: Campbell, M

abstract: Auckland Council had proposed refurbishing the Long Bay Restaurant at Long Bay Regional Park (Lot 2 DP 54616), amounting to a near full rebuild of the structure apart from the in situ foundations. Council began the project in mid-2013 with the partial demolition of the existing structure and sawing of the concrete floor slab to install new utilities. Following the discovery of human remains beneath the floor slab on 2 July 2013, work was halted. The remains were inspected by the New Zealand Police who confirmed that they were pre-European kōiwi tangata. An assessment of the site was then undertaken by Beatrice Hudson of ArchOs Archaeology (Hudson 2013) and the find was recorded as site R10/1374 in the New Zealand Archaeological Association (NZAA) Site Recording Scheme (SRS) (this site number applies to any other archaeological features associated with the wider area). Auckland Council applied to the New Zealand Historic Places Trust (now Heritage New Zealand Pouhere Taonga, HNZPT) for an archaeological authority under section 18 of the Historic Places Act 1993 to undertake archaeological test excavations to investigate the nature, extent and condition of the site, and how it would be affected by the proposed development project. Authority 2014/506 was granted on 28 November 2013 and the investigation was carried out on the 20th and 21st of January 2014 (Campbell et al. 2014) (the 2014 excavation is summarised in Chapter 3).

Auckland Council then applied to HNZPT for an authority under section 44 of the Heritage New Zealand Pouhere Taonga Act 2014 to modify or destroy any further material found during the refurbishment project, including associated car parks and footpaths. Authority 2015/19 was granted on 7 August 2014 and works resumed. On 6 November 2014 further kōiwi were found within the project footprint and work once again ceased. 

Following extensive consultation with mana whenua and HNZPT, Auckland Council determined that the refurbishment would continue but it was agreed that the entire footprint of the development would be cleared archaeologically in order to provide assurance that no further kōiwi would remain within the project area. As the scope of the archaeological investigation had changed, a new archaeological authority, superseding authority 2015/19, was required and a full archaeological assessment of efects was also required in support of the authority application (Campbell and Hudson 2015). Authority 2016/81 was granted by HNZPT on 25 August 2015. This report fulfils the conditions of both authority 2015/19 and 2016/81.

Excavation began on 5 October 2015 with site clearance and removal of the concrete pad but not the ground beam foundations, while full excavation commenced on 12 October under the direction of Matthew Campbell (Excavation Director, CFG Heritage) and Beatrice Hudson (Osteologist, ArchOs Archaeology). Excavation continued until 3 November, by which stage kōiwi of a further 10 individuals had been found, bringing the total to 12. Following an onsite hui on 4 November between representatives of mana whenua, HNZPT, Auckland Council and the excavation team, the excavation was halted but mana whenua requested that the 3 possible burials that had been located but not excavated be lifted, and on 9 November the site was shut down. At a second on site hui on 9 December Auckland Council announced that they had resolved to cancel the restaurant project, but mana whenua expressed a desire that the 13 x 12 m excavation area opened up at the time be excavated to a sterile layer to lift all kōiwi. Excavation resumed on 18 January 2016 and continued until 4 March, when all kōiwi and archaeological deposits and features had been excavated.

text: The Long Bay Restaurant site, R10/1374: Volume 1, the archaeology (HNZPTA authorities 2015/19 and 2016/81): Report to Heritage New Zealand Pouhere Taonga and Auckland Council Auckland Council had proposed refurbishing the Long Bay Restaurant at Long Bay Regional Park (Lot 2 DP 54616), amounting to a near full rebuild of the structure apart from the in situ foundations. Council began the project in mid-2013 with the partial demolition of the existing structure and sawing of the concrete floor slab to install new utilities. Following the discovery of human remains beneath the floor slab on 2 July 2013, work was halted. The remains were inspected by the New Zealand Police who confirmed that they were pre-European kōiwi tangata. An assessment of the site was then undertaken by Beatrice Hudson of ArchOs Archaeology (Hudson 2013) and the find was recorded as site R10/1374 in the New Zealand Archaeological Association (NZAA) Site Recording Scheme (SRS) (this site number applies to any other archaeological features associated with the wider area). Auckland Council applied to the New Zealand Historic Places Trust (now Heritage New Zealand Pouhere Taonga, HNZPT) for an archaeological authority under section 18 of the Historic Places Act 1993 to undertake archaeological test excavations to investigate the nature, extent and condition of the site, and how it would be affected by the proposed development project. Authority 2014/506 was granted on 28 November 2013 and the investigation was carried out on the 20th and 21st of January 2014 (Campbell et al. 2014) (the 2014 excavation is summarised in Chapter 3).

Auckland Council then applied to HNZPT for an authority under section 44 of the Heritage New Zealand Pouhere Taonga Act 2014 to modify or destroy any further material found during the refurbishment project, including associated car parks and footpaths. Authority 2015/19 was granted on 7 August 2014 and works resumed. On 6 November 2014 further kōiwi were found within the project footprint and work once again ceased. 

Following extensive consultation with mana whenua and HNZPT, Auckland Council determined that the refurbishment would continue but it was agreed that the entire footprint of the development would be cleared archaeologically in order to provide assurance that no further kōiwi would remain within the project area. As the scope of the archaeological investigation had changed, a new archaeological authority, superseding authority 2015/19, was required and a full archaeological assessment of efects was also required in support of the authority application (Campbell and Hudson 2015). Authority 2016/81 was granted by HNZPT on 25 August 2015. This report fulfils the conditions of both authority 2015/19 and 2016/81.

Excavation began on 5 October 2015 with site clearance and removal of the concrete pad but not the ground beam foundations, while full excavation commenced on 12 October under the direction of Matthew Campbell (Excavation Director, CFG Heritage) and Beatrice Hudson (Osteologist, ArchOs Archaeology). Excavation continued until 3 November, by which stage kōiwi of a further 10 individuals had been found, bringing the total to 12. Following an onsite hui on 4 November between representatives of mana whenua, HNZPT, Auckland Council and the excavation team, the excavation was halted but mana whenua requested that the 3 possible burials that had been located but not excavated be lifted, and on 9 November the site was shut down. At a second on site hui on 9 December Auckland Council announced that they had resolved to cancel the restaurant project, but mana whenua expressed a desire that the 13 x 12 m excavation area opened up at the time be excavated to a sterile layer to lift all kōiwi. Excavation resumed on 18 January 2016 and continued until 4 March, when all kōiwi and archaeological deposits and features had been excavated.

year: 2019