Discrete scale invariance connects geodynamo timescales

The geodynamo exhibits a bewildering gamut of time-dependent fluctuations, on timescales from years to at least hundreds of millions of years. No framework yet exists that comprises all and relates each to all others in a quantitative sense. The technique of bootstrapped discrete scale invariance quantifies characteristic timescales of a process, based upon log-periodic fits of modulated power-law scaling of size-ranked event durations. Four independent geomagnetic data sets are analysed therewith, each spanning different timescales: the sequence of 332 known dipole reversal intervals (0–161 Ma); dipole intensity fluctuations (0–2 Ma); archeomagnetic secular variation (5000 B.C.–1950 A.D.); and historical secular variation (1590–1990 A.D.).
Six major characteristic timescales are empirically attested: circa 1.43 Ma, 56 Ka, and 763, 106, 21 and 3 yr. Moreover, all detected wavelengths and phases of the detected scaling signatures are highly similar, suggesting that a single process underlies all. This hypothesis is reinforced by extrapolating the log-periodic scaling signal of any particular data set to higher timescales than observed, through which predictions are obtained for characteristic scales attested elsewhere. Not only do many confirm one another, they also predict the typical duration of superchrons and geomagnetic jerks. A universal scaling bridge describes the complete range of geodynamo fluctuation timescales with a single power law.     

Centennial to millennial geomagnetic secular variation

A time-varying spherical harmonic model of the palaeomagnetic field for 0–7 ka is used to investigate large-scale global geomagnetic secular variation on centennial to millennial scales. We study dipole moment evolution over the past 7 kyr, and estimate its rate of change using the Gauss coefficients of degree 1 (dipole coefficients) from the CALS7K.2 field model and by two alternative methods that confirm the robustness of the predicted variations. All methods show substantial dipole moment variation on timescales ranging from centennial to millennial. The dipole moment from CALS7K.2 has the best resolution and is able to resolve the general decrease in dipole moment seen in historical observations since about 1830. The currently observed rate of dipole decay is underestimated by CALS7K.2, but is still not extraordinarily strong in comparison to the rates of change shown by the model over the whole 7 kyr interval. Truly continuous phases of dipole decrease or increase are decadal to centennial in length rather than longer-term features. The general large-scale secular variation shows substantial changes in power in higher spherical harmonic degrees on similar timescales to the dipole. Comparisons are made between statistical variations calculated directly from CALS7K.2 and longer-term palaeosecular variation models: CALS7K.2 has lower overall variance in the dipole and quadrupole terms, but exhibits an imbalance between dispersion in   g ¹₂  and   h ¹₂  , suggestive of long-term non-zonal structure in the secular variations.     

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.     

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 choice of timescale in glacial rebound modelling: mantle viscosity estimates and the radiocarbon timescale

Most glacial rebound studies have been carried out with respect to the radiocarbon timescale, whose departures from the calendar timescale are becoming increasingly well established. In consequence, it has sometimes been argued that the choice of the radiocarbon timescale may invalidate some of the conclusions drawn from rebound and sea-level analyses. The purpose of this note is to compare rebound model results based on both timescales, using the British Isles data for the test. The results indicate that the choice of timescale is unimportant provided that the time dimension of viscosity is appropriately defined. The results confirm that the radiocarbon viscosities are about 15 per cent less than the corresponding calendar-time viscosities. Also, provided that consistency of timescales is maintained in the analysis, and that the time-accuracy estimates of the radiocarbon data reflect the departures from a linear timescale, the use of the radiocarbon timescale does not impinge on inferences drawn about the timing of melting of ice sheets or eustatic sea-level change.     

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。     

Magnetostratigraphy of mid-Cretaceous limestones from the Sierra Madre of northeastern Mexico

We present the results of a palaeomagnetic study of four mid-Cretaceous limestone sections exposed in northeastern Mexico. The limestones are weakly magnetized and exhibit two- to three-component magnetizations. These magnetization components appear to be carried by both a sulphide mineral and a magnetite-titanomagnetite mineral. The sulphide mineral carries a reverse polarity overprint that often makes it difficult to isolate definitively the higher-unblocking-temperature component. The high-unblocking-temperature component is well defined in the upper portion of the Santa Rosa Canyon section and in the Cienega del Toro section and passes the fold test. The characteristic remanent magnetization (ChRM) inclinations agree well with predicted mid-Cretaceous inclinations for these sites, although the declinations differ by more than 100°. The relative rotation between these two sites probably occurred as the thrust sheets were emplaced during Laramide deformation. At two of the sections, namely Cienega del Toro and the overturned Los Chorros sections, only normal polarity directions are observed. The La Boca Canyon and Santa Rosa Canyon sections exhibit zones of both normal and reverse polarity magnetization. Correlation of these polarity zones with the geomagnetic polarity timescale provides a time framework for lithostratigraphic and palaeoceanographic studies of these sections.     

Two years of magnetotelluric measurements in Abitibi, western Québec, using a telephone line

Continuous magnetotelluric measurements were made over a period of 600 days, with 100-m-, 30-km- and 100-km-long dipoles and a period range of 40–4000 s. Data analysis for different dipole lengths indicates the presence of static shift at various scales. It is shown that the longer the telluric dipole, the less statically shifted the resistivity curves; nevertheless, static shifts can still be present due to geological structures causing anomalies exhibiting wavelengths comparable to the dipole length. Also, a relationship is observed between the coherence and the main impedance components. This relation is explained in terms of signal-to-noise ratio. A way to reduce the bias on the impedance estimates is suggested. The apparent resistivities and phases computed from three different impedance estimates using 100-km-long dipoles are then compared to those observed in similar studies made near our observation region.     

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.     

纵向岭谷区红河的跨境径流量变化特征分析

以云南境内红河蛮耗站的多年径流量观测数据和云南的降水场、气温场观测数据为基础，应用小波变换和相关系数的统计分析方法，分析了红河的跨境径流量变化特征及其与云南气候变化的关系。结论为：近50年来，纵向岭谷区红河的跨镜径流量变化表现出了较大时间尺度的波动；径流量的年内分配不均，主要集中在云南雨季开始后的6-11月份；径流量的年际变化表现出了十分明显的多时间尺度特征，其特征时间尺度约为2年、8年和17年；红河的跨境径流量变化与云南干、雨季的降水量场变化之间存在有十分显著的相关关系，但与云南干、雨季的气温场变化之间的相关性不是很显著，说明红河的跨境径流量变化主要是由于云南降水量场的变化造成的。     

Electromagnetic core–mantle coupling—I. Explaining decadal changes in the length of day

Measured changes in the Earth's length of day on a decadal timescale are usually attributed to the exchange of angular momentum between the solid mantle and fluid core. One of several possible mechanisms for this exchange is electromagnetic coupling between the core and a weakly conducting mantle. This mechanism is included in recent numerical models of the geodynamo. The 'advective torque', associated with the mantle toroidal field produced by flux rearrangement at the core–mantle boundary (CMB), is likely to be an important part of the torque for matching variations in length of day. This can be calculated from a model of the fluid flow at the top of the outer core; however, results have generally shown little correspondence between the observed and calculated torques. There is a formal non-uniqueness in the determination of the flow from measurements of magnetic secular variation, and unfortunately the part of the flow contributing to the torque is precisely that which is not constrained by the data. Thus, the forward modelling approach is unlikely to be useful. Instead, we solve an inverse problem: assuming that mantle conductivity is concentrated in a thin layer at the CMB (perhaps D"), we seek flows that both explain the observed secular variation and generate the observed changes in length of day. We obtain flows that satisfy both constraints and are also almost steady and almost geostrophic, and therefore assert that electromagnetic coupling is capable of explaining the observed changes in length of day.     

Magnetostratigraphy of Early Cretaceous Maiolica sections of the Southern Alps (Cismon and Pra da Stua, Italy)

The bottom part of the Cretaceous Cismon section in the Southern Alps was sampled for high-resolution magnetostratigraphy. Although the almost pure pelagic nannofossil limestones ( c. 90 per cent CaCO₃) of the Maiolica/Biancone Formation are extremely weakly magnetized, stepwise thermal and alternating-field demagnetization removed overprints and isolated a characteristic remanent magnetization which is interpreted as a primary magnetization. The dominant magnetic carrier mineral is magnetite; a small fraction of haematite may be present. A clear reversal pattern can be correlated unambiguously with Mesozoic polarity chrons CM10N to CM8. A less well-constrained magnetostratigraphy from the Pra da Stua section could not be directly correlated with the global polarity scale, but biostratigraphic information allows its assignment to the interval CM10-CM5. A counterclockwise rotation of 56 and a northward translation of 28 latitude for the Cismon locality since the Early Cretaceous are derived from the palaeomagnetic data, consistent with previous results from the Southern Alps. The high-resolution magnetostratigraphy of the Cismon section is used in an effort to refine the Cretaceous timescale by the combination of magnetostratigraphic and cyclostratigraphic results from the same section. The cyclostratigraphic duration estimates of chrons CM10N to CM8 are compared to their equivalents in a number of traditional timescales and found to be shorter by a factor of 1.26-2.58.     

Geomagnetic disturbance fields: an analysis of observatory monthly means

SUMMARY
This work quantifies the extent to which disturbance phenomena contribute to the observed geomagnetic field on the time-scale of months to years. A deterministic approach was adopted in which geomagnetic monthly means were analysed in the time domain. By presupposing the time dependence of the external and induced field variations, which we assume to vary as the aa geomagnetic index, we arrived at an estimate of the relative amplitude of the disturbance to each component of the field at a number of observatories. In all some 58 000 geomagnetic monthly means from 59 observatories operating this century were analysed. Special attention was paid to the selection and validation of the data as otherwise the numerical computations would have been unduly compromised.
The results consist of 177 estimates of the relative amplitude of disturbance, one for each of three orthogonal components north ( X ), east ( Y ) and vertically down ( Z ) at each observatory. The disturbance to the X component was found to be consistently negative over the whole of the Earth's surface with an intensification in auroral regions. The disturbances to the Z component were found to be smaller than that for X except in high latitudes. Mean disturbances to the Y component were smaller still. Results were in general consistent with the dipole field of the magnetospheric ring current, aligned with, though of opposite polarity to, the Earth's main field. Typical amplitudes of the mean disturbance field from month to month were of the order 10 nT.
The results can be used to estimate the variation of the disturbance field. Subtracting this from both monthly and annual means yields an improved estimate of the field originating in the core and its secular variation. Some examples are presented.     

Periodicity of magnetic intensities in magnetic anomaly profiles: the Cretaceous of the Central Pacific

Spectral analyses of long magnetic anomaly profiles of Cretaceous age in the Phoenix and Hawaiian lineations within the Pacific Basin show two to five non-harmonic wavelength peaks, with probabilities >90 per cent, within the range of several tens to hundreds of kilometres for each profile. For each profile with four peak wavelengths, their ratios correlate strongly ( r > 0.98) with the ratios for the Earth's orbital eccentricity periodicities for this time, and hence the profile peaks necessarily correlate with each other. These observations suggest that the magnetic anomaly signal is influenced by the Earth's changing orbital parameters, probably through their influence on the internal geomagnetic field. This implies that assumptions usually made to convert the magnetic signal to the magnetization of the oceanic crust may be suspect. The observations, if confirmed, indicate that orbital periodicities can assist in improving the age calibration of the global polarity timescale and that the predicted orbital behaviour of the Earth is confirmed for the last 150 Ma.     

中国中部六省预期寿命时序加密估算研究

年龄组死亡率是利用年龄分组人口数据计算预期寿命的关键参数,而非采样年份的统计年鉴中年龄分组死亡率缺失导致无法计算预期寿命。针对该问题,本文将人口普查数据与统计年鉴数据融合,首次提出一种基于拉格朗日插值的中国省级预期寿命时间序列加强密集度（时序加密）的算法,以解决非采样（即未进行人口普查或1%人口抽样调查）年份省级预期寿命的估算问题。以中国中部六省为例,在所选取年份省级预期寿命估算实验中,绝对精度表明年龄分组人口比例线性插值计算的精度明显高于人口比例抛物线插值和直接插值算法的精度,故为推荐算法。本研究为高时间分辨率下省级预期寿命值的获取提供了一个新的可行思路,为分省较精确地进行预期寿命趋势分析奠定基础。     

Lessons from the tropics for a global geomorphology

Historically, geomorphologists have applied uniformitarian principles based on a temperate normality to all water-worn landscapes. Isolation of tropical landforms within formal morphogenetic regions, which arose during the early history of the subject, has persisted. However, in a global geomorphology, plate tectonic motion, Milankovich cycles of climate change and invasive weather systems all render fixed climatic boundaries meaningless and, on every timescale of enquiry, interaction of the tropics with extra-tropical regions is fundamental. In tropical regions, the continuity of weathering processes through geologic time emphasizes their contemporary relevance and, with knowledge of Quaternary climate changes, increases understanding of the nature of landscape sensitivity and instability and fluvial sedimentation on millennial timescales. Examples are illustrated from northeast Queensland, Australia and northwest Kalimantan, Indonesia. Global concerns centred on hazards and resources need to be addressed through a reciprocal exchange of ideas involving greater focus on tropical areas.     

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.     

Preliminary palaeomagnetic results of an Archaean dolerite dyke of west Greenland: geomagnetic field intensity at 2.8 Ga

The geomagnetic field intensity during Archaean times is evaluated from a palaeomagnetic and chronological study of a dolerite dyke intruded into the 3000 Ma Nuuk Gneisses at Nuuk (64.2°N, 51.7°W), west Greenland. Plagioclase from the dolerite dyke yields a mean K-Ar age of 2752 Ma. Palaeomagnetic directions after thermal demagnetization of the dyke and the gneiss reveal a positive baked-contact test, indicating that the high-temperature-component magnetization of the dyke is primary. Thellier experiments on 12 dyke specimens yield a palaeointensity value of 13.5±4.4 μT. The virtual dipole moment at ca. 2.8 Ga is 1.9±0.6 × 10²² Am², which is about one-quarter of the present value. The present study and other available data imply that the Earth's magnetic field at 2.7 ∼ 2.8 Ga was characterized by a weak dipole moment and that a fairly strong geomagnetic field similar to the present intensity followed the weak field after ca. 2.6 Ga.     

ARIMA-LSTM组合模型在基于SPI干旱预测中的应用——以青海省为例

开展干旱预测是有效应对干旱风险的前提基础。利用1958—2017年青海省38个气象站点逐日降水量数据计算多尺度标准化降水指数（SPI）,并建立了SPI序列自回归移动平均模型（ARIMA）、长短时记忆神经网络模型（LSTM）和基于二者优点提出的ARIMA-LSTM组合模型;对模型参数进行率定和验证后,利用所建立的模型,以西宁站点为例,对多尺度SPI值进行预测,借助均方根误差（RMSE）、平均绝对百分比误差（MAPE）和决定系数R²对所有预测模型的有效性进行判定。结果表明：ARIMA-LSTM组合模型在SPI1和SPI12的RMSE值分别为0.159 7和0.181 0,均低于ARIMA模型的1.265 4和0.293 3,说明ARIMA模型与ARIMA-LSTM组合模型对SPI的预测精度都与时间尺度有关,ARIMA模型的预测精度随着时间尺度的增加而逐渐提高;结合GIS并利用实测数据与模型的预测数据相比较说明ARIMA-LSTM组合模型相比于单一ARIMA模型的预测精度更高,且能够很好拟合不同时间尺度的SPI值。     

11 million years of Oligocene geomagnetic field behaviour

An 11 million year long record of the Oligocene geomagnetic field has been obtained from pelagic sediments of DSDP Hole 522 An average sample spacing of 4 cm yielded approximately one specimen per 4 to 8 kyr. The rock magnetics are remarkabh consistent across the entire interval. Previous work demonstrated a magnetic mineralogy dominated by magnetically stable magnetite. The natural remanent magnetism (NRM) carries an Oligocene polarity timescale that is in excellent agreement with the Oligocene reversal record as determined from marine magnetic anomalies (MMAs), including many of the so-called 'crypto-chrons'. Normalized NRM intensities from the undisturbed portions of the record yield a time series of variations with features consistent with a number of other palaeointensity time series derived from both sedimentary and lava sequences. These features include consistent, major decreases in palaeointensity (DIPs) at reversal boundaries, and occasional DIPs between reversal boundaries that could correspond to lineated 'tiny wiggles' in the MMA records. The data set suggests that the overall field strength was 40 per cent higher in the first half of the Oligocene when the average reversal frequency was 1.6 Myr^-1 than in the second half when the reversal frequency was 4 Myr^-1. There is also a weak dependence of average field strength on length of polarity interval. Finally, in the three cores suited to spectral analysis (of coherent polarity and relative intensity independent of lithological contamination), there is a persistent ca. 30–50ka periodicity in the variations of the relative intensity, suggesting that the geomagnetic field 'pulses' at about this frequency, not only during the Brunhes (as demonstrated by Tauxe & Shackleton 1994), but in the Oligocene as well.