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.     

On analysis and prediction of tides on the west coast of Great Britain

Summary. Long-period tidal records from eight ports on the west coast of Great Britain are analysed, using both the harmonic method and the response function. Time series up to 9.5 yr were used so that fine structure of certain regions of high energy in the tidal residual spectrum may be examined. This also assisted in accurate separation of tides from surges. According to the currently accepted formulation of M₁, its composition is not compatible with its actual composition in the real tide and, as such, has no useful purpose to serve in computation of predictions. Constituents Sa, Ssa, MA, and MB, are adversly affected by weather and long records are essential for their accurate separation. It has been observed that annual perturbations of S₂, similar to those confirmed in recent years for M₂, also exist but these are not readily recognisable because their speeds are the same as those of constituents T₂ and R₂. These perturbations, being highly sensitive to meteorological forces, are mainly responsible for cusps or humps in the vicinity of major tidal constituents in tidal residual spectra. The relationship of radiational and gravitational tides is found to be in very good agreement with theoretical results. In summer months non-predictable variance reduces to about half of the annual variance, reflecting the regional weather conditions of summer and winter.     

白令海峡及其邻近海域潮汐潮能数值模拟

基于非结构三角形网格的FVCOM(Finite-Volume Coastal Ocean Model)海洋数值模式,对白令海峡及其邻近海域的潮汐、潮能进行数值模拟研究。模拟结果同验潮站和实测海流资料符合良好,较好地反映了白令海峡及其邻近海域的潮汐、潮流分布特征和运动状况。根据计算结果绘制了主要分潮的同潮图和潮流椭圆图,对该海域潮汐潮流特征进行了系统分析。结果表明,白令海陆架区、白令海峡和楚科奇海主要以M2分潮为主,而在诺顿湾海域以K1分潮为主,M2分潮潮流在白令海陆架东南部及阿纳德尔湾较强,K1分潮潮流在诺顿湾潮流达到最大值。在此基础上,对其潮汐能的传播与耗散进行分析,结果发现研究海域潮能通量较小,主要分潮在研究海域潮能耗散总量约为751 MW,M2潮能耗散占该总量的52%,K1潮能耗散占38%,潮能进入白令海陆架后,M2分潮主要在圣劳伦斯岛以南陆架区耗散,K1分潮主要在诺顿湾海区耗散。     

Lunar daily geomagnetic variations at Tucson

Summary. Mean hourly values of the geomagnetic elements for Tucson, Arizona, have been analysed for the M ₂ lunar tide for the period 1909–1975. Results for the average diurnal variation are presented, and changes with season, sunspot cycle and magnetic activity are discussed.     

On the nature of regional seismic phases–II. On the influence of structural barriers

The blockage of the L _g wave by crustal barriers such as continental margins and graben structures has long been recognized as providing a very useful tool for mapping large-scale lateral crustal variations along the propagation path. Numerical simulation of L _g -wave propagation in complex anelastic media using the pseudospectral method provides insight into the nature of the propagation process using both snapshots of the wavefield and synthetic seismograms. A variety of 2-D structures have been investigated, including the influence of sediments, crustal thickness and attenuation.
Thick sedimentary basins covering a graben structure can have a major influence, since they remove L _g energy by generating P conversion and scattering–the principal mechanisms for strong L _g attenuation across a graben. The reduction of the L _g energy is reinforced by anelastic attenuation in the sediments as well as the influence of the gradually thinning crustal waveguide associated with an elevated Moho.
The extinction of L _g in a sequence of explosions fired across the central graben of the North Sea can be simulated by numerical calculations for the structure derived from refraction experiments.     

Tidal gravity and ocean tide loading in Europe

b
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.     

On the excitation of resonant double Kelvin waves in the Barents Sea Opening

In the northern Barents Sea Opening (BSO) the K₁ tidal energy is predominant in the diurnal tidal frequency band, suggesting the generation of a topographic wave with the K₁ tidal frequency. Tidal energy of the K₁ component becomes strong where bottom topography undulates in the BSO and the scale of the undulation is close to the wavelength of the K₁ wave. An analytical model is developed to investigate the energy enhancement mechanism of the tidally induced topographic wave due to a resonance between tidal current, a topographic wave and periodic topography. The wave excited by the resonance is identified as a resonant double Kelvin wave (DKW) and the significant K₁ energy in the BSO could be due to the excitation of the resonant DKW.     

Estimation of the Bingham distribution function on nearly two-dimensional data sets

Summary. In cases where directional data, such as palaeomagnetic directions, lie nearly along a great circle, a good approximation to the maximum likelihood estimate of the intermediate concentration parameter k ₂ in the Bingham probability distribution is given by: 2( t ₂/ N ) – 1 = I ₁(1/2 k ₂)/ I ₀(1/2 k ₂), where t ₂ is the intermediate eigenvalue, N is the number of samples, and the I_i are the appropriate modified Bessel functions of the first kind. This estimate, the asymptotic limit as the smallest eigenvalue t ₁→ 0, corresponds to restricting all points to lie on a great circle. The limit is also useful as an endpoint for interpolation, especially since numerical calculation in this region is difficult.     

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.     

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.     

On the linear relation between mb and Ms for discrimination between explosions and earthquakes

Summary. The statistical capability of the m _b: M _s discriminant for the discrimination of earthquake and explosion populations is examined by application of discriminant functions to a group of 83 explosions and 72 earthquakes in Eurasia. Equations are derived for the probability that an event is an earthquake or an explosion. The positive sign of DIS in the decision index equation, DIS _i = 34.3383 – 11.9569 mb _t + 7.1161 M _si , indicates that the event i is an earthquake. Its negative sign indicates that event i is an explosion. The probability of correct classification for an event, P _i , is related to its DIS _i value, by P _i = [1-exp (DIS _i )]⁻¹, where a large, positive DIS indicates a high probability that an event is an earthquake and a large, negative DIS indicates a high probability that an event is an explosion. The discrimination line M _s = 1.680 m _b– 4.825, or m _b= 0.595 M _s+ 2.872 very successfully separates the explosion population from the earthquake population. The points on this line have an equal chance of being an earthquake or an explosion; moreover, for any event, the distance parallel to the M _s-axis from the point representing that event in the m _b: M _s plane to this line is a measure of the probability for the correct classification of that event.     

A New Magnitude-Frequency Relation for Earthquakes and a Classification of Relation Types

Summary. In this paper some aspects of the deviations of frequency distributions of earthquakes from a linear trend are considered. For recurrence curves with inflexions, the formula
is proposed as a magnitude-frequency relation, with critical magnitude M _cr. Comparison with actual data shows better agreement than other formulae. The slope of the frequency graph is considered in the most general case to be a function of M and some parameters p ₁, p ₂, …. A classification of the types of magnitude-frequency relation is given and all known types of relations N : M and N: K ( K = log E , E = seismic energy) are summarized.     

Three-dimensional VP and VP /VS models of the upper crust in the Friuli area (northeastern Italy)

3-D images of P velocity and P - to S -velocity ratio have been produced for the upper crust of the Friuli area (northeastern Italy) using local earthquake tomography. The data consist of 2565 P and 930 S arrival times of high quality. The best-fitting V _P and V _P / V _S 1-D models were computed before the 3-D inversion. V _P was measured on two rock samples representative of the investigated upper layers of the Friuli crust. The tomographic V _P model was used for modelling the gravity anomalies, by converting the velocity values into densities along three vertical cross-sections. The computed gravity anomalies were optimized with respect to the observed gravity anomalies. The crust investigated is characterized by sharp lateral and deep V _P and V _P / V _S anomalies that are associated with the complex geological structure. High V _P / V _S values are associated with highly fractured zones related to the main faulting pattern. The relocated seismicity is generally associated with sharp variations in the V _P / V _S anomalies. The V _P images show a high-velocity body below 6 km depth in the central part of the Friuli area, marked also by strong V _P / V _S heterogeneities, and this is interpreted as a tectonic wedge. Comparison with the distribution of earthquakes supports the hypothesis that the tectonic wedge controls most of the seismicity and can be considered to be the main seismogenic zone in the Friuli area.     

Stacking for the frequencies and Qs of 0S0 and 1S0

Summary. Using nine IDA records for the Indonesian earthquake of 1977 August 19, we have formed an optimal linear combination of the records and have measured the frequency and Q of ₀ S ₀ and ₁ S ₀. The frequency was measured using the moment ratio method. The attenuation was measured by the minimum width method and by the time-lapse method. The frequency and attenuation were measured simultaneously by varying them to obtain a best fit to the data. A 2000-hr stack, the sum of nine individual records, for ₀ S ₀ gave a frequency of 0.814664 mHz±4 ppm. The values for the Q of ₀ S ₀ for the three different methods of measurement were 5600,5833 and 5700, respectively. The error in the estimates of Q ^-1 is about 5 per cent for the minimum power method. For ₁ S ₀ a 300-hr stack yielded a frequency of 1.63151 mHz±30 ppm. The values of Q for this mode were 1960, 1800 and 1850, respectively, with an error in Q ^-1 of about 12 per cent for the minimum power method.     

Is the seismic moment–frequency relation universal?

We evaluate the seismic moment–frequency relation for the Harvard catalogue in the period 1977–1994. This catalogue is composed of about 12 000 earthquakes. After selection of events in terms of depth and energy, we retain about 8000 data points. We estimate two parameters of the seismic moment distribution: the power exponent β and the cut-off value M _m . The method used is a least-squares linear fit on a log–log scale performed over a range selected on the basis of the standard deviation from the histogram. The analysis is carried out for different subdivisions of the Earth in square grids of different sizes. Neither parameter exhibits a dependence on cell size, suggesting the universality of their values and the interpretation of the existence of a cut-off as a finite size effect linked to a finite catalogue length. The variations of the parameters are investigated as a function of time (duration of the catalogue) and versus the number of events used for building up the distribution. Again, β and M _m do not depend on time, but M _m depends on the number of events, reaching a stable value for N ≈ 1000. The only significant change in the parameters is observed for different values of M _0upper in the catalogue, revealing the existence of universality classes.     

Monthly estimates of carbon dioxide emissions from fossil-fuel consumption in Brazil during the late 1990s and early 2000s

Detailed understanding of global carbon cycling requires estimates of CO ₂ emissions on temporal and spatial scales finer than annual and country. This is the first attempt to derive such estimates for a large, developing, Southern Hemisphere country. Though data on energy use are not complete in terms of time and geography, there are enough data available on the sale or consumption of fuels in Brazil to reasonably approximate the temporal and spatial patterns of fuel use and CO ₂ emissions. Given the available data, a strong annual cycle in emissions from Brazil is not apparent. CO ₂ emissions are unevenly distributed within Brazil as the population density and level of development both vary widely.     

Focal mechanisms of recent earthquakes in the Southern Korean Peninsula

We evaluate the stress field in and around the southern Korean Peninsula with focal mechanism solutions, using the data collected from 71 earthquakes ( M_L = 1.9–5.2) between 1999 and 2004. For this, the hypocentres were relocated and well-constrained fault plane solutions were obtained from the data set of 1270 clear P -wave polarities and 46 SH / P amplitude ratios. The focal mechanism solutions indicate that the prevailing faulting types in South Korea are strike-slip-dominant-oblique-slip faultings with minor reverse-slip component. The maximum principal stresses (σ₁) estimated from fault-slip inversion analysis of the focal mechanism solutions show a similar orientation with E–W trend (269°–275°) and low-angle plunge (10°–25°) for all tectonic provinces in South Korea, consistent with the E–W trending maximum horizontal stress (σ_Hmax) of the Amurian microplate reported from in situ stress measurements and earthquake focal mechanisms. The directions of the intermediate (σ₂) and minimum (σ₃) principal stresses of the Gyeongsang Basin are, however, about 90 deg off from those of the other tectonic provinces on a common σ₂–σ₃ plane, suggesting a permutation of σ₂ and σ₃. Our results incorporated with those from the kinematic studies of the Quaternary faults imply that NNW- to NE-striking faults (dextral strike-slip or oblique-slip with a reverse-slip component) are highly likely to generate earthquakes in South Korea.     

The traveltime perturbations for seismic body waves in factorized anisotropic inhomogeneous media

The traveltime perturbation equations for the quasi-compressional and the two quasi-shear waves propagating in a factorized anisotropic inhomogeneous (FAI) media are derived. The concept of FAI media simplifies considerably these equations. In the FAI medium, the density normalized elastic parameters a _ijkl ( X _i ) can be described by the relation a _ijkl ( X _i) = f ²( x _i ) A _ijkl, where A _ijkl are constants, independent of coordinates x _i and f ²( x _i) is a continuous smooth function of x _i . The types of anisotropy ( A _ijkl ) and inhomogeneity [ f ( x _i)] are not restricted. The traveltime perturbations of individual seismic body waves ( q ^P , qS 1 and qS 2) propagating in the FAI medium depend, of course, both on the structural pertubations [δ f ²( x _i)] and on the anisotropy perturbations (δ A _ijkl ), but both these effects are fully separated. The perturbation equations for the time delay between the two qS -waves propagating in the FAI medium are simplified even more. If the unperturbed (background) medium is isotropic, the perturbation of the time delay does not depend on the structural perturbations (δ f ²( x _i) at all. This striking result, valid of course only in the framework of first-order perturbation theory, will simplify considerably the interpretation of the time delay between the two split qS -waves in inhomogeneous anisotropic media. Numerical examples are presented.     

Regional variations of heat flow differences with depth in Alberta, Canada

Summary. Differences between estimated average heat flow values for the Mesozoic and Cenozoic formations ( Q ₁) and estimated average heat flow values for the Palaeozoic formations below the erosional unconformity ( Q ₂) are calculated for the Alberta part of the western Canadian sedimentary basin. Significant heat flow differences exist for these two intervals and the map of Δ Q = Q ₁– Q ₂ shows that Q ₂ is generally greater than Q ₁ in the western and south-western part of Alberta, while in the northern part of the province Q ₂ is generally less than Q ₁. The regional variations of Δ Q are large, with standard deviation of 26 mW m⁻² and average value –13.5 mW m⁻². A regional trend of Δ Q correlates with topographic relief and the hydraulic head variations in the basin. It is shown that there is a heat flow increase with depth in water recharge areas and a decrease in heat flow with depth in the low topographic elevation water discharge areas when comparing the average heat flow in Mesozoic + Cenozoic and Palaeozoic formations.