A frequency criterion for optimal node selection in smoothing with cubic splines

When smoothing a function with high‐frequency noise by means of optimal cubic splines, it is often not clear how to choose the number of nodes. The more nodes are used, the closer the smoothed function will follow the noisy one. In this work, we show that more nodes mean a better approximation of Fourier coefficients for higher frequencies. Thus, the number of nodes can be determined by specifying a frequency up to which all Fourier coefficients must be preserved and increasing the number of nodes until this criterion is met. A comparison of the corresponding smoothing results with those obtained by filtering using moving average and moving median filters of corresponding length and a low pass with corresponding high‐cut frequency shows that optimal cubic splines yield better results as they preserve not only the desired low‐frequency band but also important high‐frequency characteristics.     

逐步逼近曲化平方法研究

位场资料的常规处理解释方法是建立在平面数据理论之上的,然而实际的位场数据大多为曲面数据,若把曲面数据当成平面数据进行处理,必然导致很大的误差,因此有必要进行“曲化平”处理. 曲化平目前存在的主要问题是计算精度低、计算量大,因此,研究快速、精度高且适合大数据量处理的曲化平方法具有重要的价值. 本文在已有的泰勒级数曲化平方法基础上提出了逐步逼近技术和平均平面技术,使得曲面位场资料处理的精度得到了很大提高. 最后通过理论模型和实际资料的处理验证了该方法的应用效果.     

空间光滑地震活动性模型中光滑函数的比较研究

使用Frankel提出的基于空间光滑地震活动性模型的地震危险性分析方法,选择华南、华北、川滇3个地区的地震记录,比较分析了高斯、幂律和地震分形分布光滑函数3种光滑函数在不同地区的适用性．结果表明,使用交叉验证法可以为高斯光滑函数选取合适的相关距离c值,光滑得到的地震活动性模型能够真实反映研究区域的地震活动特征,根据活动性模型计算得出的峰值加速度(PGA)分布也符合人们对研究区域地震危险性的认识．幂律光滑函数适用于地震活动性较强的地区,且具有容易求取光滑参数的优点．光滑程度较低的幂律光滑函数不适用于地震活动性弱的地区,在该类地区应选择光滑程度较高的高斯光滑函数．地震分形分布光滑函数不适用于地震活动较强且地震活动强度差异较大的地区,其容易过分高估高震级地震对地震危险性的影响,而忽略了低震级地震对地震危险性的贡献．但对于地震活动较弱且地震活动强度差异较小的地区,可使用地震分形分布光滑函数,且同样具有容易求取光滑参数的优点．     

用径向基函数神经网络方法预报太阳黑子数平滑月均值

简单介绍了径向基函数神经网络方法的原理和应用,发展了用径向基函数（RBF）对平滑月平均黑子数进行预报的方法. 用不同的数据序列对网络进行训练,对未来8个月的平滑月平均黑子数进行预报. 用该方法对第23周开始后的平滑月平均黑子数进行逐月预报,并与实测值进行比较,结果表明随着预报实效的延长预报误差被逐渐放大,该方法可以较准确地做出未来４个月的预报,绝对误差可以控制在20以内,标准差为4.8,相对误差控制在38％以内,大部分相对误差不超过15%（占总预报数的89％）,具有较好的应用价值. 用于网络训练的样本数量对预报结果会产生一定的影响.     

Spatially smoothed seismicity modeling of seismic hazard in Slovenia

A progress report on the mapping effort for construction of a peak ground acceleration (PGA) map of Slovenia for 475-year return period for rock and firm soil is presented. The methodology is similar to that recently applied in Central and Eastern United States. It is based on historical seismicity spatially smoothed to different length scales. The procedure is described by Frankel (1995). He uses the characteristic earthquake recurrence relationship and in his firt version four different seismicity models. We also use four seismicity models. But instead of characteristic earthquake recurrence, we use the doubly truncated exponential magnitude-frequency relationship; no evidence of characteristic earthquakes in Slovenia has been found yet. Three of our models are similar to Frankel's first three models. Model 1 uses spatially smoothed activity rate based on magnitude 3.7 and above events since 1880. Model 2 deals with spatially smoothed activity rate based on magnitude 5.0 abd above events since 1690. Model 3 smoothes the observed activity over the entire region; it represents a uniform seismicity zone. Frankel skipped this model in his latest version (Frankel et al. 1996). In model 4, we introduce a new approach of calculating seismic activity rate taking into account released seismic energy. The ground motion attenuation model of Pugliese and Sabetta (1989) is used for all models. PGA maps for models 1, 2, 3 and 4 have been calculated, and a weighted mean map derived from them. A map of model 1 has been compared with the corresponding source zone map; the two maps do not differ significantly. A worst-case map derived from all four models has also been produced.     

Synthetic seismograms in heterogeneous media by one-return approximation

When reverberations between heterogeneities or resonance scattering can be neglected but accumulated effects of forward scattering are strong, the Born approximation is not valid but the De Wolf approximation can be applied in such cases. In this paper, renormalized MFSB (multiple-forescattering single-backscattering) equations and the dual-domain expression for scalar, acoustic and elastic waves are derived by a unified approach. Two versions of the one-return method (using MFSB approximation) are given: One is the wide-angle dual-domain formulation (thin-slab approximation); the other is the screen approximation. In the screen approximation, which involves a small-angle approximation for the wave-medium interaction, it can be seen clearly that the forward scattered, or transmitted waves are mainly controlled by velocity perturbations; while the backscattered or reflected waves, by impedance perturbations. The validity of the method and the wide-angle capability of the dual-domain implementation are demonstrated by numerical examples. Reflection coefficients of a plane interface derived from numerical simulations by the wide-angle method match the theoretical curves well up to critical angles. For the reflections of a low-velocity slab, the agreement between theory and synthetics only starts to deteriorate for angles greater than 70°. The accuracy of the wide-angle version of the method could be further improved by optimizing the wave-number filtering for the forward propagation and shrinking the step length along the propagation direction.     

Experimental study of the effect of roughness and Reynolds number on fluid flow in rough‐walled single fractures: a check of local cubic law

Local cubic law (LCL) is one of the most commonly applied physical laws for flow in single fractures (SF) and fractured media. The foundation of LCL is Darcian flow. This experimental study examines if LCL is valid for flow in a single rough fracture and how the fracture roughness and Reynolds number (Re) affect flow. Similar to the Moody diagram for flow in pipes, a diagram for flow in a single rough fracture has been generated to relate the friction coefficient with Re and the roughness. Under the experimental condition of this study, flow appears to be substantially different from Darcian flow. The flow law of q ∝ eⁿJ^m appears to be valid for describing the flow scheme where q, e, and J are the unit width flux, the average aperture, and the hydraulic gradient. The value of the power index m is found to be around 0·83 ～ 0·98, less than what has been used in Darcian flow (m = 1). The power index n is around 11·2 and 13·0, much greater than the n value used in the LCL (n = 3), and it increases with the average velocity. The Moody type of diagram shows that the friction factor for flow in SFs is influenced by Re and the roughness. It decreases with Re when Re is small, and becomes less sensitive to Re when Re is large enough. It also increases with the roughness. Copyright © 2010 John Wiley & Sons, Ltd.     

Changes in flood regime by use of the modified curve number method

Abstract

This paper describes the use of a simple two stage rainfall-runoff model in which a curve number (CN) principle is used to calculate the soil water content and, subsequently, the rainfall contribution to direct runoff and groundwater flow. The maximum soil water retention, S, is used to express various characteristics of a catchment (infiltration rate, soil cover and land use, as in the CN method) relevant to flood formation. Using historical flood events, the model is calibrated, and the statistical distribution parameters of peak flows determined. With the same historical input data scenarios (rainfall), sets of flood hydrographs are simulated for various values of the parameter S, and corresponding distribution parameters of peak flows are determined. This procedure is used to demonstrate possible changes in flood regime to be expected due to changes of the catchment soil properties and its vegetation cover. A case study is presented for the River Hron catchment, area 582 km², in the mountainous region of central Slovakia.     

Reduction of vibration by control forces

The concept of reducing vibrations in steady-state problems by introducing appropriately chosen additional or control forces, which have the same frequency and phase as the original excitation forces, has been the subject of some recent papers. In this paper the normal mode method is used to determine the magnitudes of the control forces. This method is simpler in concept than earlier approaches. It is demonstrated that with a single control force resonant response of multi-degree-of-freedom systems can be reduced substantially, particularly for the fundamental resonance in lightly and moderately damped systems.     

Reduction in ground vibrations by using shaped landscapes

Reduction in traffic-induced ground vibrations by the use of shaped landscapes is investigated here by shaping the landscape surrounding a high-tech facility, using the landscape thus produced as a wave obstacle. The effects of the geometric parameters of a shaped landscape were examined in parametric studies. An architectural landscape design was also investigated in terms of its effectiveness in reducing traffic-induced ground vibrations. Finite element models, analysed in the frequency domain, were employed. The models involve a layer of soil and the underlying bedrock. It was found that anywhere from an appreciable reduction to an appreciable amplification of the vibrations produced can occur, depending upon the geometric parameters of the shaped landscape involved. The most effective shape was found for a topography that acted as a waveguide that reduced the level of vibration by approximately 35%.     

Validity of the long-wave approximation in periodically layered media

In seismic modelling, a stack of thin layers is often replaced by an effective equivalent anisotropic homogeneous slab. For waves with finite wavelength, this is an approximation, and the error thus introduced can be quantified by considering the relative error in the phase velocity between the layer stack and the effective medium. For periodic layering, the relative phase-velocity error can be expressed in closed form as a function of wavelength, reflection coefficients and layer thicknesses. By comparing the relative phase-velocity error with laboratory measurements and numerical simulations, we find that the difference in seismic response between a periodic layer stack and an equivalent effective medium depends not only on wavelength, but it also depends significantly on reflection coefficients and the ratio between layer thicknesses. For a 1% relative error in the phase velocity, and if all layers have the same thickness measured in vertical traveltime, we find that the wavelength must be larger than approximately three times the layer period for a reflection coefficient of 0.1, but this increases to 13 times the layer period for a reflection coefficient of 0.9, which is highly unrealistic in a geological setting.     

防震减灾法制代表团赴加拿大考察

20 0 2年 1 1月 2 0日～ 1 2月 3日 ,由中国地震局和全国人大教科文卫委员会、国务院法制办公室联合组团一行 8人 ,赴加拿大进行了防震减灾法制建设考察。在加期间 ,代表团先后访问了加拿大自然资源部地质调查局太平洋地球科学中心、碑诗省紧急应变中心、加拿大地质调查所、加拿大基础设施保护与紧急应变办公室和加拿大国家研究院建筑研究所 ,对加拿大地震监测台网建设与管理、地震灾害防御和地震灾害救援制度、地震标准化建设等方面进行了深入的了解和交流。加拿大自 2 0世纪 70年代开始进行地震台的数字化建设 ,目前已经建成由 2 8个主干…     

Motions at core surface in the geostrophic approximation

Motions at the top of the core which generate the observed Secular Variation (S.V.) field are computed. To reduce the well known ambiguity of the solution, two constraints are added: the flow is a large scale one and is geostrophic. The computed flow then has a very simple geometry; its poloïdal part is roughly axisymmetrical with respect to an equatorial diameter. This geometry is almost unchanged from 1970 to 1980 while the intensity of the velocity is nearly doubled.     

Crustal structure in the Mizuho Plateau, East Antarctica, by a two-dimensional ray approximation

Studies on the crustal and upper-mantle structure in Antarctica have been one of the major contributions to Antarctic research since the International Geophysical Year of 1957–1958. Many refraction surveys with small charge size have been conducted in Antarctica, but long-range experiments were also made in 5 regions on the margin of the Antarctic continent.In 1979–1981, the scientific program of the Japanese Antarctic Research Expedition was focused on the earth sciences, and in particular, an explosion seismic experiment along a long survey line was the major item during these years. An experiment along a 300 km-long line with three shots and 27 observation stations was successfully made in the northern Mizuho Plateau, East Antarctica.From the analysis of travel times and the amplitude study of synthetic seismograms, the crustal structure of the northern Mizuho Plateau was determined. The depths of the Conrad and the Moho discontinuties were determined as 31 km and 42 km, respectively. The P-wave velocity and depth relation was determined as 6.0 km/s on the surface of the bedrock, 6.3 km/s at a depth of 2 km, 6.8 km/s at the Conrad and 7.9 km/s at the Moho. The velocity in the crust increases gradually. The crustal structure obtained is representative of East Antarctica.     

与特征断层结合的地震活动空间光滑模型在衡水市活断层地震危险性评价中的应用

在衡水市活断层地震危险性评价中,应用研究区域的地震活动性数据建立恰当的分布式地震活动性空间光滑模型,并结合断层对周边地震危险性的影响,计算前磨头断裂和衡水断裂在不同超越概率下上限震级分别为6.5、6.0级的区域基岩峰值加速度。研究发现,研究区域内50年超越概率为63%的基岩峰值加速度略有增加;50年超越概率为10%、5%的基岩峰值加速度在断层附近有所增加。研究表明在较低超越概率的情况下,断层周围如深州市、冀州市和衡水市辖区的地震危险性大于其他地区;利用仪器记录资料得到的地震活动性模型并结合断层资料计算出的地震危险性结果能够反映衡水地区现今的地震活动水平和危险性水平。     

Investigations of thermal and elastic properties of rocks by means of a cubic press

Investigations of thermal diffusivity and elastic anisotropy have been carried out under high pressure. The pressure is generated by means of a cubic press with a special piston system. The thermal diffusivity for several granulite samples was measured by an impulse method. The elastic anisotropy was investigated for pyrophyllite and calcite. The calcite crystal undergoes a phase transformation in the investigated pressure range with a change of the character of anisotropy.     

云南地区简易房屋地震失去住所人数的评估

《地震现场工作第4部分:灾害直接损失评估》(GB/T18208.4—2005)提出了简易房屋概念,并将房屋建筑原有的5个破坏等级进行了适当的合并,简化为简易房屋的3个破坏等级。遵循破坏等级合并原理,通过对云南地区已有震例房屋建筑破坏比与简易房屋地震失去住所人数之间相互关系的深入研究,给出简易房屋地震失去住所人数估算公式。     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.