On Bagnold's sediment transport equation in tidal marine environments and the practical definition of bedload

Bagnold's sediment transport equation has proved to be important in studying tidal marine environments. This paper discusses three problems concerning Bagnold's transport equation and its practical application:

• 1 Bagnold's suspended-load transport equation and the total-load transport equation with are incorrect from the viewpoint of energy conservation. In these equations the energy loss due to bedload transport has been counted twice. The correct form should be for suspended-load transport and for total-load transport with
• 2 The commonly used Bagnold's transport coefficient K varies as a non-linear function of the dimensionless excess shear stress, which can be represented best by the power law , where the coefficient A and exponent B depend on sediment grain size D. The empirical values of A and B for fine to medium grained sands are determined using Guy et al.'s (1966) flume-experiment data.
• 3 The sediment transport rates predicted from this equation are compared with bedform migration measurements in the flume and the field. This comparison shows that the sediment transport rates measured from bedform migrations are higher than the predicted bedload transport rates, but comparable to the calculated total-load (bedload plus intermittent suspended-load) transport rates. This indicates that bedform migration involves both bedload and intermittent suspended-load transport. As a logical conclusion, bedform migration data should be compared with Bagnold's total-load transport equation rather than with his bedload transport equation. In this respect the term ‘bed material’ might be more appropriate than the term ‘bedload’ for estimating sediment transport rate from bedform migration data.

The sediment transport rates predicted from this modified Bagnold transport equation are in good agreement with field measurements of bedform migration rates in four individual tidal marine environments, which cover a wide range of sediment grain size, flow velocity and bedform conditions (ranging from small ripples, megaripples to sandwaves).     

Wave propagation in an inhomogeneous cross‐anisotropic medium

Analytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross‐anisotropic medium, in which Young's moduli (E, E′) and shear modulus (G′) varied exponentially as depth increased. However, for the rest moduli in cross‐anisotropic materials, ν and ν′ remained constant regardless of depth. We assume that cross‐anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain–displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi‐wave velocities, V_P, V_SV, and V_SH, and the wave vectors, $\mathop{\mathop{l}\limits^{\rightharpoonup}}\nolimits_{P}$ $\mathop{\mathop{l}\limits^{\rightharpoonup}}\nolimits_{\mathit{SV}}$, and $\mathop{\mathop{l}\limits^{\rightharpoonup}}\nolimits_{{\mathit{SH}}}$, can be generated for the inhomogeneous cross‐anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E′, G′/E′, and ν/ν′); and (3) the phase angle, θ. Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross‐anisotropic medium. Copyright © 2009 John Wiley & Sons, Ltd.     

Carbon,part 2: diamond

In Part 1 (Minerals explained 43, Geology Today 2006, v.22, no.2, pp.71–77) graphite was examined, the polymorph of carbon that is stable over a wide temperature range, but only at relatively low pressures. The other principal polymorph of carbon, diamond, is dealt with here in Part 2. Diamond has a very large stability range over both temperatures and pressures, although it is created at similar depths in the Earth's crust, probably in the mantle ( Fig. 1 ). It would probably have remained there unsuspected, had it not been brought to the Earth's surface by volcanic mechanisms. This will be looked at in detail in the section on the genesis of diamond below, as will the apparently anomalous stability of diamond at NTP.

Figure 1 Open in figure viewer PowerPoint Pressure/temperature phase diagram for diamond.     

Surface settlement of a finite elastic layer whose modulus increases linearly with depth

An examination has been made of the behaviour of a finite layer of elastic material of constant Poisson's ratio, whose Young's modulus increases linearly with depth, and which rests on a rough rigid base. Values of surface settlement at the corner of a rectangular area of uniform loading are presented for values of Poisson's ratio of \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{2} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{3} $\end{document} and 0, and for wide ranges of degree of inhomogeneity and loading breadth to depth ratio.     

Structure and phase transition of CaGe<Subscript>2</Subscript>O<Subscript>5</Subscript> revisited

The structure of CaGe₂O₅ between room temperature and 923 K has been determined by X-ray powder diffraction. A continuous phase transition from triclinic C1¯ to monoclinic C2/c symmetry at T_c=714±3 K is observed. The transition is accompanied by a weak heat capacity anomaly. This anomaly and the strain analysis based on the measured lattice parameters indicate a classical second-order phase transition. The order parameter, as measured by the strain component e₂₃, is associated with the displacement of the Ca cation. Electronic structure optimization by density functional methods is used to verify the centric space group of the low-temperature structure of CaGe₂O₅.     

Changes in bulk properties and molecular compositions within New Zealand Coal Band solvent extracts from early diagenetic to catagenetic maturity levels

The bulk properties and bitumen molecular compositions of a rank-series of 38 humic coals from the New Zealand Coal Band (Cretaceous–Cenozoic) have been analysed to investigate early maturation processes affecting coaly organic matter through diagenesis to moderate catagenesis (Rank(S_r) 0.0–11.8, R_o 0.23–0.81%). The samples comprise a relatively restricted range of vitrinite rich coal types formed largely from higher land plant material under relatively oxic conditions, but with a significant contribution from microbial biomass. With increasing rank, total organic carbon contents show a general increase, whereas moisture and asphaltene contents decrease. Bitumen yields also decrease through the stages of diagenesis and early catagenesis (Rank(S_r) < 9, R_o < 0.55%), indicating partial loss of initial bitumen during early maturation. Thermal generation of hydrocarbons begins slowly at Rank(S_r)  5–6 (R_o  0.40%) as indicated by the constant occurrence and gradual increase of isoprenoids (e.g., pristane and phytane) and hopanoids in their more mature αβ configuration. This early phase of catagenesis, not previously recognised in New Zealand coals, is followed at Rank(S_r)  9 (R_o  0.55%) by the main catagenesis phase characterised by a more rapid increase in the generation of hydrocarbons, including total n-alkanes, isoprenoids and αβ-hopanes. Changes in the maturity of New Zealand coals can be traced by the Carbon Preference Index and several hopane maturity parameters, including 22S/(22S + 22R), αβ/(αβ + βα) and ββ/(αβ + βα + ββ).     

Equation of state,structural behaviour and phase diagram of synthetic MgFe<Subscript>2</Subscript>O<Subscript>4</Subscript>, as a function of pressure and temperature

The behaviour of synthetic Mg-ferrite (MgFe₂O₄) has been investigated at high pressure (in situ high-pressure synchrotron radiation powder diffraction at ESRF) and at high temperature (in situ high-temperature X-ray powder diffraction) conditions. The elastic properties determined by the third-order Birch–Murnaghan equation of state result in K₀=181.5(± 1.3) GPa, K=6.32(± 0.14) and K= –0.0638 GPa^–1. The symmetry-independent coordinate of oxygen does not show significant sensitivity to pressure, and the structure shrinking is mainly attributable to the shortening of the cell edge (homogeneous strain). The lattice parameter thermal expansion is described by _a0+_a1*(T–298)+_a2/(T–298)², where _a0=9.1(1) 10^–6 K^–1, _a1=4.9(2) 10^–9 K^–2 and _a2= 5.1(5) 10^–2 K. The high-temperature cation-ordering reaction which MgFe-spinel undergoes has been interpreted by the ONeill model, whose parameters are = 22.2(± 1.8) kJ mol^–1 and =–17.6(± 1.2) kJ mol^–1. The elastic and thermal properties measured have then been used to model the phase diagram of MgFe₂O₄, which shows that the high-pressure transition from spinel to orthorombic CaMn₂O₄-like structure at T < 1700 K is preceded by a decomposition into MgO and Fe₂O₃.     

Sediment suspension dynamics and a new criterion for the maintenance of turbulent suspensions

The vertical component of the turbulent flow acceleration term, , is used to determine the net positive vertical force that may support a suspended sediment load. A dimensionless criterion, Λ, is proposed for the maintenance of suspension, defined as the ratio of the maximum vertical turbulent stress to immersed weight of the suspended load above a unit bed area. In order that a suspension be maintained: where v ′ is instantaneous vertical turbulent velocity, σ and ρ are solid and fluid densities, respectively and m is the suspended load dry mass. The Λ criterion is dynamic, being a ratio of stresses and is analogous in this respect to Shields dimensionless stress criterion, θ, for the initiation of bedload motion. The new criterion is successful in predicting the maintenance of steady-state suspended sediment transport in open channel shear flow and deposition from non-uniform particulate density flows of wall jet type.     

Observations on the extended Matsuoka–Nakai failure criterion

The equivalent Mohr–Coulomb (M‐C) friction angle ? (J. Geotech. Eng. 1990; 116 (6):986–999) of the extended Matsuoka–Nakai (E‐M‐N) criterion has been examined under all possible stress paths. It is shown that ? depends only on the ratio of cohesion to confining stress c^′/σ and the frictional angle ?, where ? is the friction angle measured in triaxial compression (or extension) to which the E‐M‐N surface is fitted. It is also shown that ? is independent of c^′, when σ=0 and of σ when c^′=0, with the former representing an upper bound and the latter a lower bound of ? for any particular stress path. The closest point projection method has also been implemented successfully with the E‐M‐N criterion, and plane strain and axisymmetric element tests performed to verify some theoretical predictions relating to failure and post‐yielding behavior. Finally, a bearing capacity problem was analyzed using both E‐M‐N and M‐C, highlighting the conservative nature of M‐C for different friction angles. Copyright © 2009 John Wiley & Sons, Ltd.     

Shear wave velocity and attenuation structure for the shallow crust of the southern Korean peninsula from short period Rayleigh waves

We analyzed the short period Rayleigh waves from the first crustal-scale seismic refraction experiment in the Korean peninsula, KCRUST2002, to determine the shear wave velocity and attenuation structure of the uppermost 1 km of the crust in different tectonic zones of the Korean peninsula and to examine if this can be related to the surface geology of the study area. The experiment was conducted with two large explosive sources along a 300-km long profile in 2002. The seismic traces, recorded on 170 vertical-component, 2-Hz portable seismometers, show distinct Rayleigh waves in the period range between 0.2 s and 1.2 s, which are easily recognizable up to 30–60 km from the sources. The seismic profiles, which traverse three tectonic regions (Gyeonggi massif, Okcheon fold belt and Yeongnam massif), were divided into five subsections based on tectonic boundaries as well as lithology. Group and phase velocities for the five subsections obtained by a continuous wavelet transform method and a slant stack method, respectively, were inverted for the shear wave models. We obtained shear wave velocity models up to a depth of 1.0 km. Overall, the shear wave velocity of the Okcheon fold belt is lower than that of the Gyeonggi and Yeongnam massifs by  0.4 km/s in the shallowmost 0.2 km and by 0.2 km/s at depths below 0.2 km. Attenuation coefficients, determined from the decay of the fundamental mode Rayleigh waves, were used to obtain the shear wave attenuation structures for three subsections (one for each of the three different tectonic regions). We obtained an average value of Q_β^− 1 in the upper 0.5 km for each subsection. Q_β^− 1 for the Okcheon fold belt ( 0.026) is approximately three times larger than Q_β^− 1 for the massif areas ( 0.008). The low shear wave velocity in the Okcheon fold belt is consistent with the high attenuation in this region.     

Switzerite: Its chemical formula and crystal structure

Summary Switzerite has the following schematical chemical formula Mn ₄ ^2+(VI) (Me ^3+,2+,1+,)^(VI) (Me ^3+,2+,1+,)^(V) (PO₄)₄. 8 H₂O, whereMe is mainly iron; the mineral is monoclinic, space groupP2₁/c, Z=4; lattice parameters area=8.496,b=13.173,c=17.214 Å, -96.65°. The atomic arrangement was determined by direct methods and refined by least-squares method. FinalR index is 0.077 for 3038 observed reflections. The crystal structure of switzerite can be described as built up by octahedral sheets parallel to (001), with formula [Mn₄O₁₀(H₂O)₄]₂.Me coordination bipyramidal dimers link these units in thec direction whileMe coordination octahedra stick out from the sheets to which they are connected through a vertex. The atomic arrangement of switzerite is compared with that in ludlamite, Fe₃(PO₄)₂·4H₂O, and in whitmoreite, Fe²⁺Fe ₂ ³⁺ (OH)₂(PO₄)₂·4 H₂O. The only analogy in all these structures is the presence of octahedral slabs exhibiting, however, different shapes.

---

Switzerit: Chemische Formel und Kristallstruktur

Zusammenfassung Switzerit hat die schematische chemische Formel Mn ₄ ^2+(VI) (Me ^3+,2+,1+,)^(VI) (Me ^3+,2+,1+,)^(V) (PO₄)₄·8 H₂O, wobeiMe hauptsächlich Eisen ist. Das Mineral ist monoklin, RaumgruppeP2₁/c,Z=4; Gitterkonstanten:a=8,496,b=13,173,c=17,214 Å, =96,65°. Die Atomanordnung wurde mit direkten Methoden bestimmt und nach der Methode der kleinsten Quadrate verfeinert. Es wurde für 3038 beobachtete ReflexeR=0,077 erreicht. Man kann die Kristallstruktur des Switzerits als aus Oktaederschichten der Formel [Mn₄O₁₀(H₂O)₄]₂, die parallel zu (001) liegen, beschreiben. Dimere aus trigonalen Dipyramiden umMe verbinden diese Einheiten in Richtung derc-Achse, während Koordinationsoktaeder umMe aus diesen Schichten, an die sie über eine Ecke verknüpft sind, hervorragen. Die Atomanordnung des Switzerits wird mit denen des Ludlamits, Fe₃(PO₄)₂·4 H₂O und des Whitmoreits, Fe²⁺Fe ₂ ³⁺ (OH)₂(PO₄)₂·4 H₂O verglichen. Die einzige Analogie zwischen allen diesen Strukturen ist die Anwesenheit von Oktaederschichten, die aber verschiedene Gestalt haben.

---

---

With 3 Figures     

Pre-seismic electromagnetic phenomena in the framework of percolation and fractal theories

Understanding the electromagnetic response to geodynamic processes occurring in the earth's upper crust, in particular pre-seismic and seismic processes, is a challenging task in modern geophysics. There is increasing evidence that seismo-electromagnetic (SEM) phenomena are difficult to describe quantitatively by “linear” models using “averaged” parameters of the medium, such as electrical and hydraulic conductivities. Because the upper crust is highly inhomogeneous (at all scales), porous, and can be fully or partially water-saturated, the most natural way to describe its parameters is via fractal-theoretic and percolation-theoretic models.Recent studies indicate that the electrokinetic effect is the most likely driving mechanism for the various types of SEM signals. Here we considered the hydraulic, electric, and electrokinetic conductances of a porous water-saturated medium as a function of porosity () and moisture content (θ), utilizing a percolation/fractal approach. We show that the electric conductivity and electrokinetic current in such a medium are both proportional to (–_c)² and (θ–θ_c)², where _c and θ_c are the critical values of porosity and moisture content, respectively. This behavior admits the possibility of a relatively large change in the respective electric and electrokinetic parameters due to a small change in the mechanical strain field. This is significant because it may account for the appearance of some types of SEM signals at large distances from the earthquake origin, which is the main deficiency of most models. Indeed, the anticipated strain changes related to pre-earthquake processes is usually very small except near the focal area. The expected ‘averaged’ electromagnetic response also would be very small, unless a local underground water system exists, not necessarily near the focal area, but which is close to critical point(s).We discuss the conditions under which electrotelluric and geomagnetic variations can accompany mechanical disturbances in the earth's crust.     

Plesiosaurs

Plesiosaurs are an unusual and intriguing group of extinct aquatic reptiles ( Fig. 1 ). They are sauropterygians, a group known from an array of semi‐aquatic forms during the Triassic period: placodonts, pachypleurosaurs and nothosaurs. The first plesiosaurs are known from the very latest Triassic, but by the Early Jurassic plesiosaurs were cosmopolitan in distribution and lasted successfully to the latest Cretaceous, when they became victims of the K‐T extinction event. Plesiosaurs were predominantly marine organisms, although their fossils are not uncommon in brackish or even fresh water deposits. We know that all plesiosaurs were carnivorous; many of them were top predators in their respective ecosystems. But with no living descendants (or analogues) plesiosaurs are mysterious fossil organisms—as we will see, many questions regarding their biology remain unanswered or contentious. However, plesiosaurs are currently undergoing renewed scientific attention.

Figure 1 Open in figure viewer PowerPoint The beautifully preserved skeleton of the plesiosaur Rhomaleosaurus victor seen in ventral view, from the Lower Jurassic (Toarcian) of Holzmaden, Germany (total length 3.44 m). Redrawn from Fraas (1910).     

The nonlinear elasticity and related properties of anhydrous and hydrous γ-Mg2SiO4: a theoretical study

The second-order elastic constants up to 30 GPa, which encompass the stability field of the spinel forms, their pressure derivatives and the third-order elastic constants of both hydrous and anhydrous -Mg₂SiO₄ have been obtained theoretically. A combination of deformation theory and finite strain elasticity theory has been employed to arrive at the expressions for second-order and third-order elastic constants from the strain energy of the lattice. The strain energy is calculated by taking into account the interactions up to second nearest neighbours in the -Mg₂SiO₄ lattice. This is then compared with the strain-dependent lattice energy from continuum model approximation to obtain the expression of elastic constants. The second-order elastic constants C_ij compare favourably with the measurements in the case of anhydrous as well as hydrous -Mg₂SiO₄ and with other calculations on the anhydrous phase. All the third-order elastic constants of both the compounds are negative. The third-order elastic constant C₁₄₄(–52.41 and –45.07 GPa for anhydrous and hydrous -Mg₂SiO₄, respectively) representing the anisotropy of shear mode has a smaller value than C₁₁₁ (–2443.94 and –2101.25 GPa for anhydrous and hydrous phases, respectively), which corresponds to the longitudinal mode. The pressure-induced variations in the longitudinal elastic constants (i.e.,dC₁₁/dp) are relatively large (4.08 and 4.09 for dry and hydrous ringwoodite, respectively) compared with those for the shear (0.22 and 0.32 for dry and hydrous ringwoodite, respectively) and off-diagonal constants (1.40 and 1.41 for dry and hydrous ringwoodite, respectively). The variation of the shear moduli C_s and anisotropy factor A with pressure have also been studied. The average value of elastic anisotropy is 0.835 in the case of anhydrous -Mg₂SiO₄ and 0.830 in the hydrous phase. The reversal of sign of the Cauchy pressure C₁₂ – C₄₄, which describes the angular character of atomic bonding in metals and other compounds, at around 21 GPa for both the compounds may be a precursor to the phase transition from ringwoodite to periclase and perovskite at an elevated temperature. The aggregate elastic properties like the adiabatic bulk modulus K (175.4 and 150.2 GPa for anhydrous and hydrous phases, respectively), and the isotropic compressional (P) and shear (S) wave velocities were calculated and the mode Grüneisen Parameters (GPs) of the acoustic waves were determined based on the quasi-harmonic approximation. The low temperature limit of both hydrous and anhydrous phases of -Mg₂SiO₄ are positive (1.69 and 1.78, respectively, for hydrous and anhydrous phases) and hence we expect the thermal expansion to be positive down to absolute zero. The Anderson–Grüneisen parameter obtained for hydrous as well as anhydrous phases of -Mg₂SiO₄ from the second-order and third-order elastic constants are 2.30 and 2.29, respectively.     

The Asian Tsunami disaster,December 2004

The tragic scenes of human suffering in the wake of the Asian tsunami in late December 2004 have thrown into sharp relief the Earth's destructive power (Fig. 1 ). Caused by a tectonic event off the coast of Sumatra, it could be described as a very large earthquake, an unusual tsunami and a massive disaster. Or, with a longer view, it could be considered a normal feature of a convergent plate boundary. Both views are correct.

Figure 1 Open in figure viewer PowerPoint Mass destruction after the tsunami hit the village on the sand bar at Phi Phi Island, Thailand, with unscathed limestone hills behind (Rex Features).     

Relationship Between Solidification Depth of Granitic Rocks and Formation of Hydrothermal Ore Deposits

Chemical analysis of biotite in representative granitic rocks in Japan shows that the total Al (^TAl) content changes with the metal type of the accompanying hydrothermal ore deposits and increases in the following order: Pb‐Zn and Mo deposits < Cu‐Fe and Sn deposits < W deposits < non‐mineralized granitic rocks. The ^TAl content of biotite in granitic rocks may be a useful indicator for distinguishing between mineralized and non‐mineralized granitic rocks. A good positive correlation is seen between the ^TAl content of biotite and the solidification pressure of the granitic rocks estimated by sphalerite and hornblende geobarometers and the mineral assemblages of the surrounding rocks. These facts suggest that the ^TAl content of biotite can be used to estimate the solidification pressure (P) of the granitic rocks. The following empirical equation was obtained: where ^TAl designates the total Al content in biotite on the basis O = 22. According to the obtained biotite geobarometer, it is estimated that Pb‐Zn and Mo deposits were formed at pressures below 1 kb, Cu‐Fe and Sn deposits at 1–2 kb, W deposits at 2–3 kb and non‐mineralized granitic rocks were solidified at pressures above 3 kb.     

The Purbeck Limestone Group of Dorset,southern England

The late Jurassic to early Cretaceous Purbeck Limestone Group of Dorset has been a focus for media and academic attention for the last 150 years. For example, The Illustrated London News in 1857 carried an article by the Revd Charles Kingsley, (of The Water Babies fame), titled ‘Geological Discoveries at Swanage’. describing fossil‐hunting endeavours of Samuel Husband Beckles (1814–1890; Fig. 1 ). Beckles had been encouraged by Richard Owen (1804–1892) to go in search of the tiny fossilized mammalian remains in these strata. Beckles rose to the challenge and at his own expense employed a team of workmen to carry out the excavations; in the process they uncovered a thin layer containing the numerous remains of diminutive mammals along with the remains of other vertebrates, including turtles, crocodiles and ornithischian dinosaurs. Since then, dinosaur tracks and related discoveries from these same strata have often caught the imagination of the press, inspiring sensational headlines such as ‘Builder digs up giant lizard fight’ and ‘Dinosaur graveyard in Swanage Bay’!

Figure 1 Open in figure viewer PowerPoint Contemporary illustration of Samuel Beckles’ excavation on the cliffs of Durlston Bay, from Charles Kingsley's account of the discoveries at Swanage which appeared in The Illustrated London News in 1857.