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10.9: Kinematics - Geosciences

10.9: Kinematics - Geosciences


Kinematics is the study of patterns of motion, without regard to the forces that cause them. All have units of s–1.

We have already encountered horizontal divergence, D, the spreading of air:

( egin{align} D=frac{Delta U}{Delta x}+frac{Delta V}{Delta y} ag{10.72}end{align})

Figure 10.29 Kinematic flow-field definitions. Black arrows represent wind velocity.

Figure 10.29a shows an example of pure divergence. Its sign is positive for divergence, and negative for convergence (when the wind arrows point toward a common point).

Vorticity describes the rotation of air (Fig. 10.29b). The relative vorticity, ζr , about a locally vertical axis is given by:

( egin{align} zeta_{r}=frac{Delta V}{Delta x}-frac{Delta U}{Delta y} ag{10.73}end{align})

The sign is positive for counterclockwise rotation (i.e., cyclonic rotation in the N. Hemisphere), and negative for clockwise rotation. Vorticity is discussed in greater detail in the General Circulation chapter. Neither divergence nor vorticity vary with rotation of the axes — they are rotationally invariant.

Two types of deformation are stretching deformation and shearing deformation (Figs. 10.29c & d). Stretching deformation, F1, is given by:

( egin{align} F_{1}=frac{Delta U}{Delta x}-frac{Delta V}{Delta y} ag{10.74}end{align})

The axis along which air is being stretched (Fig. 10.29c) is called the axis of dilation (x axis in this example), while the axis along which air is compressed is called the axis of contraction (y axis in this example).

Shearing deformation, F2, is given by:

( egin{align} F_{2}=frac{Delta V}{Delta x}+frac{Delta U}{Delta y} ag{10.75}end{align})

As you can see in Fig. 10.29d, shearing deformation is just a rotated version of stretching deformation.

The total deformation, F, is:

( egin{align} F=left[F_{1}^{2}+F_{2}^{2} ight]^{1 / 2} ag{10.76}end{align})

Deformation often occurs along fronts. Most real flows exhibit combinations of divergence, vorticity, and deformation.


10.9: Kinematics - Geosciences

The discovery by Kormendy of a M•

= 109 Msolar massive dark object (MDO) in NGC 4594 is confirmed with higher resolution spectroscopy from the Canada-France-Hawaii Telescope (CFHT) and the Hubble Space Telescope (HST). CFHT measurements with the Subarcsecond Imaging Spectrograph improve the resolution from sigma * = 0."40 to 0."27 Gaussian dispersion radius of the point-spread function (PSF). The apparent central velocity dispersion rises from sigma = 250 +/- 7 km s-1 to sigma = 286 +/- 7 km s-1. As observed with the COSTAR-corrected HST, the Faint Object Spectrograph, and a 0."21 aperture, sigma = 321 +/- 7 km s-1 is still higher, and the central rotation curve is very steep. The highest-M• published dynamical model fits the new observations reasonably well when "observed" at HST resolution. The spatial resolution has now improved by a factor of

5 since the discovery measurements, and the case for a black hole (BH) has strengthened correspondingly. We confirm that NGC 4594 has a Seyfert spectrum H alpha is

5200 km s-1 wide at zero intensity. However, gas velocities are lower than the circular velocities implied by the stars, so they cannot be used to test the BH case in NGC 4594. The gas may be in a ring, or it may be associated with patchy dust. HST images with the Wide Field and Planetary Camera 2 show dust at some aperture positions. NGC 4594 appears to have a bright point nucleus. However, the central absorption-line strengths are low, consistent with dilution by enough nonthermal light to explain the "nucleus." There is no evidence for a distinct nuclear star cluster. NGC 4594 is similar to M87, which also has a nonthermal nuclear source, and not to M31 and NGC 3115, which have quiescent BHs and nuclear star clusters.


Volume 79 - Issue 1 - March 2000

Editorial

A new phase in the journal’s history

Research Article

The Holocene evolution of the barrier and the back-barrier basins of Belgium and the Netherlands as a function of late Weichselian morphology, relative sea-level rise and sediment supply

Flooding of the southern part of the North Sea occurred between 9000 and 8000 BP, when the rate of relative sea-level rise was on the order of 0.7 cm per year for the Dover Strait Region and 1.6 cm per year for the area north of the Frisian Islands, forcing the shoreline to recede rapidly. When relative sea-level rise decelerated after 7000 BP for the Belgian coast and 6000 BP for the central Netherlands coast, sediment supply by the tidal currents balanced the creation of accommodation space in the estuaries and other back-barrier basins. Consequently, the barrier started to stabilize, and the tidal basins and their inlets silted up. Between 5500 and 4500 BP, the Belgian coastal plain changed into a freshwater marsh with peat accumulation, and the same happened 500–1000 years later in the western provinces of the Netherlands. The E-W running barrier/back-barrier system of the Frisian Islands in the northern Netherlands stayed open until today, however, because of lower sediment supply.

The period between 4000 and 2000 BP was relatively quiet due to the strong deceleration of the rate of sea-level rise peat cushions developed behind the barriers, which were straightened by erosion of the headlands. Major and often catastrophic flooding occurred in the Middle Ages, when the estuaries in the southwestern part of the Netherlands formed.

About 226 (± 15%) × 10 9 m 3 sediment, mostly sand, is stored in the barriers and back-barrier basins of the Netherlands, 70% of which was deposited prior to 5000 BP. About 10% of the stored sediment is estimated to be of alluvial origin. Most of the sediment is derived by the erosion of the Pleistocene basement during recession of the barriers, but tide-induced crossshore transport from the North Sea forms an additional source for the barriers and back-barriers of the west-facing coast of the Netherlands.

Late Permian (Zechstein) carbonate-facies maps, the Netherlands

The Late Permian Zechstein carbonates in the Southern Permian Basin were deposited under marine conditions. The carbonates form part of a largely progradational infill, with a gradual northward facies shift. The paleogeography of the Zechstein carbonate deposits has been reviewed recently on the base of well data, cores and publications. This has resulted in three updated maps of the carbonate units. These maps reflect the increase in knowledge of the palaeogeography of the Zechstein as a result of several decades of subsurface exploration. It is found that deposition of the carbonates was controlled by various factors, i.e., rifting during deposition of the basal Zechstein, sea-level fluctuations and basin subsidence. This resulted in an overall E-W orientated facies distribution in the Zechstein carbonates, and in the gradual northward shift of the various facies belts in time.

Reefs in the Zl Carbonate Member and off-platform highs and turbidites in the Z2 Carbonate Member have been identified as potential future exploration targets.

Modelling the hydrocarbon generation and migration in the West Netherlands Basin, the Netherlands

The hydrocarbon systems of the Mesozoic, inverted West Netherlands Basin have been analyzed using 2-D forward modelling. Three source rocks are considered in the modelling: Lower Jurassic oil-prone shales, Westphalian gas-prone coal deposits, and Lower Namurian oil-prone shales. The Lower Namurian hydrocarbon system of the basin is discussed for the first time.

According to the modelling results of the Early Jurassic oil system, the oil accumulations were filled just after the main inversion event. Their predicted locations are in agreement with exploration results. Modelling results of the Westphalian gas system, however, show smaller and larger sized accumulations at unexplored locations. The gas reservoirs were filled during the Late Jurassic-Early Cretaceous rifting phase. Results of modelling of the Lower Namurian oil system indicate that gas formed by secondary cracking of the oils can have mixed with the Westphalian coal-derived gas. Such a mixing is inferred from geochemical analyses. The existence of a Lower Namurian hydrocarbon system in the West Netherlands Basin implies that hydrocarbons are possibly trapped in the Westphalian and Namurian successions. These potential traps in the basin have not yet been explored.

Fracture networks in Rotliegend gas reservoirs of the Dutch offshore: implications for reservoir behaviour

Fracture systems of Rotliegend gas fields in and at the margins of the northern Broad Fourteens Basin in the Dutch offshore are described in terms of orientation, frequency, origin and type, and in relation to larger-scale structures. First, fracture data collected from core and image logs have been corrected to account for the bias related to the 1-D sampling. Second, these results were integrated with data on fracture cements and diagenesis in order to assess the timing of the fracture network development.

(1) at Triassic times and related to early diagenesis and burial, NW-SE to NNW-SSE and NE-SW to ESE-WNW particulate-shear fractures developed

(2) during the Mid-Kimmerian and related to the main burial stage, shear-related and dilational-shear-fault-related fracturing occurred parallel with larger-scale faults

(3) during the Cretaceous and related to uplift, NW-SE and NE-SW joints propagated a regional joint system developed outside the Jurassic rift basin, preferentially oriented E-W to ESE-WNW these joints have not been dated accurately.

The fault-related shear fractures tend to compartmentalise the reservoirs, whereas the regional joints tend to enhance reservoir flow properties. These fracture systems are thought to play a negative or positive role, respectively, but only in fields with poor reservoir quality. Consequently, in such cases small-scale fractures should be taken into account in field development planning.

Composition and genesis of rattlestones from Dutch soils as shown by Mössbauer spectroscopy, INAA and XRD

The chemical and mineralogical composition of rattlestones found near the main Dutch rivers has been studied by Mössbauer spectroscopy, INAA and XRD. Rattlestones are concretions of iron, formed in an environment of lateral iron accumulation, under the influence of periodical oxidation, around a fine core of ferruginous sediments, mainly clay and sand. The core has shrunk and detached itself from the mantle around it. 57 Fe Mössbauer spectroscopy was applied to identify the iron oxides, among which goethite is predominant. The goethite crystallinity was investigated by measuring its magnetic properties and its crystallinity, which is poorest at the outer side of the stone. The latter is confirmed by the broadening of the different X-ray reflections. In addition, illite and vermiculite were identified by XRD these clay minerals were found mainly in the core.

The elemental composition was determined by INAA. The iron content in the mantle is about 50% by weight and gradually decreases outwards, while the core contains 2–15% Fe by weight. Differences between rattlestones from the Middle Pleistocene East of the Meuse river and those from the Late Pleistocene North of it are the absence of lepidocrocite and a richer mineralogy in the former.

It is concluded that the rattlestones are formed around a fine clayey core. Groundwater supplied the iron and other (trace) elements for the genesis. It is unlikely that rattlestones are the result of oxidation of siderite.

A seismologically motivated survey of blasting activity in the northern Rhine area

Discrimination between quarry blasts and earthquakes has gained importance due to signature of the Comprehensive Test Ban Treaty. In this context, large chemical explosions are significant. In the routine analysis of data from local seismograph networks, discrimination between smaller blasts and micro-earthquakes is not always clear. Many quarries are in operation and blasts far outnumber natural earthquakes in the highly industrialized northern Rhine area.

We compiled a list of active quarries in the Northern Rhine Area and mapped their locations. We then created a database from a questionnaire sent out to all quarries on the list. From the 33% of questionnaires that were returned, we discerned some representative values for the main blasting parameters and explosive consumption. In the study area of 72,000 km 2 , approx. 21,000 blasts are fired per year (80 per working day). Most of the blasts (72%) have total explosive charges between 400 and 4500 kg. Shots with charges above 10 tons are rare (20-30 per year). Some 80% of the blasts are ripple-fired with a nominal firing time interval of 20 ms.

Based on empirical amplitude vs. distance curves from vibration control measurements, a relation between maximum charge weight per delay time, L (kg), and a ‘quarry blast’ magnitude, M QB , is derived: M QB = 0.6·log 10 (L) + 0.131. Using this relation and extrapolating the database from the questionnaire shows that for magnitudes between 1 and 2, blasts occur 200–250 times more frequently than micro-earthquakes in the Northern Rhine area.

Wedge equilibrium in fold-and-thrust belts: prediction of out-of-sequence thrusting based on sandbox experiments and natural examples

Thrust tectonics are dealt with on the basis of primarily experiments focusing on the dynamics of a developing thrust belt and on understanding and predicting normal-sequence and out-of-sequence thrusting. Field examples are presented in addition to the examples of sandbox-model experiments. The results have improved the insight into thrust-belt-forming mechanisms the validity of the conclusions is supported by natural examples.

The experimental program was aimed at examining the effect of changes in a selection of key parameters in thrust tectonics on the geometry and the successive phases in the development of thrust sheets. Sandbox experiments were used to analyse the effects of basal friction, detachment lithology, basement relief and syntectonic sedimentation. Multilayer experiments were performed to simulate the effects of ductile detachment lithologies.

It was found that a thrust belt’s cross-sectional geometry is formed in a dynamic process during which the wedge may develop from subcritical through critical to supercritical and back to critical again. The process is illustrated with sandbox experiments, analysed by time-lapse computed tomography scans and in-situ stress measurements. On the basis of the sandbox-model results and the natural examples, we conclude that a critical examination of the boundary conditions of a fold-and-thrust belt and of changes in these conditions during the deformation process enables predictions about the geometry and kinematics of the thrust belt.

Subaerial terminoglacial fans III: overview of sedimentary characteristics and depositional model

A general model is presented for the small type of fans (not to be confused with sandurs) that develop subaerially in the zone immediately before an ice front. These fans have in common with other fans that a proximal, a middle and a distal subenvironment– with distinctly different sedimentary facies– can be distinguished. The characteristics of these fans differ in several respects, however, from those formed under other conditions, particularly by the high proportion of mass-flow deposits in the proximal part, by the relative scarcity of fine particles in the middle fan, and by the relatively uniform character of the sediments in the distal fan.

The special character of this type of fan is ascribed to the interaction of a continuously changing distance between the ice front and the fan (as a result of alternating phases of ice advance and ice retreat), its position that may be surrounded by ice for a large part, and the irregular supply of debris-laden meltwater that comes sometimes even in the form of more or less catastrophic floods.

Due to the fact that terminoglacial fans have a good preservation potential only during phases of ice retreat, these fas tend to show a slight fining-upward tendency. The slope of terminoglacial fans tends to be more gentle (rarely over 2–5°) than that of fans formed under different conditions.

Provenance of coarse ice-rafted detritus near the SE Greenland margin

The provenance of coarse-grained ice-rafted detritus has been studied, based on material collected from the SE Greenland margin. The sediment was sampled by a 1.5 m 3 video-grab from 1256 m water depth. The fraction > 1cm was macroscopically investigated and a thin-section analysis was made. The results clearly show that East Greenland north of the Denmark Strait is the source region of the material sampled. The main provenance is from areas adjoining Kangerdlugssuaq Fjord, Blosseville Kyst, Scoresby Sund, Kong Oskar Fjord, and Kejser Franz Joseph Fjord. It can thus be demonstrated that significant ice-stream activity and iceberg calving occurred there. Present-day iceberg production is mainly concentrated to the Scoresby Sund, but the other areas apparently represent locations of larger ice-stream activity during periods prior to the Holocene.

More generally, it can be concluded that southerly surface-water flow similar to the present East Greenland Current must also have occurred prior to the Holocene. Although either North America (Canada) or Scandinavia - or both - are generally referred to as important regions for the provenance of ice-rafted detritus, we conclude that (East) Greenland may have been an important source for (late) glacial North Atlantic ice-rafted detritus production as well.


Acknowledgements

We thank R. Bürgmann for comments that helped to improve the paper. We thank J. Armbruster, who installed the initial 6 stations in 2003, and N. Feldl, who helped install 12 stations in 2007. We also thank the Dhaka University students who helped maintain the GPS network and the people at the many sites that host the GPS stations. Without their efforts and UNAVCO support, this project would not have been possible. We thank M. Kogan for help with processing. We thank C. Rangin, F. Masson and T. Maurin for sharing their Myanmar GPS data with us. This material is based on equipment and engineering services provided by the UNAVCO Facility with support from the National Science Foundation (NSF) and National Aeronautics and Space Administration (NASA) under NSF Cooperative Agreement EAR-0735156. This project was supported by NSF INT 99-00487, NSF EAR-06 36037 and NSF IIA 09-68354. L.F. and E.M.H. were supported by Singapore National Research Foundation Fellowship number NRF-NRFF2010-064. Lamont-Doherty Earth Observatory publication number 8204.


10.9: Kinematics - Geosciences

We use Multi Unit Spectroscopic Explorer (MUSE) observations of the galaxy cluster MACS J1149.5+2223 to explore the kinematics of the grand-design spiral galaxy (Sp1149) hosting the supernova `Refsdal'. Sp1149 lies at z ≃ 1.49, has a stellar mass M * ≃ 5 × 10 9 M ⊙ , has a star formation rate (SFR) ∼eq 1-6 M_ <⊙>yr^<-1>, and represents a likely progenitor of a Milky Way-like galaxy. All the four multiple images of Sp1149 in our data show strong [O II>-line emissions pointing to a clear rotation pattern. We take advantage of the gravitational lensing magnification effect (≃4×) on the [O II> emission of the least distorted image to fit three-dimensional kinematic models to the MUSE data cube and derive the rotation curve and the velocity dispersion profile of Sp1149. We find that the rotation curve steeply rises, peaks at R ≃ 1 kpc, and then (initially) declines and flattens to an average = 128^<+29>_ <-19>km s -1 . The shape of the rotation curve is well determined, but the actual value of V flat is quite uncertain because of the nearly face-on configuration of the galaxy. The intrinsic velocity dispersion due to gas turbulence is almost constant across the entire disc with an average of 27 ± 5 km s -1 . This value is consistent with z = 0 measurements in the ionized gas component and a factor of 2-4 lower than other estimates in different galaxies at similar redshifts. The average stellar-to-total mass fraction is of the order of one-fifth. Our kinematic analysis returns the picture of a regular star-forming, mildly turbulent, rotation-dominated (V/σ ≃ 5) spiral galaxy in a 4-Gyr-old Universe.


FALL3D : A computational model for transport and deposition of volcanic ash ☆

FALL3D is a 3-D time-dependent Eulerian model for the transport and deposition of volcanic ashes and lapilli. The model solves the advection–diffusion–sedimentation (ADS) equation on a structured terrain-following grid using a second-order finite differences (FD) explicit scheme. Different parameterizations for the eddy diffusivity tensor and for the particle terminal settling velocities can be used. The code, written in FORTRAN 90 , is available in both serial and parallel versions for Windows and Unix/Linux/Mac X operating systems (OS). A series of pre- and post-process utility programs and OS-dependent scripts to launch them are also included in the FALL3D distribution package. Although the model has been designed to forecast volcanic ash concentration in the atmosphere and ash loading at ground, it can also be used to model the transport of any kind of airborne solid particles. The model inputs are meteorological data, topography, grain-size distribution, shape and density of particles, and mass rate of particle injected into the atmosphere. Optionally, FALL3D can be coupled with the output of the meteorological processor CALMET , a diagnostic model which generates 3-D time-dependent zero-divergence wind fields from mesoscale forecasts incorporating local terrain effects. The FALL3D model can be a tool for short-term ash deposition forecasting and for volcanic fallout hazard assessment. As an example, an application to the 22 July 1998 Etna eruption is also presented.


Summary and Final Tasks

Kinematics describes the behavior of atmospheric motion but not the cause. Streamlines provide snapshots of that motion and trajectories show where individual air parcels actually go. All atmospheric motion in the horizontal is made up of one or more of five distinct types of motion: translation, stretching deformation, shearing deformation, vorticity, and divergence. Stretching and shearing deformation lead to the formation or the dissolution of surface weather fronts. Vorticity describes the counter-clockwise rotation around low pressure (in the Northern Hemisphere) and clockwise rotation around high pressure (in the Northern Hemisphere) and is thus associated with much of weather. Divergence/convergence aloft leads to vertical winds that connect to convergence/divergence at the surface, and through this mechanism, air motion aloft communicates with air motion at the surface.

This lesson showed the mathematics necessary to quantify all of these processes. So besides identifying streamline confluence/diffluence, you practiced quantifying the five flow types from weather maps of streamlines with wind vectors. Finally, you calculated the vertical wind and its direction (up or down) based on the divergence/convergence of the winds aloft.

Reminder - Complete all of the Lesson 9 tasks!

You have reached the end of Lesson 9! Double-check that you have completed all of the activities before you begin Lesson 10.


Differencing: Classification of GPS Positioning

GPS work is sometimes divided into three categories positioning, navigation, and timing (PNT). Most often, GPS surveying is concerned with the first of these, positioning. In general, there are two techniques used in surveying. They are kinematic and static. In static GPS surveying sessions, the receivers are motionless on the Earth during the observation. Because static work most often provides higher accuracy and more redundancy than kinematic work, it is usually done to establish control. The results of static GPS surveying are processed after the session is completed. In other words, the data is typically post-processed. The majority of GPS surveying control and geodetic work still relies on static applications.

In kinematic GPS surveying, the receivers are either in periodic or continuous motion. Kinematic GPS is done when real-time, or near real-time, results are needed. When the singular objective of kinematic work is positioning, the receivers move periodically using the start and stop methodology originated by Dr. Benjamin Remondi in the 1980s. When the receivers are in continuous motion, the objective may be acquisition of the location, attitude, and velocity of a moving platform (i.e., navigation), or positioning. The distinction between navigation and positioning is lessening.

Kinematic applications imply movement, one or more GPS receivers actually in motion during their observations. A moving GPS receiver on land, sea, or air is characteristic of kinematic GPS. Other characteristics of the application include results in real time and little redundancy. Hydrography, aerial mapping, gravimetric, and more and more land surveying projects are done using kinematic GPS.

Relative positioning is different than autonomous positioning. An independent receiver, an autonomous receiver, must rely on the information in the Navigation Message. In that sort of configuration, it has no way to improve on the corrections. In relative (aka differential) positioning, there are two receivers one on a known point whose coordinates are well-established, and a second receiver on an unknown point. With this arrangement, the new unknown position can be established relative to the known point. Relative (differential) positioning creates solutions that are positionally superior to autonomous positioning, in large part because it is possible to improve on the corrections available in the Navigation Message

The term differential GPS, or DGPS, has come into common usage as well. Use of this acronym usually indicates a method of relative positioning where usually coded pseudorange measurements are used rather than carrier phase, though it is sometimes used in context of carrier phase solutions.


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