Computation of Ray Integrals and Ray Amplitudes in Radially Symmetric Media

A new approximation of the velocity-depth distribution in radially symmetric media is suggested. This approximation guarantees the continuity of velocity and its first and second derivatives, and does not generate false low-velocity layers. It removes false anomalies from the amplitude-distance curve and considerably increases its stability. The evaluation of ray integrals and ray amplitudes using this velocity-depth approximation does not require the computation of any transcendental function and is, therefore, very fast. Numerical examples are presented.     

Computation of ray integrals and ray amplitudes in radially symmetric media

Summary A new approximation of the velocity-depth distribution in radially symmetric media is suggested. This approximation guarantees the continuity of velocity and its first and second derivatives, and does not generate false low-velocity layers. It removes false anomalies from the amplitude-distance curve and considerably increases its stability. The evaluation of ray integrals and ray amplitudes using this velocity-depth approximation does not require the computation of any transcendental function and is, therefore, very fast. Numerical examples are presented.     

A new approximation of the velocity-depth distribution and its application to the computation of seismic wave fields

Summary A new approximation of the velocity-depth distribution in a vertically inhomogeneous medium is suggested. This approximation guarantees the continuity of velocity and of its first and second derivatives and does not generate false low-velocity zones. It is very suitable for the computations of seismic wave fields in vertically inhomogeneous media by ray methods and its modifications, as it removes many false anomalies from the travel-time and amplitude-distance curves of seismic body waves. The ray integrals can be evaluated in a closed form; the resulting formulae for rays, travel times and geometrical spreading are very simple. They do not contain any transcendental functions (such asln (x) orsin ^–1, (x)) like other approximations; only the evaluation of one square root and of certain simple arithmetic expressions for each layer is required. From a computational point of view, the evaluation of ray integrals and of geometrical spreading is only slightly slower than for a system of homogeneous parallel layers and even faster than for a piece-wise linear approximation.     

Modellseismische Untersuchungen an 2- und 3-dimensionalen Testmodellen,Teil 1

Summary Following the recommendation of the European Seismological Commission (Copenhagen 1966) to carry out comparative measurements on simple seismic models with a prescribed velocity-depth distribution (test models), an attempt was made to compare results obtained with different model techniques. In the present paper, model investigations with the first two proposed test models carried out by 2- and 3-dimensional model techniques are described. Seismogrammes, travel-time curves and amplitude-distance curves of the models investigated are given. A quantitative comparison of the results shows a satisfactory agreement.     

Interference amplitude curves of short period PKP waves

Summary Theoretical short-period amplitude-distance curves of PKP waves are calculated in the range of distances corresponding to the interference zone of the different branches of this waves. The combination of the zero-order approximation of the ray method and the Gaussian beam approach are used for the calculation. The calculated amplitudes are compared with the observed ones. A relatively good coincidence between the theoretical and observational curves has been found.     

Amplitude curves ofP waves for the region of central Asia

Summary The amplitude-distance curves of P waves, valid for the region of Central Asia, were derived in the distance range between 13° and 36° using observations of a network of eight Caucasian seismic stations. The curves are characterized by an anomalous increase of amplitudes between 13° and 20° followed by a large decrease of amplitudes in the distance range between 20° and 35°. Both the increase and decrease of amplitudes are interrupted by several local maxima. A comparison of the present amplitude curves with those derived for the regions of South-Eastern Europe and Asia Minor enabled us to correlate the individual local maxima of amplitude curves and to investigate the variation of their position due to the lateral inhomogeneity of the upper mantle structure in Eurasia.A. Tskhakaya deceased in 1970.     

Exact Solutions for Spine Reconnective Magnetic Annihilation

Solutions for spine reconnective annihilation are presented which satisfy exactly the three-dimensional equations of steady-state resistive incompressible magnetohydrodynamics (MHD). The magnetic flux function ( A ) and stream function have the form $$A = A_{0}(R) \sin \phi + A_{1}(R)z, \qquad \Psi = \Psi _{0}(R) \sin \phi + \Psi _{1}(R)z,$$ in terms of cylindrical polar coordinates ( R , { , z ). First of all, two non-linear fourth-order equations for A 1 and 1 are solved by the method of matched asymptotic expansions when the magnetic Reynolds number is much larger than unity. The solution, for which a composite asymptotic expansion is given in closed form, possesses a weak boundary layer near the spine ( R = 0). These solutions are used to solve the remaining two equations for A 0 and 0 . Physically, the magnetic field is advected across the fan separatrix surface and diffuses across the spine curve. Different members of a family of solutions are determined by values of a free parameter n and the components ( B Re , B ze ) and ( v Re , v ze ) of the magnetic field and plasma velocity at a fixed external point ( R , { , z ) = (1, ~ /2,0), say.     

ON THE SIGNIFICANCE OF AMPLITUDE STUDIES IN SHALLOW REFRACTION SEISMICS*

An analysis of amplitudes of refraction records of some shallow refraction profiles shot primarily for detailing the near-surface structure in a granitic terrain has yielded information on refractor properties: reduced amplitudes are plotted on amplitude-distance graphs. The negative power n to which distance should be raised to represent (elastic) amplitude decay with respect to distance due to spreading of the critically refracted wave involved is examined. Computed values of this “spreading index”n are close to n = 2 as predicted by the theory. With this value of n, amplitude data are processed to determine residual attenuation attributable to elastic absorption in the bedrock. A graphical approach for this purpose from comparison of amplitude-distance graphs with the plots of amplitude decay due to spreading which is applicable to flat and horizontal refractor situations is suggested. Assuming residual attenuation to represent absorption in the granite bedrock, the computed coefficients of absorption, which vary from 0.5 to 3.90 km^?1 for a frequency of 50 Hz, are obtained. From amplitude graphs of reversed profiles it is shown that the amplitude differences plot bears a relation to lateral velocity changes in the refractor. From comparison of practical amplitude decay graphs with those computed for different subsurface models, it appears possible to detect fractured rock occurrences in the refractor.     

A modelling approach to assessing variations of total suspended solids (tss) mass fluxes during storm events

Connections between the catchment hydrology and accumulation, washoff and transport of pollutants in wet weather greatly affect the management of urban drainage and its wet‐weather effluents. In recent years, the concept of the first flush has gained on prominence and was further developed for analyzing the interaction between the hydrology and transport of runoff pollutants. One of the most important definitions of the first flush can be derived from the analysis of the m(v) curves (i.e. the curves in which the normalized cumulative pollutant mass is plotted vs the normalized cumulative runoff volume). Indeed the m(v) curves, indicating the distribution of pollutant mass versus volume in wet‐weather flow (WWF) discharges, are commonly used for comparing pollutant discharges for different rainfall events and catchments. In this study, the m(v) curves were used to define the concepts of flow‐limited and mass‐limited WWF events. These two different behaviours have been analysed for rainfall/runoff events observed in the urbanized part of the Liguori catchment in Cosenza (Italy). In order to advance the understanding of the intra‐event variability of m(v) curves, the mathematical rainfall/runoff model Storm Water Management Model of the US Environmental Protection Agency (SWMM) was calibrated for eight observed rainfall/runoff events and the differences between observed and simulated m(v) curves were analysed. The results showed a good correlation between the observed and simulated m(v) curves, and this finding offers further benefits in SWMM model calibration. Copyright © 2013 John Wiley & Sons, Ltd.     

二度体重、磁异常频谱与三度体重、磁异常频谱关系的理论问题

设F（x-ξ,y,z,η,ζ,α,…）为一在x方向无限薄的层的异常,若物体的异常可表示为: T（x,y）=integral from n=a to （a+2c）（F（x-ξ,y,z,η,ζ,α,…））dξ T（y）=integral from n=-∞ to ∞（F（x-ξ,y,z,η,ζ,α,…））dξ 则有 式中T（v）和T（u,v）分别为T（y）和T（x,y）的频谱,2c是物体在x方向的宽度,（x,y,z）和（ξ,η,ζ）分别为观测点和物体上任一点的坐标。 如果2c=dξ,则物体即为薄层本身;如果2c=dξ,薄层的面积无限缩小,则物体即为一质点;如果2c=dξ,薄层只有长度而无宽度,则物体即为一曲线。 对于形状复杂的物体,可以将物体分成若干简单而又符合所述条件的物体元,而有式中2c_m为第m个物体元在x方向的宽度,T_m（v）为第m个物体元当其沿x方向的长度为无限长时的异常的频谱。     

Propagation of Rayleigh waves in an axially symmetric heterogeneous layer lying between two homogeneous halfspaces

Summary The propagation of Rayleigh type waves in an axially symmetric inhomogeneous layer lying between two halfspaces is studied. The halfspaces are supposed to be identical in their elastic properties. The variation of the parameters in the layer is assumed to be of the form where is a constant andz is the distance measured from one interface into the layer. With this assumption, the vector wave equation for the layer is separable. The solution is obtained in terms ofWhittaker's functions and the frequency equation of Rayleigh type waves is derived.     

重、磁场三维傅里叶变换的若干问题

本文利用极限变换的概念,推导了质点的重力位及偶极子的磁位的三维傅里叶变换。在这个基础上,推导了任意形状物体的重、磁场的三维傅里叶变换的一般表达式。根据这些式子,讨论了文[1]中由三维谱求二维谱存在的问题,即对三维谱而言,不存在u²+v²+w²=0。     

关于非均匀介质中电导率按深度变化时的势及其视电阻率函数

本文共分六部分内容。在前言中,简述了电测深方面有关研究的情况,尤其叙述了E.S.Sampaio（1976）的结果。 因本文采用的方法不同,从而求解了适合要求的微分方程定解问题,获得了电导率以 （其中α、σ₀、σ₁均为正实数,β为实数）按深度变化时势的分布。 其次,当β=0时,对电导率σ=（σ₀+σ₁z）^α按深度变化时势的分布,应用Bessel函数的积分表达时,明显地改进和推广了E.S.Sampaio（1976）结果中的重要部分。 最后,结合实际作出了第一类、第二类标准化视电阻率函数。这种视电阻率函数,推广了Wenner和Schlumberger分别作出的视电阻率函数的有关部分,对电阻率法和激发极化法,都有其理论价值和实际意义。     

Amplitudes of core waves recorded in Macedonia

Summary The amplitude-distance function of the short period PKP waves, recorded at Macedonian seismological stations from sources in the SW Pacific Ocean, is investigated. The dependences found for sources with depths under 100 km and for sources with depths over 500 km are compared with the results of some other authors.     

The fractal geometry of interfaces and the multifractal distribution of dissipation in fully turbulent flows

We describe scalar interfaces in turbulent flowsvia elementary notions from fractal geometry. It is shown by measurement that these interfaces possess a fractal dimension of 2.35±0.05 in a variety of flows, and it is demonstrated that the uniqueness of this number is a consequence of the physical principle of Reynolds number similarity. Also, the spatial distribution of scalar and energy dissipation in physical space is shown to be multifractal. We compare thef() curves obtained from one- and two-dimensional cuts in several flows, and examine their value in describing features of turbulence in the three-dimensional physical space.     

地脉动在系舟山北麓断裂次级断裂探测中的应用

系舟山北麓断裂为1038年定襄■级地震的发震构造，在盆地内部可能存在一条或多条次级断裂，并有可能非常邻近忻州城区，使用地脉动方法对系舟山北麓断裂是否存在次级隐伏断裂进行探测。通过共振频率的横向变化以及基岩深度和频率的关系获得了约17个比较显著的断点位置，指示出系舟山山前存在三条比较显著的次级断裂，以及它们的断点位置、相对错距和相应的走向分布，为忻州市区防震减灾提供基础资料。     

基于MDT测试资料的储层油水界面自动提取方法研究

通过对MDT地层压力数据以及地层压力梯度线形态的分析,提出了利用三次样条插值函数将有限个数据点的地层压力梯度线进行深度等间距采样,以得到连续分布的地层压力梯度线.在抛物线形式的地层压力梯度线上,油水界面对应于该抛物线的顶点.根据最大值原理可以在地层压力梯度线上提取油藏油水界面深度,利用Fortran语言编制了相应的计算机程序,实现了油藏油水界面自动提取的目的.利用该程序可以减小油田现场处理过程中带入的额外误差,节省操作人员的处理时间,减少工作量.实际应用表明,该方法是可靠的,计算结果完全符合油田储量计算的误差标准,利用其获取的结果真实有效.     

On conditions for the unique inversion of seismic travel-time curves

It is shown that when the travel-time curve of a refracted wave from a surface source is known and at least one of the following conditions is satisfied, i.e. when

1. the travel-time curve of a wave reflected from a horizontal interface lying below the deepest low velocity layer is known, or
2. the travel-time curve of a wave from a deep source situated below the deepest low velocity layer is known, or
3. the measureH(u)=mes {z∶z≥0,v ^?1 (z)≥u} is analytical in some segment [c, d], where \(0< c< d< \infty , c< a_n , H(a_n ) = \bar z_n ,\bar z_n\) is the depth of the lower end of the deepest low velocity layer and in the interval [c, ∞) an analytical functionH(u)) exists which providesH(u)≡H(u)) ifu∈[c, d], then (1) velocityv(z) outside the low velocity layers and (2) the measureH _k (u)=mes {z∶z∈L _k,v ^?1 (z)≥u} for each low velocity layerL _k,k=1, 2, ..., n, are defined unambiguously.

     

Elektronenproduktion,Rekombination, Elektronendichte und Absorption in der ionosphärischenD-Region und ihre jahreszeitlichen Variationen

Zusammenfassung Es wird die Gleichung für die Elektronenproduktionq(z) abgeleitet, die die meteorologischen Elemente der Mesosphäre berücksichtigt. Nach Angaben über die mit Satelliten und Raketen gemessene Röntgenstrahlung mit 8 Å wird das Differentialspektrum des ionisierenden Energieflusses für eine mittlere Sonnenaktivität konstruiert. Auf dieser Grundlage und nach der bekannten Intensität der Strahlung Ly- sowie nach Angaben über dieElektronenproduktion der kosmischen Strahlung werden die Profileq _Rö(z),q _Ly-(z) undq _CR(z) für mittlere geographische Breiten und Standardatmosphäre entwickelt. Nach eingehender Analyse der vollständigen Gleichung für den effektiven Rekombinationskoeffizienten wird für die Verhältnisse in der tiefen Ionosphäre der Beitrag jeder einzelnen Komponente der Gleichung bestimmt. ist eine recht veränderliche Grösse, die von den aeronomischen und meteorologischen Verhältnissen und der Sonnenzenitdistanz abhängt. Aus den fürq(z) und (z) erhaltenen Angaben werden zwei ElektronendichteprofileN(z) für =30° und 75° erhalten. Das ProfilN(z) bei =30° wird mit dem gemittelten Profil einer umfangreichen Gruppe experimentell gefundener VerteilungenN(z) verglichen; das Profil bei =75° wird durch Messung der deviativen und nondeviativen Absorption für eine längere Zeitperiode überprüft. In beiden Fällen hat sich die Richtigkeit der theoretisch erhaltenen Profile bestätigt. Die jahreszeitlichen Variationen der nondeviativen Absorption in derD-Region sind ausschliesslich durch die Variationen der meteorologischen Parameter im Bereich der Mesopause bei konstantem Energiefluss der ionisierenden Strahlung bedingt.

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Summary An equation about the electron production is deduced in which the meteorological elements of the mesosphere are taken into account. The differential spectrum of the ionizing energy flux with 3 Å for average solar activity is constructed on evidence from rocket and satelitc measurements. The profilesq _Rö(z),q _Ly-(z) andq _CR(z) for mean geographical latitudes and standard atmosphere are plotted on that basis as well as on data fot the known intensity of the Ly- emission and the electron production of the cosmic rays. An exhaustive analysis is made of the full equation for the effective recombination coefficient and the contribution of all its components at lower ionosphere conditions is determined. is a rather variable quantity, dependent on the aeronomical and meteorological condition of the area under consideration, as well as on the solar zenith angle. Two profiles for the electron concentrationN(z) at =30° and 75° are drawn on the basis of data forq(z) and (z). The profileN(z) at =30° is compared with the averaged profile of a large group experimentally obtained distributionsN(z); the profile at =75° is checked by measurements of the deviative and nondeviative absorption taken for a lengthy period. Both checks are in good agreement with the theoretically obtained profiles. The seasonal variations of the nondeviative absorption in theD region could be completely explained with the variations of the meteorological parameters in the mesopause area at constant energy flux of the ionizing radiation.

     

Bayesian estimation of intensity–duration–frequency curves and of the return period associated to a given rainfall event

Intensity–duration–frequency (IDF) curves are used extensively in engineering to assess the return periods of rainfall events and often steer decisions in urban water structures such as sewers, pipes and retention basins. In the province of Québec, precipitation time series are often short, leading to a considerable uncertainty on the parameters of the probabilistic distributions describing rainfall intensity. In this paper, we apply Bayesian analysis to the estimation of IDF curves. The results show the extent of uncertainties in IDF curves and the ensuing risk of their misinterpretation. This uncertainty is even more problematic when IDF curves are used to estimate the return period of a given event. Indeed, standard methods provide overly large return period estimates, leading to a false sense of security. Comparison of the Bayesian and classical approaches is made using different prior assumptions for the return period and different estimation methods. A new prior distribution is also proposed based on subjective appraisal by witnesses of the extreme character of the event.