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.     

Postglacial sea-level history of Edgeøya and Barentsøya, eastern Svalbard

Four relative sea-level curves from Edgeøya and Barentsøya are constructed based on 81 radiocarbon age determinations on carefully selected and levelled samples in raised beaches, mostly driftwood embedded in beach gravel. All the dates, covering the period from the deglaciation to the present, are calibrated to calendar years, and the sea-level curves are defined by fitting the data with a least square regression curve. The dates are internally very consistent, and the results are some of the most precise sea-level curves from the Arctic.
The four curves are quite similar, and from the marine limit at 85-90 m a.s.l. they show a rapid emergence (ca 40 mm/year), formed about 11,000 cal yrs BP (∼10,000¹⁴C yrs BP). A minimum rate of emergence close to 8000 cal years ago is explained by a decreased rate in isostatic uplift parallel with a sustained rate of eustatic sea-level rise. During the last 7000 cal years, the emergence rate has decreased linearly. The uplift rates have been slightly higher on southern Edgeøya than further north during the last 7000 years. By comparing the sea-level curves from Storøya (ca 270 km to the north) and Hopen (ca 150 km to the south), we suggest that a memory of an earlier and larger glacio-isostatic downwarping in the southern Barents Sea is detected in the sea-level curves from Hopen and southern Edgeøya.     

Bootstrapped discrete scale invariance analysis of geomagnetic dipole intensity

The technique of bootstrapped discrete scale invariance allows multiple time-series of different observables to be normalized in terms of observed and predicted characteristic timescales. A case study is presented using the SINT2000 time-series of virtual axial dipole moment, which spans the past 2 Myr. It is shown that this sequence not only bears a clear signature of a preferred timescale of about 55.6 Ka, but additionally predicts similar features (of shorter and longer duration) that are actually observed on the timescales of historical secular variation and dipole reversals, respectively. In turn, the latter two empirical sources both predict the characteristic timescale found in the dipole intensity sequence. These communal scaling characteristics suggest that a single underlying process could be driving dynamo fluctuations across all three observed timescales, from years to millions of years.     

夏季风作用下的纵向岭谷区夏季降水量年际变化的时空特征和规律

应用三维数据的时间小波变换方法, 分析研究了夏季风作用下的纵向岭谷区夏季降水量 在年际变化上的时空特征和规律。结论为: 夏季风作用下的云南纵向岭谷区夏季降水量在年际变 化上的特征时间尺度分别约为2 年、7 年和16 年; 2 年、7 年和16 年特征时间尺度的较大振幅能 量活动区分别与纵向岭谷区的山脉走向一致或正交; 与2 年特征时间尺度相对应的较大振幅能 量活动中心纬度的夏季降水量表现出了明显的东西向波动的时间演变特征, 而与7 年和16 年特 征时间尺度相对应的较大振幅能量活动中心纬度的夏季降水量则分别表现出了一种向西和向东 移动的时间演变趋势; 与2 年特征时间尺度相对应的较大振幅能量活动中心经度的夏季降水量 也表现出了明显的南北向波动的时间演变特征, 而与7 年和16 年特征时间尺度相对应的较大振 幅能量活动中心经度的夏季降水量则分别表现出了一种明显向北和向南移动的时间演变趋势。     

On the construction of geomagnetic timescales from non-prejudicial treatment of magnetic anomaly data from multiple ridges

When marine magnetic-anomaly data are used to construct geomagnetic polarity timescales, the usual assumption of a smooth spreading-rate function at one seafloor spreading ridge forces much more erratic rate functions at other ridges. To eliminate this problem, we propose a formalism for the timescale problem that penalizes non-smooth spreading behaviour equally for all ridges. Specifically, we establish a non-linear Lagrange multiplier optimization problem for finding the timescale that (1) agrees with known chron ages and with anomaly-interval distance data from multiple ridges and (2) allows the rate functions for each ridge to be as nearly constant as possible, according to a cumulative penalty function. The method is applied to a synthetic data set reconstructed from the timescale and rate functions for seven ridges, derived by Cande & Kent (1992) under the assumption of smooth spreading in the South Atlantic. We find that only modest changes in the timescale (less than 5 per cent for each reversal) are needed if no one ridge is singled out for the preferential assumption of smoothness. Future implementation of this non-prejudicial treatment of spreading-rate data from multiple ridges to large anomaly-distance data sets should lead to the next incremental improvement to the pre-Quaternary geomagnetic polarity timescale, as well as allow a more accurate assessment of global and local changes in seafloor spreading rates over time.     

低纬高原地区降水量资源年际变化的特征时间尺度及其时空演变

应用三维数据的时间小波变换方法，分析研究了低纬高原地区降水量资源在年际变化上的特征时间尺度及其时空演变。结论为：低纬度高原地区降水量资源在年际变化上的特征时间尺度分别约为2a、7a和15a。2a、78和158特征时间尺度的较大振幅能量活动区，分别主要位于滇西北到滇东南、滇东北到滇西南和滇中一带。与2a特征时间尺度相对应的较大振幅能量活动中心纬度的降水量，表现出了明显的东西向波动的时间演变特征，而与78和158特征时间尺度相对应的较大振幅能量活动中心纬度的降水量，则表现出了在东西向较为稳定少变的时间演变特征。与2a特征时间尺度相对应的较大振幅能量活动中心经度的降水量，也表现出了明显的南北向波动的时间演变特征，而与7a和15a特征时间尺度相对应的较大振幅能量活动中心经度的降水量，则表现出了一种明显向南移动的时间演变趋势。     

Glacial rebound of the British Isles—II. A high-resolution, high-precision model

Observations of ice movements across the British Isles and of sea-level changes around the shorelines during Late Devensian time (after about 25 000 yr BP) have been used to establish a high spatial and temporal resolution model for the rebound of Great Britain and associated sea-level change. The sea-level observations include sites within the margins of the former ice sheet as well as observations outside the glaciated regions such that it has been possible to separate unknown earth model parameters from some ice-sheet model parameters in the inversion of the glacio-hydro-isostatic equations. The mantle viscosity profile is approximated by a number of radially symmetric layers representing the lithosphere, the upper mantle as two layers from the base of the lithosphere to the phase transition boundary at 400 km, the transition zone down to 670 km depth, and the lower mantle. No evidence is found to support a strong layering in viscosity above 670 km other than the high-viscosity lithospheric layer. Models with a low-viscosity zone in the upper mantle or models with a marked higher viscosity in the transition zone are less satisfactory than models in which the viscosity is constant from the base of the lithosphere to the 670 km boundary. In contrast, a marked increase in viscosity is required across this latter boundary. The optimum effective parameters for the mantle beneath Great Britain are: a lithospheric thickness of about 65 km, a mantle viscosity above 670 km of about (4-5) 10²⁰ Pa s, and a viscosity below 670 km greater than 4 × 10²¹ Pa s.     

Regional variation in modern radiocarbon ages and the hard-water effects in Lakes Michigan and Huron

Eight new radiocarbon ages, all determined by accelerator mass spectrometry, on modern (pre-bomb) mollusks have been added to similar data provided from three samples in the Lake Michigan and Huron basins. These data confirm the existence of a substantial hard water effect correction ranging from about 250 years to 500 years in these lakes. They also show that the magnitude of these corrections form a spatially coherent pattern that can be related to the pattern of outcrop of Paleozoic (radioactively inert) carbonates that surround the basins and the pattern of circulation within the basins.     

Some remarks about the degree-one deformation of the Earth

The degree-one deformation of the Earth (and the induced discrepancy between the figure centre and the mass centre of the Earth) is computed using a theoretical approach (Love numbers formalism) at short timescales (where the Earth has an elastic behaviour) as well as at long timescales (where the Earth has a viscoelastic or quasi-fluid behaviour). For a Maxwell model of rheology, the degree-one relaxation modes associated with the viscoelastic Love numbers have been investigated: the M_o mode does not exist and there is only one transition mode (instead of two) generated by a viscosity discontinuity.
The translations at each interface of the incompressible layers of the earth model [surface, 670 km depth discontinuity, core-mantle boundary (CMB) and inner-core boundary (ICB)] are computed. They are elastic with an order of magnitude of about 1 mm when the excitation source is the atmospheric continental loading or a magnetic pressure acting at the CMB. They are viscoelastic when the earth is submitted to Pleistocene deglaciation, with an order of magnitude of about 1 m. In a quasi-fluid approximation (Newtonian fluid) because of the mantle density heterogeneity their order of magnitude is about 100 m (except for the ICB, which is in quasi-hydrostatic equilibrium at this timescale).     

On the age calibration of the geomagnetic polarity timescale

Knowledge of the age of undated events is not null if a time-order relationship can be found among these events. The knowledge of such a time-ordered sequence can be formalized by using non-informative (uniform) prior probability densities for the ages of undated events and Bayes' theorem to introduce the time-order relationship condition. We show that the conditional probability densities of the ages of events of unknown age are given by various forms of Euler's beta distribution. These distributions yield an estimate of the probability for an undated event to occur in a given age interval.
  We use this method to propose appropriate probabilistic representations of our actual knowledge of the dating of the magnetic polarity reversals during the Cenozoic. These representations take into account the uncertainties arising from irregularities in accretion process and from the quality of a few calibration points. Both types of uncertainties generate large ambiguities in the age of magnetic reversals, which should be taken into consideration when the geomagnetic polarity timescale is used for dating purposes. We propose to use the entropy function to quantify these ambiguities.     

基于SSA和MGF的海面变化长期预测及对比

海面变化预测受到建模思路、方法选择、数据长度及数据质量等因素的影响,导致了海面变化预测的不确定性。本文以国内6个验潮站自20世纪50年代以来的月平均潮位序列为基础,采用奇异谱分析(SSA)与均值生成函数(MGF)模型相结合的方案,以各站位最初20余年数据为基础建立预测模型,以后续年份的实测数据进行了多方案对比验证及检验。预测试验显示MGF模型具有较高的预测精度,并表现出较好的长期预测的稳定性特点。以SSA去噪序列为基础,应用MGF模型预测了各站位至2050年的月尺度海面值,年均值计算结果表明至2050年海面波动上升的幅度不超过20cm,海面变化速率同样表现出阶段性和波动性。与前人相关研究成果对比表明,本文所采用的SSA与MGF相结合的预测结果具有可比性,在方法原理和验证结果上看具有较好的长期预测潜力。     

Non-Poissonian earthquake occurrence in coupled stress release models and its effect on seismic hazard

Most seismic hazard estimations are based on the assumption of a Poisson process for earthquake occurrence, even though both observations and models indicate a departure of real seismic sequences from this simplistic assumption. Instrumental earthquake catalogues show earthquake clustering on regional scales while the elastic rebound theory predicts a periodic recurrence of characteristic earthquakes on longer timescales for individual events. Recent implementations of time-dependent hazard calculations in California and Japan are based on quasi-periodic recurrences of fault ruptures according to renewal models such as the Brownian Passage Time model. However, these renewal models neglect earthquake interactions and the dependence on the stressing history which might destroy any regularity of earthquake recurrences in reality. To explore this, we investigate the (coupled) stress release model, a stochastic version of the elastic rebound hypothesis. In particular, we are interested in the time-variability of the occurrence of large earthquakes and its sensitivity to the occurrence of Gutenberg–Richter type earthquake activity and fault interactions. Our results show that in general large earthquakes occur quasi-periodically in the model: the occurrence probability of large earthquakes is strongly decreased shortly after a strong event and becomes constant on longer timescales. Although possible stress-interaction between adjacent fault zones does not affect the recurrence time distributions in each zone significantly, it leads to a temporal clustering of events on larger regional scales. The non-random characteristics, especially the quasi-periodic behaviour of large earthquakes, are even more pronounced if stress changes due to small earthquakes are less important. The recurrence-time distribution for the largest events is characterized by a coefficient of variation from 0.6 to 0.84 depending on the relative importance of small earthquakes.     

Differential responses of hillslope and channel elements to rainfall events in a semi-arid area

The degree of hydrological connectivity of hillslope elements in a semi-arid climate was studied at the season and event timescales. Field data were obtained in Rambla Honda, a Medalus project field site situated in SE Spain, on micaschist bedrock and with 300 mm annual rainfall. The season timescale was assessed using correlation analysis between soil moisture and topographic indices. The event timescale was studied by a quasi-continuous monitoring of rainfall, soil moisture, runoff and piezometric levels. Results show that widespread transfers of water along the hillslope are unusual because potential conditions for producing overland flow or throughflow are spatially discontinuous and extremely short-lived. During extreme events, runoff coefficients may be locally high (ca. 40% on slope lengths of 10 m), but decrease dramatically at the hillslope scale (<10% on slope lengths of 50 m). Two mechanisms of overland flow generation have been identified: infiltration excess, and local subsurface saturation from upper layers. The former occurs during the initial stages of the event while the latter, which is quantitatively more important, takes place later and requires a certain time structure of rainfall intensities that allow saturation of the topsoil and the subsequent production of runoff. Hillslopes and alluvial fans function as runoff sources and sinks respectively. Permanent aquifers are lacking in Rambla Honda. Variable proportions of hillslope areas may contribute to flash floods in the main channel, but their contribution to the formation of saturated layers within the sediment fill is very limited.     

Numerical models of ductile rebound of crustal roots beneath mountain belts

Crustal roots formed beneath mountain belts are gravitationally unstable structures, which rebound when the lateral forces that created them cease or decrease significantly relative to gravity. Crustal roots do not rebound as a rigid body, but undergo intensive internal deformation during their rebound and cause intensive deformation within the ductile lower crust. 2-D numerical models are used to investigate the style and intensity of this deformation and the role that the viscosities of the upper crust and mantle lithosphere play in the process of root rebound. Numerical models of root rebound show three main features which may be of general application: first, with a low-viscosity lower crust, the rheology of the mantle lithosphere governs the rate of root rebound; second, the amount of dynamic uplift caused by root rebound depends strongly on the rheologies of both the upper crust and mantle lithosphere; and third, redistribution of the rebounding root mass causes pure and simple shear within the lower crust and produces subhorizontal planar fabrics which may give the lower crust its reflective character on many seismic images.     

Holocene lake-level fluctuations and beach-ridge development along the northern shore of Lake Michigan, USA

Geomorphology of a beach-ridge complex and adjacent lake basins along the northern shore of Lake Michigan records fluctuations in the level of Lake Michigan for the last 8000 to 10 000 ¹⁴C yr B.P. (radiocarbon years Before Present). A storm berm at 204.7–206 m (671.6–675.9 ft) exposed in a sandpit provides evidence of a pre-Chippewa Low lake level that is correlated with dropping water levels of Glacial Lake Algonquin (c. 10 300–10 100 ¹⁴C yr B.P.). Radiocarbon dates from organic material exposed in a river cutbank and basal sediments from Elbow Lake, Mackinac Co., Michigan, indicate a maximum age of a highstand of Lake Michigan at 6900 ¹⁴C yr B.P., which reached as high as 196.7 m (645 ft), during the early-Nipissing transgression of Lake Michigan. Basal radiocarbon dates from beach swales and a second lake site (Beaverhouse Lake, Mackinac Co.) provide geomorphic evidence for a subsequent highstand which reached 192.6 m (632 ft) at 5390±70 ¹⁴C yr B.P.Basal radiocarbon dates from a transect of sediment cores, along with tree-ring data, and General Land Office Surveyor notes of a shipwreck, c. A.D. 1846, reveal a late-Holocene rate for isostatic rebound of 22.6 cm/100 radiocarbon years (0.74 ft/100 radiocarbon years) for the northern shore of Lake Michigan, relative to the Lake Michigan-Lake Huron outlet at Port Huron, Michigan. Changes in sediment stratigraphy, inter-ridge distance, and sediment accumulation rates document a mid- to late-Holocene retreat of the shoreline due to isostatic rebound. This regression sequence was punctuated by brief, periodic highstands, resulting in progressive development over the past 5400 ¹⁴C yr of 75 pairs of dune ridges and swales each formed over an interval of approximately 72 years. Times of lake-level fluctuation were identified at 3900, 3200, and 1000 ¹⁴C yr B.P. based on changes in inter-ridge spacing, shifts in the course of Millecoquins River, and reorientation of beach-ridge lineation. Soil type, dune development, and selected pollen data provide supporting evidence for this chronology. Late-Holocene beach-ridge development and lake-level fluctuations are related to a retreat of the dominant Pacific airmass and the convergence of the Arctic and Tropical airmasses resulting in predominantly meridional rather than zonal air flow across the Great Lakes region.This is the 13th in a series of papers published in this special AMQUA issue. These papers were presented at the 1994 meeting of the American Quaternary Association held 19–22 June, 1994, at the University of Minnesota, Minneapolis, Minnesota, USA. Dr Linda C. K. Shane served as guest editor for these papers.     

Linear correlations between Florida Current volume transport and surface speed with Miami sea-level and weather during 1964-70

Summary. The 1964-70 Florida Current data of Niiler & Richardson are examined for linear correlation with observed sea-level and weather, because their data provide an independent test of similar correlations reported in Maul et al. Seventy-five values of directly measured volume transport and 67 values of surface speed from Niiler & Richardson's unevenly spaced data are correlated with available daily mean values of Miami Beach sea-level, Bimini sea-level, Bimini-Miami Beach sea-level difference, and Miami weather (barometric pressure, air temperature, and north and east components of wind speed). Statistical frequency distribution of transport and of surface speed suggest variability that is not dominated by annual and/or semiannual cycles. Volume transport is most highly correlated with Bimini minus Miami Beach sea-level difference, and surface speed is most highly correlated with inverted Miami Beach sea-level. Including certain weather variables results in statistically significant improvements in linear multivariate modelling of transport and surface speed from sea-level; the standard errors are ± 2.6 sverdrup and ±10 cms⁻¹ respectively. Linear correlation coefficients and multivariate regression parameters from Niiler & Richardson's data are in agreement with those from Maul et al. , except that the standard error of estimating volume transport from sea-level is smaller in Maul et al. , apparently because of smaller errors in the direct measurements.     

SPATIAL COHERENCE AND DECAY OF WIND SPEED AND POWER IN THE NORTH-CENTRAL UNITED STATES

Hourly wind data from a network of climate stations in the north-central United States (drawn from the states of Illinois, lowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, South Dakota, and Wisconsin) are analyzed to evaluate the efficacy of spatial analyses of near-surface wind speed and power. Spatial autocorrelation functions (acfs) were calculated at a number of timescales: annual, monthly, daily, and hourly. Annual wind speeds have virtually no coherent distance-decay relationship; monthly data produce a more consistent relationship, but still exhibit a large amount of scatter. Both daily and hourly data have classical decay with increasing distance between stations and there appears to be an optimal level of temporal aggregation, near the daily timescale, for spatial analysis of wind. In general, however, spatial acfs overestimate the spatial coherence of both wind speed and power. Temporal nonstationarities in wind data (i.e., diurnal and annual cycles) bias spatial autocorrelation functions and need to be removed before using spatial acfs to estimate characteristics of wind fields. Because mean absolute differences (MAD) of interstation wind speed and power are less affected by temporal nonstationarities, they produce more-robust representations of the spatial variability of wind speed and power. As a result, spatial MADs are recommended over spatial acfs for analyzing spatial coherence and decay of any spatial variable that contains nonstationarities. Methods for improving the spatial analysis of wind are discussed. [Key words: wind energy, spatial autocorrelation, spatial analysis, nonstationarity, north-central United States.]     

THE NONPARAMETRIC ANALYSIS OF VARIANCE AND MULTIPLE COMPARISONS PROCEDURES IN GEOGRAPHY*

Geographers employing the parametric F statistic in analyses of variance should consider that it can be highly sensitive to departures from normality. The Friedman and Kruskal-Wallis tests offer geographers nonparametric alternatives to the analysis of variance, for k dependent and independent samples respectively. Associated with the tests are little known methods for examining ordered alternatives and making multiple comparisons between samples, thereby permitting in-depth analysis of sample data. Both tests and these latter procedures are illustrated by examples drawn from population and urban retailing geography.     

An examination of some uncertainties associated with estimates of sedimentation rates and tectonic subsidence

Abstract The sensitivity of backstripping calculations (sedimentation rates and tectonic subsidence) to uncertainties regarding porosity reduction is examined. Models simulating compaction and externally sourced cementation are considered to provide first-order bounds on the thickness and mass changes for individual sedimentary units. These bounds can be used to estimate uncertainties in sedimentation rate and subsidence estimates. With these models, the timing of cement development can be regarded as unimportant for backstripping calculations. Calculations have been made to evaluate the effect on backstripping calculations of uncertainties in sediment porosity, density and the mechanisms of porosity reduction. Departures from theoretically predicted subsidence curves of the order of 100 m or so have been variously interpreted as the result of fluctuations or uncertainties in sea-level, palaeobathymetry, tectonic stress, sedimentation rates and stratigraphic age. Two examples are given to illustrate that such departures may occur in some subsidence curves merely as a result of imprecise assumptions regarding porosity reduction. Consideration should be given to the uncertainties in models for porosity reduction when using subsidence curves to infer second order tectonic influence during basin evolution.     

Holocene environmental changes of the Hwajinpo Lagoon on the eastern coast of Korea

Lithologic and geochemical data of a core from the Hwajinpo Lagoon, located on the eastern coast of Korea, provided the evolutionary history of the lagoon related to Holocene sea-level changes of the East Sea (Sea of Japan). Grain size analysis, water content analysis, and soft X-ray analysis of core samples were used to reconstruct sedimentary environments, as were total organic carbon, C/N, S and C/S chemical records. Assemblages of mollusc and diatom remains also provided paleoenvironmental information. The reconstruction of paleoenvironments from these multi-proxy data allows the establishment of an evolutionary model of the Hwajinpo Lagoon. The environmental changes of the Hwajinpo Lagoon can be divided into seven different depositional facies: (l) Exposed basement rock; (2) Estuarine; (3) Stagnant brackish lagoon (isolated); (4) Oxic condition lagoon (organic activity); (5) Fresh water lake; (6) Oxic brackish lagoon (recent condition); (7) Prograding river delta. These environmental changes can be related to sea-level change during the Holocene. The trends of sea-level change in the Hwajinpo Lagoon from this study can be compared to those of the Japanese coastal areas located on the other side of the East Sea such as Lakes Shinji and Nakaumi.