Multiple-taper spectral analysis of terrestrial free oscillations: part I

We present a new method for estimating the frequencies of the Earth's free oscillations. This method is an extension of the techniques of Thomson (1982) for finding the harmonic components of a time series. Optimal tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived. Multiplying the data by the best K tapers creates K time series. A decaying sinusoid model is fit to the K time series by a least squares procedure. A statistical F -test is performed to test the fit of the decaying sinusoid model, and thus determine the probability that there are coherent oscillations in the data. The F -test is performed at a number of chosen frequencies, producing a measure of the certainty that there is a decaying sinusoid at each frequency. We compare this method with the conventional technique employing a discrete Fourier transform of a cosine-tapered time-series. The multiple-taper method is found to be a more sensitive detector of decaying sinusoids in a time series contaminated by white noise.     

The influence of fluid-sensitive dispersion and attenuation on AVO analysis

Analysis of seismic data suggests that hydrocarbon deposits are often associated with higher than usual values of attenuation, but this is generally ignored during amplitude-versus-offset (AVO) analysis. The effect can be modelled with equivalent medium theory based on the squirt flow concept, but the excess attenuation is associated with strong velocity dispersion. Consequently, when we study reflections from the interface between such an equivalent medium and an elastic overburden we find that the reflection coefficient varies with frequency. The impact of this variation depends on the AVO behaviour at the interface; class I reflections tend to be shifted to higher frequency while class III reflections have their lower frequencies amplified. We calculate synthetic seismograms for typical models using the reflectivity method for materials with frequency dependent velocities and attenuations, and find that these effects are predicted to be detectable on stacked data. Two field data sets show frequency anomalies similar to those predicted by the analysis, and we suggest that our modelling provides a plausible explanation of the observations.     

土地利用变化对鄂尔多斯高原周边地区沙尘暴的影响

以鄂尔多斯高原周边地区为例 ,研究土地利用变化对沙尘暴的影响 ,建立了多年平均沙尘暴日数与沙漠化土地面积百分比之间的关系。该关系表明 ,当沙漠化土地面积百分比Rd大于 30 %以后 ,沙尘暴日数随Rd的增大而急剧增加。年均沙尘暴日数与耕地面积和大风日数之间的回归方程 ,结果表明 ,耕地面积减少和大风日数减少对沙尘暴减少的贡献率分别为5 9 7%和 4 0 3%。通过在干旱、半干旱脆弱生态条件下的地区进行土地利用结构调整和退耕还草 ,恢复草原生态系统 ,可以在一定程度上减低沙尘暴发生的频率。     

Maximum entropy regularization of time-dependent geomagnetic field models

We incorporate a maximum entropy image reconstruction technique into the process of modelling the time-dependent geomagnetic field at the core–mantle boundary (CMB). In order to deal with unconstrained small lengthscales in the process of inverting the data, some core field models are regularized using a priori quadratic norms in both space and time. This artificial damping leads to the underestimation of power at large wavenumbers, and to a loss of contrast in the reconstructed picture of the field at the CMB. The entropy norm, recently introduced to regularize magnetic field maps, provides models with better contrast, and involves a minimum of a priori information about the field structure. However, this technique was developed to build only snapshots of the magnetic field. Previously described in the spatial domain, we show here how to implement this technique in the spherical harmonic domain, and we extend it to the time-dependent problem where both spatial and temporal regularizations are required. We apply our method to model the field over the interval 1840–1990 from a compilation of historical observations. Applying the maximum entropy method in space—for a fit to the data similar to that obtained with a quadratic regularization—effectively reorganizes the magnetic field lines in order to have a map with better contrast. This is associated with a less rapidly decaying spectrum at large wavenumbers. Applying the maximum entropy method in time permits us to model sharper temporal changes, associated with larger spatial gradients in the secular variation, without producing spurious fluctuations on short timescales. This method avoids the smearing back in time of field features that are not constrained by the data. Perspectives concerning future applications of the method are also discussed.     

The Resolving Power of Gross Earth Data

A gross Earth datum is a single measurable number describing some property of the whole Earth, such as mass, moment of interia, or the frequency of oscillation of some identified elastic-gravitational normal mode. We show how to determine whether a given finite set of gross Earth data can be used to specify an Earth structure uniquely except for fine-scale detail; and how to determine the shortest length scale which the given data can resolve at any particular depth. We apply the general theory to the linear problem of finding the depth-variation of a frequency-independent local Q from the observed quality factors Q of a finite number of normal modes. We also apply the theory to the non-linear problem of finding density vs depth from the total mass, moment, and normal-mode frequencies, in case the compressional and shear velocities are known.     

Forthcoming events

Abstract

This is the second of two papers which elaborates a framework for embedding urban models within GIS. In the first paper (Batty and Xie 1994), we outlined how the display functions of a proprietary GIS could be used to organize a series of external software modules which contained the central elements of the modelling process, namely dataset selection and analysis, and model specification, calibration, and prediction. In that paper, we dwelt on display and data analysis functions whereas here we outline the model-based functions of the system. We begin by reviewing residential location models based on population density theory, stating continuous and discrete model forms, and calibration methods. We then illustrate a pass through the software using data for the Buffalo urban region, showing how observed data and model estimates can be evaluated through graphic display. We present ways in which the system can be used to explore and fit a variety of models to different zoning systems and in so doing, show how subset selection and aggregation can be used to find models with good fit. Finally we draw conclusions and outline an agenda for further research.     

近50年来淮河流域极端降水的时空变化及统计特征(英文)

Based on the daily precipitation data of 27 meteorological stations from 1960 to 2009 in the Huaihe River Basin, spatio-temporal trend and statistical distribution of extreme precipitation events in this area are analyzed. Annual maximum series (AM) and peak over threshold series (POT) are selected to simulate the probability distribution of extreme precipitation. The results show that positive trend of annual maximum precipitation is detected at most of used stations, only a small number of stations are found to depict a negative trend during the past five decades, and none of the positive or negative trend is significant. The maximum precipitation event almost occurred in the flooding period during the 1960s and 1970s. By the L-moments method, the parameters of three extreme distributions, i.e., Generalized extreme value distribution (GEV), Generalized Pareto distribution (GP) and Gamma distribution are estimated. From the results of goodness of fit test and Kolmogorov-Smirnov (K-S) test, AM series can be better fitted by GEV model and POT series can be better fitted by GP model. By the comparison of the precipitation amounts under different return levels, it can be found that the values obtained from POT series are a little larger than the values from AM series, and they can better simulate the observed values in the Huaihe River Basin.     

Observation and modelling of fault-zone fracture seismic anisotropy – II. P-wave polarization anomalies

Summary. In Part I of this paper we modelled shear-wave splitting observed in crystalline rock bordering an active, normal fault-zone at Oroville, California, with Červený's ray-tracing system applied to anisotropic heterogeneous media using Hudson's formulation of elastic constants for a medium containing aligned cracks. In Part II we use the ray-tracing results of Part I to quantitatively interpret P -wave polarization anomalies observed in the three-component seismograms recorded in the Oroville fault zone. We show that the eigenvectors of the first-order Christoffel tensor defined by the ray-tracing slowness vector and Hudson's first-order anisotropic corrections to the isotropic elastic tensor correctly account for P -wave first motion that deviates from the ray vector.     

Frequency dependence of magnetic susceptibility for populations of single-domain grains

A recent paper (Dearing et al . 1996) on the use of frequency dependence of magnetic susceptibility (Xfd) in magnetic grain-size investigations of environmental materic has proposed a fundamentally new model for the magnetic susceptibility of single-domain (SD) grains measured at different frequencies, and is divergent from the no well-established theory of SD behaviour. This new model appears to be founded on a confusion about the behaviour of SD grains, as predicted by theory, and magnetic measurements of real materials, which naturally have a distribution of magnetic grain sizes. Here I try to clear up this confusion by showing how different log-normal distributions of magnetic grain sizes affect the frequency dependence of magnetic susceptibility measurement. This analysis highlights that the limiting maximum Xfd value of ˜ 15 per cent obtained for environmental materials can be explained simply as a constraint imposed by the magnetic grain-size distribution having a finite minimum width (˜1.0 on a natural log scale). There is no reason to suppose that if the grain-size dispersion was narrower higher Xfd values could not be observed. Furthermore, the Xfd value is non-unique and so cannot be used quantitatively to determine the amount or grain-size distribution of SD grains in a sample     

基于Copula函数的洞庭湖流域水沙丰枯遭遇频率分析

受人类活动的影响,水沙灾害事件相继发生,对人们的生产、生活造成了威胁。以洞庭湖流域代表性水文站的年径流量和年输沙量系列数据为基础,应用P-III型曲线分别拟合并求得“松滋口、太平口、藕池口”三口入湖、“湘江、资江、沅水、澧水”四水入湖和城陵矶站出湖年径流量、年输沙量的边缘分布函数,再采用水文事件遭遇分析中广泛应用的Copula函数,建立洞庭湖流域水沙联合分布模型,分析洞庭湖流域水沙丰枯遭遇频率。研究结果表明洞庭湖三口、四水和城陵矶站的水沙丰枯遭遇频率关系与洞庭湖流域的水沙运动有密切联系,运用该水沙耦合模型可以为洞庭湖流域防洪减灾提供重要的理论依据。     

Observed geomagnetic field intensity in London since 1820

Our main purpose is to collect all magnetic intensity data observed in the vicinity of London and to adjust these to a common site (Greenwich) to complement the 400-year series of declination ( D ) and inclination ( I ) data of Malin & Bullard (1981 ). The present series is necessarily shorter, since a method for the measurement of intensity in absolute units was not devised until 1832. We have also supplemented the D and I series of Malin & Bullard with recently acquired data.
We have also made observations of D , I and total intensity ( F ) at a number of the sites, partly to bring the series up to date and partly to check on the site differences. With the increasing urbanization of London it is necessary to seek data from remoter sites. It is shown that the site differences change significantly with time, but that allowance can be made for this.
We present curves of our best estimates of the variation of D , I , F and the horizontal intensity ( H ) that define the complete geomagnetic vector at Greenwich for the interval 1820–1998. Frequency analysis shows little support for a 60-year line in the power spectrum. Within the uncertainty of their determinations, there is good continuity between archaeomagnetic intensity measures and the present results. The moving eddy hypothesis of Malin & Bullard is found to be untenable.     

紫色土坡耕地水土流失试验分析

实地试验了影响水土流失的主要因子,应用通用土壤流失方程预报本地紫色土坡耕地在耕种情况下的水土流失量,经实测资料检验精度良好,说明确定的Ｒ、Ｋ、ＬＳ、Ｃ、Ｐ算法符合这类区域的具体条件。     

海南岛周边海域表层沉积物磁化率 空间分布特征及其物源指示意义

海洋表层沉积物的磁学性质逐渐被证明是分析海洋沉积物物源的有效手段之一。选取海南岛周边海域39个站位的表层沉积物进行了磁学特征研究。结果表明：海南岛周边海域表层沉积物的低频磁化率和频率磁化率具有明显的空间分异特征,表现为高值区主要出现在海南岛以南海域,而海南岛以东和以西海域则呈现从岸向海逐渐降低的趋势。磁化率的影响因素分析表明：研究区海洋表层沉积物的磁化率主要由陆源碎屑物质贡献,因此可以认为沉积物低频磁化率和频率磁化率的空间分布特征能指示陆源输入的变化。利用多个环境磁学参数对采样点进行Q型聚类,并结合低频磁化率和频率磁化率的空间分布特征及采样点的地理位置将研究区划分为4个区域：海南岛以东水深超过100 m的海域（Ⅰ区）沉积物主要来源于其东北面的珠江水系,同时粤西沿岸河流携带来的物质也有一定程度的影响;海南岛以东水深小于100 m和海南岛以南海域（Ⅱ区）沉积物可能主要来自于海南岛沿岸侵蚀搬运以及入海河流输入;北部湾北部海域（Ⅲ区）沉积物受琼州海峡和北部湾沿岸河流输入物质的共同影响;海南岛以西海域（Ⅳ区）沉积物受来自海南岛西南侧河流输入、沿岸侵蚀物和由南向北的洋流所携带的沉积物的共同影响。研究表明：低频磁化率和频率磁化率组合可有效指示近岸表层沉积物的物源变化。     

Automatic mapping of lunar landforms using DEM-derived geomorphometric parameters

Developing approaches to automate the analysis of the massive amounts of data sent back from the Moon will generate significant benefits for the field of lunar geomorphology. In this paper, we outline an automated method for mapping lunar landforms that is based on digital terrain analysis. An iterative self-organizing (ISO) cluster unsupervised classification enables the automatic mapping of landforms via a series of input raster bands that utilize six geomorphometric parameters. These parameters divide landforms into a number of spatially extended, topographically homogeneous segments that exhibit similar terrain attributes and neighborhood properties. To illustrate the applicability of our approach, we apply it to three representative test sites on the Moon, automatically presenting our results as a thematic landform map. We also quantitatively evaluated this approach using a series of confusion matrices, achieving overall accuracies as high as 83.34% and Kappa coefficients (K) as high as 0.77. An immediate version of our algorithm can also be applied for automatically mapping large-scale lunar landforms and for the quantitative comparison of lunar surface morphologies.     

基于DEM和地貌计量的月球形貌类型自动制图（英文）

Developing approaches to automate the analysis of the massive amounts of data sent back from the Moon will generate significant benefits for the field of lunar geomorphology.In this paper,we outline an automated method for mapping lunar landforms that is based on digital terrain analysis.An iterative self-organizing(ISO)cluster unsupervised classification enables the automatic mapping of landforms via a series of input raster bands that utilize six geomorphometric parameters.These parameters divide landforms into a number of spatially extended,topographically homogeneous segments that exhibit similar terrain attributes and neighborhood properties.To illustrate the applicability of our approach,we apply it to three representative test sites on the Moon,automatically presenting our results as a thematic landform map.We also quantitatively evaluated this approach using a series of confusion matrices,achieving overall accuracies as high as 83.34% and Kappa coefficients(K)as high as 0.77.An immediate version of our algorithm can also be applied for automatically mapping large-scale lunar landforms and for the quantitative comparison of lunar surface morphologies.     

Place matters in sports: effects of the length of championship series on winning probabilities for the team with home field advantage

In this paper, I address the question of how the length of championship series between two teams can affect the probability that a team wins the series. The geographical element of the question enters through consideration of ‘home-field advantage’. This refers to the fact that in championship series, one of the teams has the benefit of one additional game that is scheduled to be played at home. This, coupled with the fact that teams typically have a higher likelihood of winning at home, leads to an interesting and surprisingly complex relationship between the length of a series and the probability of winning that series. Conclusions include the facts that (1) when the team with home-field advantage has a relatively small probability of winning away from home, it will fare relatively better in shorter series, and (2) the probability of winning a series can first become lower, but then become higher, as one progresses from 1-game series to 3-, 5- and 7-game series.     

Could the energy near the FCN and the FICN be explained by luni-solar or atmospheric forcing?

The observed time-series of precession/nutation show residuals with respect to an empirical model based on the rigid Earth theoretical nutations and a frequency dependent transfer function with resonances to the Earth's normal modes. These residuals display energy mainly in the frequency domain around 430 and 500 days in the inertial frame. In this frequency band, the energy is possibly related to two normalmode frequencies: the free core nutation (FCN) and the free inner core nutation (FICN). In this paper, we examine the possibility of obtaining this energy from the resonance effect induced by a luni-solar (or planetary) forcing, or by an atmospheric forcing at a frequency very close to these Earth free nutations. The amplification factor due to the resonance is computed from an analytical formula expressed in the case of a simplified three-layer ellipsoidal rotating earth (with an elastic inner core, a liquid outer core and an elastic mantle), as well as the empirical formula based on the analysis of VLBI observations. For the tidal forcing, the theoretical results do not show any resonance at the level of precision we have examined but it is still possible to find one frequency near the FCN or FICN frequencies which could be excited. In contrast, for the atmospheric pressure the level of energy needed could be obtained from the diurnal pressure, depending on the noise level of the Earth's global pressure. We also show that the combination of three waves can explain the observed decrease of energy with time. While the tidal potential amplitudes are too small, a pressure noise level of 0.5 Pa would be sufficient to excite these waves.     

Methodologies for estimating t*(f) from short-period body waves and regional variations of t*(f) in the United States

Summary. In this paper we discuss some aspects of estimating t * from short-period body waves and present some limits on t* (f) models for the central and south-western United States (CUS and SWUS). We find that for short-period data, with frequencies above 1 or 2 Hz, while the average spectral shape is stable, the smaller details of the spectra are not; thus, only an average t *, and not a frequency-dependent t *, can be derived from such information. Also, amplitudes are extremely variable for short-period data, and thus a great deal of data from many stations and azimuths must be used when amplitudes are included in attenuation studies.
The predictions of three pairs of models for t* (f) in the central and south-western United States are compared with time domain observations of amplitudes and waveforms and frequency domain observations of spectral slopes to put bounds on the attenuation under the different parts of the country. A model with the t * values of the CUS and SWUS converging at low frequencies and differing slightly at high frequencies matches the spectral domain characteristics, but not the time domain amplitudes and waveforms of short-period body waves. A model with t * curves converging at low frequencies, but diverging strongly at high frequencies, matches the time domain observations, but not the spectral shapes. A model with nearly-parallel t* (f) curves for the central and south-western United States satisfies both the time and frequency domain observations.
We conclude that use of both time and frequency domain information is essential in determining t* (f) models. For the central and south-western United States, a model with nearly-parallel t* (f) curves, where Δ t *∼ 0.2 s, satisfies both kinds of data in the 0.3–2 Hz frequency range.     

Sampling efficiency of vertical array aeolian sand traps

Previous investigations have indicated that the sampling efficiency of aeolian sand traps is low and varies greatly in the near-bed region. Outside this region, the efficiency tends to be consistently higher for all types of trap. An evaluation was carried out to compare the sampling efficiency of different types of aeolian sand trap based on the comparison of the “actual” and the measured sand mass flux profiles, with emphasis on the single-tube vertical array trap, conventional array trap, and step-like array trap. A simple formula is proposed to express the actual vertical profile of sand mass flux, which has been validated with the unique data obtained with an isokinetic trap by [Sedimentology 45 (1998) 789]. Using the experimental data collected by the present authors and those by other investigators, sampling efficiencies of three types of trap are examined in terms of the frequency distribution of all the samples. For the single-tube traps, the sampling efficiency varies from 65% to 95%, with a mode at 75%. For both the conventional array and step-like array traps, sampling efficiencies range from 15% to 85%, with the modal frequencies at 35% and 75%, respectively. This review seems to suggest that the peak frequency with higher sampling efficiency coincides with the maximum sand-grain Reynolds number.     

Joint Inversion of Geophysical Data

Summary. By jointly inverting several different kinds of geophysical measurements at a site we avoid some of the ambiguity inherent in the individual methods. We show how this can be done for the combination of DC resistivity and magnetotelluric measurements on a layered medium by considering a simple 3-layer model. The combination resolves the resistivity of the thin resistive second layer, even though neither of the two methods can do so alone.
The method is then applied to field data from a shallow sedimentary basin. A blind zone occurs beneath a thick near-surface conductive shale. By a study of the eigenvalue structure of the model it can be seen that resolution in this zone would be slightly enhanced by higher frequency magnetotelluric data, but additional DC data at larger spacing would yield no improvement.