Response of the barrier island coastal region of southwestern Nigeria to climate and non-climate forcing

Despite threats emanating from the influence of climate and non-climate forcing on the barrier island coastal region of southwestern Nigeria, the extent of the coastal erosion is poorly understood. We report evidence of coastal erosion and sediment accumulation in the region over a 34-year period (1973–2017), using Landsat imagery at intervals of approximately six years. Landsat image corrections and various water-extraction algorithms were used to systematically delineate coastal erosion and accumulation in the area. The region was subdivided into western and eastern subregions separated by Lagos Harbour. In the west, erosion took place during the periods 1973–1979, 1979–1984, 1990–1999 and 2005–2011, whereas in the east, erosion occurred during 1973–1979, 1990–1999 and 1999–2005. Coastal sediment accumulation occurred in the east during 1979–1984, 1984–1990, 2005–2011 and 2011–2017, whereas gains in the west occurred during 1984–1990, 1999–2005 and 2011–2017. The study revealed substantial net erosion of 1 228.1 ha in the region as a whole, over the full period. Sediment accumulation accompanying the coastal erosion appears to be linked to longshore drift. Erosion between 1973 and 2011 was probably attributable to climate change (storms and tidal conditions), longshore drift, the inflow and outflow of water at Lagos Harbour, coastal morphology and, possibly, human impacts. However, the coastal changes between 2011 and 2017 were more obviously associated with human activities, such as development of the Eko Atlantic construction project. Coastal surveillance, together with the use of environmentally sensitive protective measures, could possibly help to reduce coastal erosion in the region. Careful coastal management practices, including artificial nourishing and the installation of resilient structures (e.g. seawalls), should be undertaken to protect human settlements that are already at risk from sea-level rise.     

The stream function and Gauss' principle of least constraint: Two useful concepts for structural geology

To the extent that rock deformation can be approximated by a two-dimensional Newtonian model, a powerful stream-function simulation method is applicable. The significance of stream functions is that velocity, strain, stress and energy derived from the same stream function satisfy automatically three basic conditions of dynamics:

1. (1) the condition of continuity.

2. (2) the Navier-Stokes equations.

3. (3) conservation of energy.

Hence we state with Jaeger: “If a stream function can be found which satisfies the boundary conditions of a dynamic model the complete solution follows.” All pertinent bits of dynamic information are implied in the stream function from which they can be directly derived, guaranteed—so to speak—not to violate the basic conditions of dynamics. Stream functions useful in structural geology are solutions of: A double-polynomial solution of max. degree 14 is developed, in which the coefficients are related controlled by the ⁴ψ = 0 constraint, and their absolute values are determined by the boundary conditions of specific models and by the condition of maximum rate of energy dissipation or maximum rate of decline of potential energy. The polynomial stream function is applied to a collapsing viscous “nappe” consisting of a thin basal layer with low viscosity on which a thicker layer with high viscosity slides due to gravitational spreading. The velocity of forward movement depends upon absolute and relative values of the following parameters: viscosity, thickness, the aspect ratio and density. The velocity of a variety of nappes with different thicknesses, aspect ratios, viscosities and densities is determined.     

Studies on flow till in Denmark

Profiles with till and stratified meltwater sediments have been examined. Structural and morphological conditions indicate a deposition of till in the same environment as the stratified sediments. The till is interpreted as flow till which originated from considerable amounts of supraglacial material.     

Horizontal and vertical cylinders in waves

The present investigation examines a vertical cylinder and a horizontal cylinder in progressive waves. The physical differences between the flows are explored and experimental results are compared to previous planar harmonic flow measurements. It is found that modifications to the usual Morison approach are required in some cases to adequately account for the orbital motions of the fluid and to account for the orientation of the orbits with respect to the cylinder axis. The axial variations of the wave force on vertical cylinders are considered in order to evaluate the common practice of assuming constant values of $\text{C}{}_{\mathrm{m}}\text{and}\text{C}{}_{\mathrm{D}}$ over the entire span. Lastly, the methods of computing force transfer coefficients from a force record are examined and several sources of error are identified and briefly discussed.     

Gravity studies of the Fen complex,Norway, and their petrological significance

The Fen alkaline complex, which is about 2 km in diameter, is an example of the carbonatite-ijolite-pyroxenite rock association. A Bouguer anomaly map reveals a sharp and almost circular gravity high centered above the complex, the residual peak value being about + 23 mgal. The gravity interpretation supports the ideas that the carbonatites represent only the volatile end fraction accumulated in the upper part of a long vertical magma chamber such as could form in an abyssal fissure, and that the major part of the pipe consists of an ultramafic parental or cogenetic rock originating from great depth (deep crust or upper mantle).Contribution No. 68 in the Norwegian Geotraverse Project.On leave to Dept. of Geology, University of Wyoming, Laramie, Wyoming 82070.     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: V. asymmetric folding in interbedded chert and shale of the franciscan complex, san francisco bay area, california

The origin of tight, asymmetric, kink-like or chevron-like folds in interbedded shales and radiolarian cherts of the Franciscan Complex in the San Francisco Bay area has been somewhat of a mystery for many years. Stephenson Ellen provided many clues as to the origin and indicated that the folds became asymmetric as a result of layer-parallel shear. He believed that the original folds were conjugate kink folds.As a result of reexamination of most of the folds studied by Ellen, of experimentation with elastic multilayers and of the theories developed in Parts III and IV of this series of papers, we believe that the original folds were mostly chevron rather than kink folds. Thus, we suggest that the folds formed by a combination of layer-parallel shortening and layer-parallel shear when the rocks were soft and pore pressures were high.Several lines of evidence suggest that typical folds in the Franciscan are asymmetric chevron folds. A combination of theory of finite simple shear and of experimentation with elastic multilayers indicates that the tight folds of the Franciscan could have been produced by smaller angles of simple shear if the original folds were typical chevron folds rather than typical kink folds. Several field observations, including thickening of shales but not of cherts in hinges of folds and lack of deformation of radiolaria in the cherts, indicate that the cherts were soft and the shales very soft at the time of folding. The pore-water pressures in the shales probably were high. Such conditions theoretically favor concentric-like and chevron folding, not kink folding. Finally, most of the asymmetric folds in a quarry exposure can be reconstructed geometrically as typical chevron folds but not as typical kink folds subjected to simple shear.     

The Trachybasaltic Suite of Jan Mayen

The alkalic suite of Jan Mayen is of the trachybasaltic typewith a K₂O/Na₂O ratio of about 1·64. The suite includesall intermediate types of lavas between ankaramite and trachyte,with ankaramites being particularly prevalent. The major andtrace element trends are well defined. A new method allows distinctionbetween fractionated and accumulative ankaramites, and it isshown that the most primitive ankaramite contains 13–14per cent MgO. Experimentally determined P-T phase relationsof this composition suggest that it might be a primary composition,formed by partial melting of a spinel lherzolitic source at19·5kb and 1415°C. The fractionation from ankaramiteto trachybasalt occurred at low pressure, and was controlledby delayed gravitative settling of phenocrysts, while the fractionationfrom trachybasalt to trachyte is explained by crystallizationon the walls of the magma chambers.     

Braid perthite in nepheline syenite pegmatite, Langesundsfjorden, Oslo Region (Norway)

Three occurrences of braid perthite (lamellae parallel to (110) and ( )) and micro braid perthite (lamellae parallel to ( ) and ( )) from Permian nepheline syenite pegmatites in monzonite (larvikite) of the Oslo Graben are described. All the crystals studied show a zoned arrangement with either alternating mmacro- and microperthitic bands parallel to (010) or with microperthitic cores surrounded by macroperthite and a marginal zone of plagioclase. Both types of perthite are mesoperthitic and composed of maximum microcline and low albite. Chemical analyses suggest that the alkali feldspar is stoichiometric, while precession exposures imply unusual cell parameters in the host K-feldspar phase. The macroperthite seems to have crystallized at the expense of the microperthite. The braided texture of exsolved albite lamellae may be due to some kind of strain causing cracking along the prism and pyramidal planes.