Numerical study of a Whitham equation exhibiting both breaking waves and continuous solutions

We consider a Whitham equation as an alternative for the Korteweg–de Vries (KdV) equation in which the third derivative is replaced by the integral of a kernel, i.e., ηxxx in the KdV equation is replaced by ∫∞−∞Kν(x−ξ)ηξ(ξ,t)dξ. The kernel Kν(x) satisfies the conditions limν→∞Kν(x) = δ″(x), where δ(x) is the Dirac delta function and limν→0Kν(x) = 0. The questions studied here, by means of numerical examples, are whether adjustment of the parameter ν produces both continuous solutions and shocks of the kernel equation and how well they represent KdV solutions and solutions of the underlying hyperbolic system. A typical example is for resonant forced oscillations in a closed shallow water tank governed by the kernel equation, which are compared with those governed by a partial differential equation. The continuous solutions of the kernel equation associated with frequency dispersion in the KdV equations limit to the shocks of the shallow water equations as ν → 0. Two experimental problems are solved in a single equation. As another example, suitable adjustment of ν in the kernel equation produces solutions reminiscent of a hydraulic and undular bore

Prelithification and synlithification tectonic foliation development in a clastic sedimentary sequence

The current view regarding the timing of regionally developed penetrative tectonic fabrics in sedimentary rocks is that their development postdates lithification of those rocks. In this case, fabric development is achieved by a number of deformation mechanisms, including grain rigid body rotation, crystal-plastic deformation, and pressure solution. The latter is believed to be the primary mechanism responsible for the domainal structure of cleavage in low-grade metamorphic rocks. In this study we combine field observations with strain studies to characterize considerable (>50%) Acadian crustal shortening in a Devonian clastic sedimentary sequence from southwest Ireland. Despite these high levels of shortening there is a marked absence of the domainal cleavage structure and intraclast deformation that are expected with this level of deformation. Fabrics in these rocks are predominantly a product of rigid body rotation and repacking of extraformational clasts during deformation of a clastic sedimentary sequence before lithification was complete

Prelithification and synlithification tectonic foliation development in a clastic sedimentary sequence

The current view regarding the timing of regionally developed penetrative tectonic fabrics in sedimentary rocks is that their development postdates lithification of those rocks. In this case, fabric development is achieved by a number of deformation mechanisms, including grain rigid body rotation, crystal-plastic deformation, and pressure solution. The latter is believed to be the primary mechanism responsible for the domainal structure of cleavage in low-grade metamorphic rocks. In this study we combine field observations with strain studies to characterize considerable (>50%) Acadian crustal shortening in a Devonian clastic sedimentary sequence from southwest Ireland. Despite these high levels of shortening there is a marked absence of the domainal cleavage structure and intraclast deformation that are expected with this level of deformation. Fabrics in these rocks are predominantly a product of rigid body rotation and repacking of extraformational clasts during deformation of a clastic sedimentary sequence before lithification was complete

The provenance of the Devonian Old Red Sandstone of the Dingle Peninsula, SW Ireland; the earliest record of Laurentian and peri-Gondwanan sediment mixing in Ireland

The Lower Old Red Sandstone in southern Ireland is hosted in the Early Devonian Dingle Basin, which lies immediately south of the Iapetus Suture on the Dingle Peninsula, County Kerry. The basin developed as a post-Caledonian pullapart structure prior to Acadian deformation, which in turn was followed by end-Carboniferous Variscan deformation. Detrital zircon U–Th–Pb geochronology is complemented by mica Ar–Ar and apatite U–Pb geochronology to gain a comprehensive understanding of the provenance of the Lower Devonian Lower Old Red Sandstone of the Dingle Basin and assess contributions of major tectonic components (e.g. Laurentia, Ganderia). Sedimentary rocks in the Lower Old Red Sandstone have similar detrital zircon age distributions, which are dominated by c. 1.2 Ga zircons as well as late Neoproterozoic grains. This indicates a dominant contribution of detritus of Laurentian affinity as well as contributions from westerly and southerly derived Ganderian detritus. Caledonian uplift of the area north of the Iapetus Suture would have facilitated a large contribution of (peri-)Laurentian material. The Upper Old Red Sandstone on the Dingle Peninsula has a distinctly different detrital zircon character including few late Neoproterozoic zircons and abundant zircons of c. 1.05 Ga age, indicating sediment derivation only from Laurentia and no recycling from the Lower Old Red Sandstone

Constraining Basin Parameters Using a Known Subsidence History

Temperature history is one of the most important factors driving subsidence and the overall tectono-stratigraphic evolution of a sedimentary basin. The McKenzie model has been widely applied for subsidence modelling and stretching factor estimation for sedimentary basins formed in an extensional tectonic environment. Subsidence modelling requires values of physical parameters (e.g., crustal thickness, lithospheric thickness, stretching factor) that may not always be available. With a given subsidence history of a basin estimated using a stratigraphic backstripping method, these parameters can be estimated by quantitatively comparing the known subsidence curve with modelled subsidence curves. In this contribution, a method to compare known and modelled subsidence curves is presented, aiming to constrain valid combinations of the stretching factor, crustal thickness, and lithospheric thickness of a basin. Furthermore, a numerical model is presented that takes into account the effect of sedimentary cover on thermal history and subsidence modelling of a basin. The parameter fitting method presented here is first applied to synthetically generated subsidence curves. Next, a case study using a known subsidence curve from the Campos Basin, offshore Brazil, is considered. The range of stretching factors estimated for the Campos basin from this study is in accordance with previous work, with an additional estimate of corresponding lithospheric thickness. This study provides insight into the dependence of thermal history and subsidence modelling methods on assumptions regarding model input parameters. This methodology also allows for the estimation of valid combinations of physical lithospheric parameters, where the subsidence history is known

Image based Particle Shape Analysis Toolbox (IPSAT)

Shape analysis can provide vital information regarding the origin, transport and deposition history of grains. Particle shape measurement has been an active area of research for sedimentologists since the 20th century. With advancement in the field of computation and image analysis, shape analysis can be done in a faster and much more accurate way compared to manual measurements. The results obtained are reproducible as compared to visual qualitative analysis. However, there is a lack of image analysis software tools aimed at the field of sedimentology where the fine details of a particle boundaries are required. Image based Particle Shape Analysis Toolbox (IPSAT) developed in the Mathematica environment for the quantitative characterisation of sedimentary grains in 2-dimensions is presented here. This image analysis toolbox can be used to analyse consolidated as well as loose sediment samples. A total of 12 parameters are available for shape measurement comprising conventional shape parameters (roundness, angularity, circularity and irregularity), mathematically complex shape parameters (fractal dimension and Fourier descriptors) and common geometrical shape parameters (aspect ratio, convexity, solidity, mod ratio, rectangularity and compactness). Additionally, IPSAT offers to compute 6 particle size measurement parameters. Furthermore, 2-D particle size distribution can be transformed to a 3-D size distribution for thin section analysis. Example analyses have been carried out on a sandstone and a loose sediment sample. The toolbox presented here aims to establish a textural analysis methodology to be used by geologists and sedimentologists in particular. It will allow users to quantitatively characterise a large set of grains with a fast, cheap and robust methodology

Factors affecting finite strain estimation in low-grade, low-strain clastic rocks

The computer strain analysis methods SAPE, MRL and DTNNM have permitted the characterization of finite strain in two different regions with contrasting geodynamic scenarios; (1) the Talas Ala Tau (Tien Shan, Kyrgyzs Republic) and (2) the Somiedo Nappe and Narcea Antiform (Cantabrian to West Asturian-Leonese Zone boundary, Variscan Belt, NW of Iberia). The performed analyses have revealed low-strain values and the regional strain trend in both studied areas. This study also investigates the relationship between lithology (grain size and percentage of matrix) and strain estimates the two methodologies used. The results show that these methods are comparable and the absence of significant finite strain lithological control in rocks deformed under low metamorphic and low-strain conditions. © 2009 Elsevier Ltd. All rights reserved.Critical and constructive reviews by Richard Lisle and an anonymous reviewer have helped to improve the manuscript. Financial support was supplied by Research Project ODRE (“Oroclinales Delaminación Relaciones y Efectos”) No. CGL2006-00902, from the Spanish Ministry of Science and Innovation and an ACPI grant from the Junta de Castilla y León.Peer reviewe

Deterministic and stochastic effects in spreading dynamics: a case study of bovine viral diarrhea

Bovine viral diarrhea (BVD) is a disease in cattle with complex transmission dynamics that causes substantial economic losses and affects animal welfare. The infection can be transient or persistent. The mostly asymptomatic persistently infected hosts are the main source for transmission of the virus. This characteristic makes it difficult to control the spreading of BVD. We develop a deterministic compartmental model for the spreading dynamics of BVD within a herd and derive the basic reproduction number. This epidemiological quantity indicates that identification and removal of persistently infected animals is a successful control strategy if the transmission rate of transiently infected animals is small. Removing persistently infected animals from the herd at birth results in recurrent outbreaks with decreasing peak prevalence. We propose a stochastic version of the compartmental model that includes stochasticity in the transmission parameters. This stochasticity leads to sustained oscillations in cases where the deterministic model predicts oscillations with decreasing amplitude. The results provide useful information for the design of control strategies