Tidal gravity in Britain: tidal loading and the spatial distribution of the marine tide

Summary. Tidal gravity measurements have been made at six sites in Britain with two nulled LaCoste and Romberg Earth tide gravitymeters. The M ₂ observations from these and two further sites are compared with calculations of the tidal loading from the seas around the British Isles and the major oceans. Models of the M ₂ marine tides are convolved with Green's functions for appropriate radially stratified Earth models. The differences between the M ₂ observations and the theoretical calculations are less than 0.6 μ gals and it is shown that these differences contain further information concerning the errors in the marine tide models. The M ₂ marine tides on the north-west European continental shelf are reasonably well known and this allows a useful test of the feasibility of using tidal gravity measurements for the inverse ocean tide problem in areas where the ocean tides are less well known. The differential gravity loading signal between pairs of gravity stations is shown to be important for considerations of the uniqueness and accuracy of the inverse problem. M ₂ tidal gravity loading maps for the British Isles and Europe have been produced which are of use in making corrections to various geodetic measurements.     

Tidal gravity and ocean tide loading in Europe

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The results are presented from tidal gravity measurements at five sites in Europe using LaCoste and Romberg ET gravimeters. Improvements that we have made to the accuracies of these gravimeters are discussed. It is shown that the 'standard' calibration of the International Center for Earth Tides, used for worldwide tidal gravity profiles, is 1.2 per cent too high. The M₂ and O₁ observations are compared with model calculations of the Earth's body tide and ocean tide loading and it is shown that there is a very significant improvement in the agreement between observations and models compared to that obtained with previous tidal gravity measurements. For O₁, where the ocean tide loading and attraction in central Europe is only 0.4 per cent of the body tide, our measurements verify that the Dehant-Wahr anelastic body tide model gravimetric factor is accurate to 0.2 per cent. It is also shown that the effects of lateral heterogeneities in Earth structure on tidal gravity are too small to explain the large anomalies in previously published tidal gravity amplitudes. The observations clearly show the importance of conserving tidal mass in the Schwiderski ocean tide model. For sites in central Europe, the M₂ and O₁ observations and the models are in agreement at the 0.1 μgal (10⁻⁹ m s⁻²) level and tidal corrections to this accuracy can now be made to absolute gravity measurements.     

Gravity measurements with a portable absolute gravimeter A10 in Syowa Station and Langhovde,East Antarctica

Absolute gravity values were measured with a portable absolute gravimeter A10 in East Antarctica, for the first time by the Japanese Antarctic Research Expedition. This study aims to investigate regional spatiotemporal variations of ice mass distributions and associated crustal deformations around Syowa Station by means of repeated absolute gravity measurements, and we obtained the first absolute gravity value in Southern Langhovde on the Antarctic Continent. The average absolute gravity value at the newly installed benchmark AGS01 in Langhovde (obtained on 3 February 2012) was 982535584.2 ± 0.7 μgal (1 [μgal] = 1 × 10^?8 [m/s²]), which was in agreement with the gravity values obtained by the past relative gravity measurements within 1 mgal. In addition, the average absolute gravity value obtained at AGSaux in Syowa Station was consistent with both previous absolute gravity values and those obtained by simultaneous measurements using an FG5 gravimeter, owing to adequate data corrections associated with tidal effects and time variations in atomic clock frequencies. In order to detect the gravity changes associated with the ice mass changes and other tectonic phenomena, we plan to conduct absolute gravity measurements at AGS01 again and at other campaign sites around Syowa Station as well in the near future, with careful attention paid to the impacts of severe environmental conditions in Antarctica on gravity data collection.     

Self-consistent equilibrium ocean tides

Summary. We compute the static response of the world ocean to an external zonal gravitational potential. The computation includes the effects of the self-attraction of the ocean, and the yielding of the Earth caused both by the external potential and the change in ocean load. We compare the computed tide with measurements of the fortnightly and monthly ocean tides. The short-wavelength departures from equilibrium found by Wunsch are still present. An average of observations at Pacific islands shows that the fortnightly tide departs significantly from equilibrium but the monthly may not. We have also calculated the effects of our computed tide on measurements of tidal gravity and tidal fluctuations in the length of day. Existing tidal gravity data are too imprecise to enable us to determine whether or not the spatial average of the ocean tides departs from equilibrium. The length of day data suggest that the monthly tide is farther from equilibrium than the fortnightly. We have not been able to resolve the apparent discrepancy between the length of day and ocean tide data.     

Detailed gravity-tide spectrum between one and four cycles per day

Summary. The results of previous work by the authors is used to remove most of the effects of ocean and atmospheric loading from an 18-month Earth gravity-tide record. The remaining signal is examined for additional influence of ocean and atmosphere and for evidence of the frequency-dependence of the response of the solid earth. Variations in time of the measured tides are shown to result from the atmospheric tide at S ₂ and appear to result from variations in ocean tides at other frequencies. The frequency-dependence of the solid earth response near 1 cycle per siderial day is found to be consistent with the nearly diurnal free wobble. However, the influence of the ocean on the small but crucial Ψ₁ tide is uncertain. Anomalous responses are observed at several other frequencies but except for the case of ρ₁ it is argued that anomalous ocean tides are plausible and could therefore explain the observations.     

Combining geomorphological and geodetic data to determine postglacial tilting in Manitoba

Estimates of postglacial rebound in central North America from Laurentide deglaciation to the present time are uncertain as a result of lack of data from the continental interior. A more precise knowledge of postglacial tilt history will assist studies of the evolution of the major lakes in Manitoba and will facilitate the engineering and environmental management of the present-day hydrological system. This paper explores the benefits of combining geomorphological data with high-precision, real-time geodetic data (GPS positioning and absolute gravity) and lake-gauge tilt data now being collected for postglacial rebound studies in Manitoba and adjacent regions in the US. Presently-available data sets representing these data types are (1) tilting of the 9.5 kyr B.P. Campbell strand line south and west of Lake Winnipeg, (2) the rate of decrease in absolute gravity values measured from 1987 to 1995 at Churchill, Manitoba, and (3) the present-day regional tilt rate derived from water-level gauges in southern Manitoba lakes. These data are compared to theoretical predictions based on the published ICE-3G loading history and on a model of Earth rheology characterized by a 1066B density and elastic structure, an upper-mantle viscosity of 10 ²¹Pa s, a lower-mantle viscosity of 2 × 10 ²¹Pa s, and a lithosphere thickness of 120 km (Tushingham & Peltier, 1991). All three data types show disagreement in Manitoba with ICE-3G and the standard Earth model. ICE-4G does better but could not be investigated in any detail. The constraints on model parameters provided by the different data types were investigated by varying, one at a time, three key parameters, (1) the thickness of the lithosphere in excess of 120 km, (2) the lower mantle viscosity, and (3) the thickness of Laurentide ice over the Prairies, to obtain better fits to the data. The present data do not appear to constrain lithosphere thickness in excess of 120 km very well. While both the Campbell strand line data and the Churchill absolute gravity data are consistent with an increase in lower-mantle viscosity, the present-day, lake-gauge data are not. All three data types are consistent with a thinning of the Laurentide ice-sheet over the Prairies relative to the ICE-3G model. Simultaneous adjustment of model parameters with the advantage of anticipated new data in Manitoba and adjacent regions in the US will lead to better understanding of the trade-offs between Earth rheology and ice sheet history and hence to an improved Laurentide postglacial rebound model.     

The absolute gravity measurement by FG5 gravimeter at Great Wall Station,Antarctica

Gravity measurement is of great importance to the height datum in Antarctica.The absolute gravity measurement was carried out at Great Wall Station,Antarctica,using FG5 absolute gravity instrument.The gravity data was processed with corrections of earth tide,ocean tide,polar motion and the atmospher,and the RMS is within ±3×10-8 ms-2.The vertical and horizontal gravity gradients were measured using 2 LaCoaste & Romberg(LCR) gravimeters.The absolute gravity measurement provides the fundamental data for the validation and calibration of the satellite gravity projects such as CHAMP,GRACE and GOCE,and for the high accuracy geoid model.     

南极中山站固体潮观测分析

中国南极中山站位于南极拉斯曼丘陵地区（λ＝７６°２２′Ｅ，φ＝６９°２２′Ｓ），１９９１年３月至１９９３年２月，用ＬａｃｏｓｔｅＥＴ型重力仪，在这个地区进行了为期近两年的观测，取得了６００多天的有效资料，经调和分析和流变模型、海潮负荷改正后得到：δｏ１＝１．２２５３±０．００３１，Δφｏ１＝０．７３°±０．１４°；δｍ２＝１．０７８５±０．００４５，Δφｍ２＝－３．５５°±０．２９°从资料分析的精度来看，观测资料是比较好的；但由于海潮负荷改正缺少附近海域的资料，会对最终结果造成较大的影响     

New aspects of the equilibrium pole tide

Summary. We have developed a new spherical harmonic algorithm for the calculation of the loading and self-gravitating equilibrium pole tide. Based on a suggestion of Dahlen, this approach minimizes the distortions in tide height caused by an incomplete representation of the ocean function. With slight modification our approach easily could be used to compute self-gravitating and loading luni-solar tides as well.
Using our algorithm we have compared the static pole tide with tide observations at a variety of locations around the world. We find statistically significant evidence for pole tide enhancements in mid-ocean as well as the shallow seas.
We have also re-investigated the effect of the static tide on the Chandler wobble period. The difference between the wobble period of an oceanless, elastic earth with a fluid core (Smith & Dahlen) and the period of an earth minus static oceans yields a 7.4-day discrepancy. We conclude from tide observations that much of the discrepancy can probably be accounted for by non-equilibrium pole tide behaviour in the deep oceans.     

利用FG5绝对重力仪进行南极长城站绝对重力测定

在南极地区进行重力测量是建立高程基准的基础,2005年,在南极长城站进行了绝对重力测量,观测仪器采用FG5绝对重力仪,经固体潮改正、海潮改正、极移改正及气压改正等,精度达±3×10-8m s-2,并同时利用2台LCR相对重力仪进行了重力垂直梯度测量和水平梯度测量。长城站绝对重力测量的实施,对于新一代卫星重力计划如CHAMP、GRACE和GOCE的地面校准及建立南极地区的高精度、高分辨率的大地水准面模型提供了基础数据。     

Postglacial rebound and fault instability in Fennoscandia

The best available rebound model is used to investigate the role that postglacial rebound plays in triggering seismicity in Fennoscandia. The salient features of the model include tectonic stress due to spreading at the North Atlantic Ridge, overburden pressure, gravitationally self-consistent ocean loading, and the realistic deglaciation history and compressible earth model which best fits the sea-level and ice data in Fennoscandia. The model predicts the spatio-temporal evolution of the state of stress, the magnitude of fault instability, the timing of the onset of this instability, and the mode of failure of lateglacial and postglacial seismicity. The consistency of the predictions with the observations suggests that postglacial rebound is probably the cause of the large postglacial thrust faults observed in Fennoscandia. The model also predicts a uniform stress field and instability in central Fennoscandia for the present, with thrust faulting as the predicted mode of failure. However, the lack of spatial correlation of the present seismicity with the region of uplift, and the existence of strike-slip and normal modes of current seismicity are inconsistent with this model. Further unmodelled factors such as the presence of high-angle faults in the central region of uplift along the Baltic coast would be required in order to explain the pattern of seismicity today in terms of postglacial rebound stress. The sensitivity of the model predictions to the effects of compressibility, tectonic stress, viscosity and ice model is also investigated. For sites outside the ice margin, it is found that the mode of failure is sensitive to the presence of tectonic stress and that the onset timing is also dependent on compressibility. For sites within the ice margin, the effect of Earth rheology is shown to be small. However, ice load history is shown to have larger effects on the onset time of earthquakes and the magnitude of fault instability.     

Relict Shorelines and Ice Flow Patterns of the Northern Puget Lowland From Lidar Data and Digital Terrain Modelling

Airborne lidar data from the northern Puget Lowland provide information on the spatial variability and amplitude of raised postglacial shorelines, marine deltaic features and glaciomarine sediments deposited between approximately c. 12 920 and 11 050 ¹⁴C yr BP (15 960‐12 364 cal yr BP). Relict shorelines preserved in embayments on Whidbey and Camano islands (between 47°54′N and 48°24′N) are found up to an altitude of c. 90 m and record glacio‐isostatic movements attributed to postglacial rebound. The tilt of the regional minimum highstand sea level surface to the north of 0.80 m km^?1, with local variability from 0.25 m km^?1 to 0.77 m km^?1, is consistent with previous studies (Thorson 1989; Dethier et al. 1995). The local variability is related to the uncertainty in the depth of the water column above these features at the time of deposition and probable tectonic deformation. The information generated by these lidar data is most valuable in posing new research questions, generating alternative research hypotheses to those already formulated in the northern Puget Lowland.     

Inference of mantle viscosity from GRACE and relative sea level data

Gravity Recovery And Climate Experiment (GRACE) satellite observations of secular changes in gravity near Hudson Bay, and geological measurements of relative sea level (RSL) changes over the last 10 000 yr in the same region, are used in a Monte Carlo inversion to infer-mantle viscosity structure. The GRACE secular change in gravity shows a significant positive anomaly over a broad region (>3000 km) near Hudson Bay with a maximum of ∼2.5 μGal yr⁻¹ slightly west of Hudson Bay. The pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ICE-5G deglaciation history, strongly suggesting a postglacial rebound origin for the gravity change. We find that the GRACE and RSL data are insensitive to mantle viscosity below 1800 km depth, a conclusion similar to that from previous studies that used only RSL data. For a mantle with homogeneous viscosity, the GRACE and RSL data require a viscosity between  1.4 × 10²¹  and  2.3 × 10²¹  Pa s. An inversion for two mantle viscosity layers separated at a depth of 670 km, shows an ensemble of viscosity structures compatible with the data. While the lowest misfit occurs for upper- and lower-mantle viscosities of  5.3 × 10²⁰  and  2.3 × 10²¹  Pa s, respectively, a weaker upper mantle may be compensated by a stronger lower mantle, such that there exist other models that also provide a reasonable fit to the data. We find that the GRACE and RSL data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle.     

A diurnal resonance in the ocean tide and in the Earth's load response due to the resonant free 'core nutation'

Summary. The luni-solar forced nutations and body tide are believed to be resonant at frequencies near (1 + 1/460) cycle sidereal day⁻¹ as seen from the rotating Earth. This resonance is due to the Earth's rotating, elliptical fluid core. We show here that tides in the open ocean and the Earth's response to those tides must also be resonant at (1 + 1/460) cycle day⁻¹. We examine these resonant oceanic effects on the Earth's nutational motion and on the body tide. Effects on the forced nutations might be as large as 0.002 arcsec at 18.6 yr. The effects on the observed resonance in the body tide are more important. For tidal gravity, for example, the difference between K ₁ and 0 ¹ which is usually used to determine the resonance, can be perturbed by 30 per cent or more due to the oceanic resonance effects.     

A high-resolution pigment and productivity record from the varved Ponte Tresa basin (Lake Lugano,Switzerland) since 1919: insight from an approach that combines hyperspectral imaging and high-performance liquid chromatography

Eutrophication, prompted by anthropogenic activities and climate change has led to multiple adverse effects in freshwater systems across the world. As instrumental measurements are typically short, lake sediment proxies of aquatic primary productivity (PP) are often used to extend the observational record of eutrophication back in time. Sedimentary pigments provide specific information on PP and major algal communities, but the records are often limited in the temporal resolution. Hyperspectral imaging (HSI) data, in contrast, provide very high seasonal (sub-varve-scale) resolution, but the pigment speciation is limited. Here, we explore a combined approach on varved sediments from the Ponte Tresa basin, southern Switzerland, taking the advantages of both methods (HSI and high performance liquid chromatography, HPLC) with the goal to reconstruct the recent eutrophication history at seasonal to interannual resolution. We propose a modified scheme for the calibration of HSI data (here: Relative Absorption Band Depth between 590 and 730 nm RABD_590–730) and HPLC-inferred pigment concentrations (here: ‘green pigments’ {chlorophyll a and pheophytin a}) and present a calibration model (R²?=?0.82; RMSEP?~?12%). The calibration range covers >?98% of the spectral index values of all individual pixels (68 µm?×?68 µm) in the sediment core. This allows us to identify and quantify extreme pigment concentrations related to individual major algal blooms, to identify multiple algal blooms within one season, and to assess interannual variability of PP. Prior to the 1930s, ‘green pigment’ concentrations and fluxes (~?50 µg g^?1;?~?2 µg cm^?2a^?1, chlorophyll a and pheophytin a) and interannual variability was very low. From the 1930s to 1964, chlorophyll a and pheophytin a increased by a factor of ~?4, and ββ-carotene appeared in substantial amounts (~?0.4 µg cm^?2a^?1). Interannual variability increased markedly and a first strong algal bloom with ‘green pigment’ concentrations as high as 700 µg g^?1 is observed in 1958. Peak eutrophication (~?12 µg cm^?2a^?1 chlorophyll a and pheophytin a) and very high interannual variability with extreme algal blooms (‘green pigment’ concentrations up to 1400 µg g^?1) is observed until ca. 1990, when eutrophication decreases slightly. Maximum PP values after 2009 are likely the result of internal nutrient cycling related to repeated deep mixing of the lake.     

Pleistocene deglaciation and the Earth's rotation: implications for mantle viscosity

Summary. Recent results from the analysis of postglacial rebound data suggest that the viscosity of the Earth's mantle increases through the transition region. Models which fit both relative sea-level and free air gravity data have viscosities which increase from a value near 10²² poise in the upper mantle beneath the lithosphere to a value of about 10²³ poise in the lower mantle. In this paper we analyse the effect of deglaciation upon the Earth's rotation and thereby show that the observed secular trend (polar wander) evident in the ILS—IPMS pole path, and measurements of the non-tidal acceleration of the length of day, are both consistent with the viscosity profile deduced from postglacial rebound. The two analyses are therefore mutually reinforcing.     

A model for underpressure development in a glacial valley,an example from Adventdalen,Svalbard

The underpressure observed in the glacial valley Adventdalen at Svalbard is studied numerically with a basin model and analytically with a compartment model. The pressure equation used in the basin model, which accounts for underpressure generation, is derived from mass conservation of pore fluid and solid, in addition to constitutive equations. The compartment model is derived as a similar pressure equation, which is based on a simplified representation of the basin geometry. It is used to derive analytical expressions for the underpressure (overpressure) from a series of unloading (loading) intervals. The compartment model gives a characteristic time for underpressure generation of each interval, which tells when the pressure state is transient or stationary. The transient pressure is linear in time for short‐time spans compared to the characteristic time, and then it is proportional to the weight removed from the surface. We compare different contributions to the underpressure generation and find that porosity rebound from unloading is more important than the decompression of the pore fluid during unloading and the thermal contraction of the pore fluid during cooling of the subsurface. Our modelling shows that the unloading from the last deglaciation can explain the present day underpressure. The basin model simulates the subsurface pressure resulting from erosion and unloading in addition to the fluid flow driven by the topography. Basin modelling indicates that the mountains surrounding the valley are more important for the topographic‐driven flow in the aquifer than the recharging in the neighbour valley. The compartment model turns out to be useful to estimate the orders of magnitude for system properties like seal and aquifer permeabilities and decompaction coefficients, despite its geometric simplicity. We estimate that the DeGeerdalen aquifer cannot have a permeability that is higher than 1 · 10^?18 m², as otherwise, the fluid flow in the aquifer becomes dominated by topographic‐driven flow. The upper value for the seal permeability is estimated to be 1 · 10^?20 m², as higher values preclude the generation and preservation of underpressure. The porosity rebound is estimated to be <0.1% during the last deglaciation using a decompaction coefficient α_r = 1 · 10^?9 Pa^?1.     

Iceocean mass balance during the Late Pleistocene glacial cycles in view of CHAMP and GRACE satellite missions

During the last glacial cycles, global sea level dropped several times by about 120 m and large ice sheets covered North America, northern Europe and Antarctica during the glacial stages. The changes in the iceocean mass balance have displaced mantle material mainly via viscous flow, and the perturbation of the equilibrium figure of the Earth by glacial isostatic adjustment is still observable today in timedependent changes of gravitational and rotational observations. Contemporary iceocean mass balance from volume changes of polar ice caps also contributes to secular variations of the Earth's gravitational field.
In the near future, several satellite gravity missions will significantly improve the accuracy of the observed timedependent gravitational field. In view of the expected improvements in the observations, we predict glacially induced perturbations of the gravitational field, induced by Late Pleistocene and contemporary ice volume changes, for a variety of radial mantle viscosity profiles. We assess the degree of uncertainty for the glacially induced contributions to gravitational and rotational parameters, both in the spectral and the spatial domain.
Predictions of power spectra for the glacially induced freeair gravity and geoid anomalies are about one order of magnitude lower than the observed values, and uncertainties arising from different plausible viscosity profiles are around 0.150.4 mGal and 0.21.5 m, respectively. Uncertainties from different ice models are of secondary importance for the predicted power spectra. Predicted secular changes in geoid anomalies in formerly glaciated areas are mainly controlled by the viscosity profile and contemporary ice volume changes. We also show that the simple threelayer viscosity profiles currently employed for the majority of postglacial rebound studies represent a limited subset for model predictions of the timedependent gravitational field.     

The bodily tide and the yielding of the Earth due to tidal loading

Summary. The theory of the bodily tide and of the yielding of the Earth to tidal loading is re-examined, with the purpose of checking the standard formula for the gravity tide which is used in the interpretation of tidal gravity measurements. Some remarks are made concerning the Green's function occurring in the theory of the gravity tide.     

Temporal variations of tides on the west coast of Great Britain

Summary. Temporal variations of tides are investigated by analysing tidal observations from five ports on the west coast of Great Britain. Variations considered here are those occurring in the semi-diurnal species daily, in the tidal constituents resolved from analyses of 29 day sets over a period of two years, 1980–81, and in the tidal constituents resolved from 1 yr sets over a period of 19 yr. The time variations of tidal constituents are mainly due to inseparable terms grouping with the principal term due to the short length of data and the insufficiency of the procedures to account for them. Surges and surge-tide interaction are affecting the resolution of tides. Time variations of constituents of the diurnal species induced by non-tidal forces are spatially consistent. The use of equilibrium relationships to account for modulations of principal constituents by waves separable in an 18.61 yr nodal cycle improves the analysis. However, the modulation is smaller in the real tide than in the equilibrium tide. When the application of this principle is extended to a wider frequency band to cover constituents which cannot be resolved from one month of observations, it may produce the opposite effect. These problems start compounding with decreasing length of data, i.e. increasing band width of resolution.
Functional approximations of interaction coefficients (bi-admittance) of non-linear tides, similar to the response (admittance) of linear tides are computed for semi-diurnal, fourth-diurnal and sixth-diurnal bands. These functional estimates may be used to interpolate unseparable constituents to improve the quality of analyses. The results are consistent with the fact that the response of the sea does not change in a narrow frequency band covering a nodal cycle of the Moon. The change in the equilibrium relationship between the principal term and its nodal term can be interpreted in terms of the damping effect of bottom friction.