Tidal flow simulation in the English Channel and Southern North Sea

This paper presents the results of the II Tidal Flow Forum experiment of the English Channel and the southern North Sea. The model applies the FADI (falsified alternating direction implicit) scheme and uses the data base of the Tidal Flow Forum. Discrepancies between the model results and the distributed field data of 11 tide stations and 8 tidal current measurement points are shown graphically and are quantified by calculating the RMS (root mean square) errors and the standard deviations. Sensitivity tests have been carried out by changing some parameters (frictions, Coriolis, …). The results which best fit the reference data were obtained by using the Manning's friction law. By doing so, the model can more appropriately adapt the complex bathymetry. The improvements are shown graphically.     

大连台重力固体潮受海潮负荷影响特征研究

大连台重力固体潮汐观测受海潮负荷影响较大,选取2015年1月1日～2019年8月14日的重力数据进行预处理,获得重力潮汐参数,基于选取的8个海潮模型对O₁、K₁和M₂波进行海潮负荷改正及评价分析。数值分析结果表明,O₁、K₁和M₂波的重力海潮负荷振幅分布频段在2.4～2.8μGal之间,3个主潮波的残差负荷改正有效性为43％～53％,8个海潮模型对大连台主潮波的海潮负荷改正差别较小。     

Tidal effects on the thermosphere

Theoretical understanding of the earth's atmosphere is not possible without accounting for tidal waves and their interactions. In the thermosphere, tides represent the dominant motion system. Current observational efforts are aimed at providing tidal morphologies, i.e., maps of the vertical profiles of the tidal fields as a function of time for various locations. These are in hand for the mesosphere and have proved extraordinarily useful in deriving appropriate inputs for numerical models of the thermosphere. The basic latitudinal, seasonal, and solar cycle variation of the tides in the thermosphere is much less well known but the advent of coordinated global multi-day campaigns promises to ameliorate the situation. Progress would be facilitated by agreement on a standard data reduction procedure. Theoretical efforts are focused on simulating the observed morphologies and understanding the day to day variations while investigating mutual interactions and feedback between the mean atmosphere and the tidal, gravity, and planetary waves.     

Tidal triggering of deep moonquakes

Matching signals have previously been identified from about eighty repeating deep moonquake sources. These moonquakes clearly display tidal periodicities in their histories of origin times and signal amplitudes; they are presumably triggered by the solid-body tide in the moon, raised primarily by the earth. The A1 hypocentre has been the most active and has also produced seismograms with signals of reversed polarity. In an attempt to deduce focal mechanisms for these events, we calculated various tidal stress functions at the Al hypocentre using a homogeneous moon model, and correlated them with the origin times of events. No good correlation was found, either for tidal stress peaks of consistent polarity, or for tidal stress peaks of opposite polarity at the times of “inverted” events. This could be due to an inaccurate moon model, but it has also been noted that the relative amplitudes of signals recorded at different seismic stations vary between events from the same hypocentre. Earthquake swarms often contain events with fault-plane solutions in very different orientations. A similar variation between events from each deep moonquake hypocentre would explain the different amplitude ratios and also the “inverted” events.     

Tidal corrections to gravity measurements

Methods taking into account the effect of tidal forces on gravity measurements are considered. Corrections for the effect of tidal forces can exceed 250 μGal. Only the structure of the Earth and positions of tide-generating celestial bodies are necessary for taking into account earth tides, while cotidal charts are additionally required for the correct incorporation of the effect of ocean tides. The effect can reach a few tens of μGal near shorelines. The modern accuracy of gravity measurements being 1–2 μGal, the ocean tide effect, together with other less significant factors, should be considered for the correct interpretation of gravity data.     

Tidal observations near an amphidrome

The signal to noise ratio in tidal data in the diurnal and semidiurnal frequency bands is ordinarily so large that the noise contribution to the tidal harmonic constants is unimportant. However, as the observational locations are selected progressively closer to an amphidrome (point of no tide), the signal to noise ratio decreases, making the tidal harmonic constants less dependable. Standard deviations in amplitude of M₂ and S₂ obtained from 12 29-day analyses of a year of tide data obtained at a standard tide station, estimated to be 280 and 550 km away from the amphidromes for these constituents in the eastern Caribbean, are roughly one-third of the mean amplitudes for these constituents; the standard deviations in epoch are 38° and 30° respectively. Therefore, a program to locate an amphidrome precisely is self-defeating and the location can only be approximated by a grid of tide observations spanning the geographic position and/or by longer series of observations, using higher resolution to increase the signal to noise ratio. Amplitudes of 0.64 cm and 1.24 cm were calculated for M₂ and S₂ from a one-month series of pelagic observations obtained very close to an inferred position of the M₂ amphidrome in the northeast Caribbean Sea.Abbreviations C&GS Coast and Geodetic Survey - CICAR Cooperative Investigation of the Caribbean and Adjacent Regions - IAPSO International Association for the Physical Sciences of the Ocean - ICOT Institute of Coastal Oceanography and Tides - IDOE International Decade of Ocean Exploration - NOAA National Oceanic and Atmospheric Administration - NOS National Ocean Survey - NSF National Science Foundation - SCOR Scientific Committee of Oceanic Research - UNESCO United Nations Educational, Scientific, and Cultural Organization     

Tidal correction of hydrographic measurements

Summary A simple procedure is presented to eliminate the influence of tidal oscillation from hydrographic measurements. This is done with a transformation from a co-ordinate system fixed in space to a co-ordinate system fixed in time using results of a numerical tidal model. The procedure is applied to a hydrographic survey in the German Bight. The hydrographic structure transformed onto a co-ordinate system fixed in time is much more similar to the structure obtained by satellite pictures and shows dynamical processes much clearer than in a co-ordinate system fixed in space.

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Gezeitenkorrektur von hydrographischen Messungen

Zusammenfassung In dieser Arbeit wird ein Verfahren vorgestellt, das hydrographische Messungen vom Einfluß periodischer Variationen durch die Gezeiten bereinigt. Dies geschieht unter Benutzung von Ergebnissen eines numerischen Modells durch eine Transformation einer gemessenen hydrographischen Struktur von einem ortsfesten in ein zeitfestes System. Dieses Verfahren wird auf eine hydrographische Aufnahme der Deutschen Bucht angewandt. Die auf ein zeitfestes Koordinatensystem transformierte hydrographische Messung zeigt sehr viel Ähnlichkeit mit einer synoptischen Messung, die bei einem Satellitenüberflug gewonnen wurde. Bestimmte dynamische Prozesse in der Deutschen Bucht lassen sich zudem im zeitfesten Koordinatensystem besser erkennen als im ortsfesten Koordinatensystem.

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Correction de l'influence de la marée sur les mesures hydrologiques

Résumé L'article présente une méthode simple pour éliminer l'influence de la marée sur les mesures hydrologiques. Cela est obtenu par le passage d'un système de coordonnées fixe dans l'espace à un système de coordonnées fixe dans le temps utilisant les résultats d'un modèle numérique de marée. La méthode est appliquée à un levé hydrologique dans la Baie Allemande. La structure hydrologique obtenue dans un système de coordonnées fixe dans le temps est beaucoup plus proche de celle qui est obtenue par les images satellites et décrit le processus dynamique beaucoup plus clairement que dans un système de coordonnées fixe dans l'espace.

     

Tidal boundary conditions in SEAWAT

SEAWAT, a U.S. Geological Survey groundwater flow and transport code, is increasingly used to model the effects of tidal motion on coastal aquifers. Different options are available to simulate tidal boundaries but no guidelines exist nor have comparisons been made to identify the most effective approach. We test seven methods to simulate a sloping beach and a tidal flat. The ocean is represented in one of the three ways: directly using a high hydraulic conductivity (high-K) zone and indirect simulation via specified head boundaries using either the General Head Boundary (GHB) or the new Periodic Boundary Condition (PBC) package. All beach models simulate similar water fluxes across the upland boundary and across the sediment-water interface although the ratio of intertidal to subtidal flow is different at low tide. Simulating a seepage face results in larger intertidal fluxes and influences near-shore heads and salinity. Major differences in flow occur in the tidal flat simulations. Because SEAWAT does not simulate unsaturated flow the water table only rises via flow through the saturated zone. This results in delayed propagation of the rising tidal signal inland. Inundation of the tidal flat is delayed as is flow into the aquifer across the flat. This is severe in the high-K and PBC models but mild in the GHB models. Results indicate that any of the tidal boundary options are fine if the ocean-aquifer interface is steep. However, as the slope of that interface decreases, the high-K and PBC approaches perform poorly and the GHB boundary is preferable.     

Tidal friction for semidiurnal tides

The quadratic law of bottom friction demands an increased frictional coefficient for the S₂ and N₂ tides with respect to a dominant M₂ tidal signal. A numerical model of the semidiurnal tides in the northeast Atlantic gives an increase in friction of ∼35% for the N₂, S₂ and K₂ tides with respect to the M₂ tide and this value is close to a theoretically derived estimate for the region, providing confirmation of the general widescale applicability of the quadratic friction law. Small differences in friction also occur for the N₂, S₂ and K₂ tides and this is attributed to the interaction of the L₂ and μ₂ tides with the M₂ tide in the presence of quadratic friction. Energy dissipation relationships, anomalous K₂/S₂ amplitude ratios and the role of quadratic friction on 18.6 year variations of semidiurnal forcing are examined.     

Tidal deformations of viscoelastic body

Summary The tidal deformations of a viscoelastic body are studied using the simple Kelvin-Voigt model. Expressions for the phase lag and amplitude change of the displacement vector are derived. The energy dissipation rate is calculated for the main disturbing bodies and for diurnal and semidiurnal tidal waves.

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Tidal theory with Newtonian cooling

Summary Processes representable by Newtonian cooling models are found to be of importance for tides in various planetary atmospheres. The equations of tidal theory are, therefore, rederived to include a rather general Newtonian cooling, and some of the effects of this inclusion are investigated.     

Tidal components of geomagnetic variations

The natural geomagnetic field is constantly disturbed. The total registered effect of geomagnetic variations depends on both planetary and local processes. Planetary sources and sources in the Earth’s core respond to tidal effects. In the accepted model, the complex MHD processes in the Earth’s outer core are approximated by the assumed ring current in the equatorial plain of the liquid core. The geomagnetic variation originating as a result of tidal deformations of ring currents are ～10^?4 and 0.10–1 nT in the liquid core and magnetosphere, respectively. The calculated values coincide in order of magnitude with the processed geomagnetic measurements at Paratunka observatory (Kamchatka region).     

Penny-shaped fractures revisited

All methods of seismic characterization of fractured reservoirs are based on effective media theories that relate geometrical and material properties of fractures and surrounding rock to the effective stiffnesses. In exploration seismology, the first-order theory of Hudson is the most popular. It describes the effective model caused by the presence of a single set of thin, aligned vertical fractures in otherwise isotropic rock. This model is known to be transversely isotropic with a horizontal symmetry axis (HTI). Following the theory, one can invert the effective anisotropy for the crack density and type of fluid infill of fractures, the quantities of great importance for reservoir appraisal and management.Here I compute effective media numerically using the finite element method. I deliberately construct models that contain a single set of vertical, ellipsoidal, non-intersecting and non-interconnected fractures to check validity of the first-order Hudson’s theory and establish the limits of its applicability. Contrary to conventional wisdom that Hudson’s results are accurate up to crack density e ≈ 0.1, I show that they consistently overestimate the magnitudes of all effective anisotropic coefficients ε^(V), δ^(V), and γ^(V). Accuracy of theoretically derived anisotropy depends on the type of fluid infill and typically deteriorates as e grows. While the theory gives | ε^(V)|, |δ^(V)|, |γ^(V)| and close to the upper bound of the corresponding numerically obtained values for randomly distributed liquid-filled fractures, theoretical predictions of ε^(V), δ^(V) are not supported by numerical computations when the cracks are dry. This happens primarily because the first-order Hudson’s theory makes no attempt to account for fracture interaction which contributes to the final result much stronger for gas- than for liquid-filled cracks. I find that Mori-Tanaka’s theory is superior to Hudson’s for all examined crack densities and both types of fluid infill.The paper was presented at the 11th International Workshop on Seismic Anisotropy (11IWSA) held in St. John’s, Canada in 2004.     

Forensic seismology revisited

The first technical discussions, held in 1958, on methods of verifying compliance with a treaty banning nuclear explosions, concluded that a monitoring system could be set up to detect and identify such explosions anywhere except underground: the difficulty with underground explosions was that there would be some earthquakes that could not be distinguished from an explosion. The development of adequate ways of discriminating between earthquakes and underground explosions proved to be difficult so that only in 1996 was a Comprehensive Nuclear Test Ban Treaty (CTBT) finally negotiated. Some of the important improvements in the detection and identification of underground tests—that is in forensic seismology—have been made by the UK through a research group at the Atomic Weapons Establishment (AWE). The paper describes some of the advances made in identification since 1958, particularly by the AWE Group, and the main features of the International Monitoring System (IMS), being set up to verify the Test Ban. Once the Treaty enters into force, then should a suspicious disturbance be detected the State under suspicion of testing will have to demonstrate that the disturbance was not a test. If this cannot be done satisfactorily the Treaty has provisions for on-site inspections (OSIs): for a suspicious seismic disturbance for example, an international team of inspectors will search the area around the estimated epicentre of the disturbance for evidence that a nuclear test really took place. Early observations made at epicentral distances out to 2,000 km from the Nevada Test Site showed that there is little to distinguish explosion seismograms from those of nearby earthquakes: for both source types the short-period (SP: ∼1 Hz) seismograms are complex showing multiple arrivals. At long range, say 3,000–10,000 km, loosely called teleseismic distances, the AWE Group noted that SP P waves—the most widely and well-recorded waves from underground explosions—were in contrast simple, comprising one or two cycles of large amplitude followed by a low-amplitude coda. Earthquake signals on the other hand were often complex with numerous arrivals of similar amplitude spread over 35 s or more. It therefore appeared that earthquakes could be recognised on complexity. Later however, complex explosion signals were observed which reduced the apparent effectiveness of complexity as a criterion for identifying earthquakes. Nevertheless, the AWE Group concluded that for many paths to teleseismic distances, Earth is transparent for P signals and this provides a window through which source differences will be most clearly seen. Much of the research by the Group has focused on understanding the influence of source type on P seismograms recorded at teleseismic distances. Consequently the paper concentrates on teleseismic methods of distinguishing between explosions and earthquakes. One of the most robust criteria for discriminating between earthquakes and explosions is the m _b : M _s criterion which compares the amplitudes of the SP P waves as measured by the body-wave magnitude m _b, and the long-period (LP: ∼0.05 Hz) Rayleigh-wave amplitude as measured by the surface-wave magnitude M _s; the P and Rayleigh waves being the main wave types used in forensic seismology. For a given M _s, the m _b for explosions is larger than for most earthquakes. The criterion is difficult to apply however, at low magnitude (say m _b < 4.5) and there are exceptions—earthquakes that look like explosions. A difficulty with identification criteria developed in the early days of forensic seismology was that they were in the main empirical—it was not known why they appeared to work and if there were test sites or earthquakes where they would fail. Consequently the AWE Group in cooperation with the University of Cambridge used seismogram modelling to try and understand what controls complexity of SP P seismograms, and to put the m _b : M _s criterion on a theoretical basis. The results of this work show that the m _b : M _s criterion is robust because several factors contribute to the separation of earthquakes and explosions. The principal reason for the separation however, is that for many orientations of the earthquake source there is at least one P nodal plane in the teleseismic window and this biases m _b low. Only for earthquakes with near 45° dip-slip mechanisms where the antinode of P is in the source window is the m _b:M _s criterion predicted to fail. The results from modelling are consistent with observation—in particular there are earthquakes, “anomalous events”, which look explosion-like on the m _b:M _s criterion, that turn out to have mechanisms close to 45° dip-slip. Fortunately the P seismograms from such earthquakes usually show pP and sP, the reflections from the free surface of P and S waves radiated upwards. From the pP–P and sP–P times the focal depth can be estimated. So far the estimated depth of the anomalous events have turned out to be ∼20 km, too deep to be explosions. Studies show that the observation that P seismograms are more complex than predicted by simple models can be explained on the weak-signal hypothesis: the standard phases, direct P and the surface reflections, are weak because of amongst other things, the effects of the radiation pattern or obstacles on the source-to-receiver path; other non-standard arrivals then appear relatively large on the seismograms. What has come out of the modelling of P seismograms is a criterion for recognising suspicious disturbances based on simplicity rather than complexity. Simple P seismograms for earthquakes at depths of more than a few kilometres are likely to be radiated only to stations that lie in a confined range of azimuths and distances. If then, simple seismograms are recorded over a wide range of distances and particularly azimuths, it is unlikely the source is an earthquake at depth. It is possible to test this using the relative amplitudes of direct P and later arrivals that might be surface reflections. The procedure is to use only the simple P seismograms on the assumption that whereas the propagation through Earth may make a signal more complex it is unlikely to make it simpler. From the amplitude of the coda of these seismograms, bounds can be placed on the size of possible pP and sP. The relative-amplitude method is then used to search for orientations of the earthquake source that are compatible with the observations. If no such orientations are found the source must be shallow so that any surface reflections merge with direct P, and hence could be an explosion. The IMS when completed will be a global network of 321 monitoring stations, including 170 seismological stations principally to detect the seismic waves from earthquakes and underground explosions. The IMS will also have stations with hydrophones, microbarographs and radionuclide detectors to detect explosions in the oceans and the atmosphere and any isotopes in the air characteristic of a nuclear test. The Global Communications Infrastructure provides communications between the IMS stations and the International Data Centre (IDC), Vienna, where the recordings from the monitoring stations is collected, collated, and analysed. The IDC issues bulletins listing geophysical disturbances, to States Signatories to the CTBT. The assessment of the disturbances to decide whether any are possible explosions, is a task for State Signatories. For each Signatory to do a detailed analysis of all disturbances would be expensive and time consuming. Fortunately many disturbances can be readily identified as earthquakes and removed from consideration—a process referred to as “event screening”. For example, many earthquakes with epicentres over the oceans can be distinguished from underwater explosions, because an explosion signal is of much higher frequency than that of earthquakes that occur below the ocean bed. Further, many earthquakes could clearly be identified at the IDC on the m _b : M _s criterion, but there is a difficulty—how to set the decision line. The possibility has to be very small that an explosion will be classed by mistake, as an earthquake. The decision line has therefore to be set conservatively, consequently with routine application of current screening criteria, only about 50% of earthquakes can be positively identified as such. Various methods have been proposed whereby a “determined violator” could avoid the provisions of a CTBT and carry out a test that would be either undetected or detected but not identified as an explosion. The increase in complexity and cost of such a test should discourage any State from attempting it. In addition, there is always the possibility of some stations detecting the test, the test being identified as suspicious, and so subject to an OSI. With time as the IMS becomes more efficient and effective it will act increasingly to deter anyone contemplating a clandestine test, from going ahead. What has emerged is several robust criteria. The criteria include: location, which when combined with hydro-acoustic data can identify earthquakes under the sea; m _b : M _s; and depth of focus. More detailed study is required of any remaining seismic disturbance that is regarded as suspicious: for example, is close to a site where nuclear tests have been carried out in the past. Any disturbance that is shown to be explosion-like, may be the subject of an OSI. One surprise is how little plate tectonics has contributed to resolving problems in forensic seismology. Much of the evidence for plate tectonics comes from seismological studies so it would be expected that the implications for Earth structure arising from forensic seismology would be consistent with plate-tectonic models. So far the AWE Group have found little synergy between plate tectonics and forensic seismology. It is to be hoped that the large volume of seismological data of high quality now being collected by the IMS and the increasing number of digital stations, will result in a revised Earth model that is consistent with the findings of forensic seismology, so that a future review of progress will show that the forensic seismologist can draw on this model in attempting to interpret apparently anomalous seismograms.

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Tidal energy flow in solid earth

The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 243–246, 1992.     

Tidal evolution of the earth-sun system

Summary The tidal decrease in the Earth's heliocentric longitude generated by the Sun has been computed. It represents the increase in the length of year10^–7 s per century. The resonant angular velocity of the Earth's rotation is approximately equal to the present Earth's mean motion, however, for the model used, i.e., considering the Sun as the point-mass.

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The Lisse effect revisited

The Lisse effect is a rarely noted phenomenon occurring when infiltration caused by intense rain seals the surface soil layer to airflow, trapping air in the unsaturated zone. Compression of air by the advancing front results in a pressure increase that produces a water-level rise in an observation well screened below the water table that is several times as large as the distance penetrated by the wetting front. The effect is triggered by intense rains and results in a very rapid water-level rise, followed by a recession lasting a few days. The Lisse effect was first noted and explained by Thal Larsen in 1932 from water-level observations obtained in a shallow well in the village of Lisse, Holland. The original explanation does not account for the increased air pressure pushing up on the bottom of the wetting front. Analysis of the effect of this upward pressure indicates that a negative pressure head at the base of the wetting front, psi(f), analogous to that postulated by Green and Ampt (1911) to explain initially rapid infiltration rates into unsaturated soils, is involved in producing the Lisse effect. Analysis of recorded observations of the Lisse effect by Larsen and others indicates that the water-level rise, which typically ranges from 0.10 to 0.55 m, should be only slightly larger than psi(f) and that the depth of penetration of the wetting front is no more than several millimeters.