Scattering of horizontally-polarized shear waves by surface irregularities

Summary. The problem of the scattering of harmonic SH waves by an arbitrary surface irregularity in an otherwise semi-infinite elastic, homogeneous, isotropic two-dimensional half-space is examined in this study in order to ascertain the effect of topography on this type of seismic ground motion and to develop a useful scheme which can realistically handle arbitrary two-dimensional topography. Three geometric models are considered: a semicircular hill which is of academic interest; a mountain with a Gaussian shape which utilizes realistic dimensions and the combination of a ridge and a depression that models a region in Sylmar, California.
A singular Fredholm integral equation of the second kind for the displacement at the free surface is developed and solved numerically. In the case of the semicircular hill, horizontal ground motion can be more than twice that occurring in the case of smooth topography. The mountain simulated by a Gaussian profile experiences at its crest amplifications for certain angles of incidence and de-amplifications for other angles of incidence, as well as displacements whose amplitudes vary slowly with frequency on the side of the mountain which is in the same direction as the incident waves. The ridge-depression combination which is approximated by a sixth-order polynomial actually experienced shattered earth at its ridge crest during the San Fernando, California earthquake of 1971. This amplification is also exhibited by the results of the analysis which, predicts amplifications of over 75 per cent at the top of the ridge for waves arriving on the same side as the ridge.     

塔克拉玛干沙漠腹地大气气溶胶散射特征研究

利用沙漠腹地塔中气象站积分浊度计的2004年观测资料,结合同期PM10质量浓度、能见度和常规气象资料,分析了塔克拉玛干沙漠腹地气溶胶散射系数的变化特征,以及气溶胶散射系数与PM10质量浓度、能见度的关系。研究表明,2004年塔中气溶胶散射系数、PM10质量浓度、能见度日平均值分别为124.74±187.30 Mm-1,538.9±841.7 μg·m-3,12 748±7 274 m。塔中气溶胶散射系数小时平均值出现频率最高的区间主要在100 Mm-1以下,中午气溶胶散射系数小,早晚气溶胶散射系数大;冬春两季的凌晨空气中含有较多的粒子,气溶胶散射系数较大;气溶胶散射系数小时平均值与PM10质量浓度变化规律基本一致,2004年1—6月的气溶胶质量散射系数平均值为0.37 m2·g-1;散射系数与能见度日平均值非线性相关较好,两者呈负幂函数关系。     

沙漠与城市气溶胶散射系数变化比较

利用塔克拉玛干沙漠大气环境观测试验站和中国气象局乌鲁木齐沙漠气象研究所承担的乌鲁木齐大气成分观测站2010年1月1日至12月31日的单波段积分浊度计的观测资料,分析了沙漠（塔中）和城市（乌鲁木齐）两种不同下垫面地区的气溶胶散射系数的变化特征。（1）散射系数小时平均值：塔中地区变化范围在39.6～8 442.8 Mm^-1,平均值318.4 Mm^-1;乌鲁木齐变化范围在28.9～6 590.0 Mm^-1,平均值451.5 Mm^-1;乌鲁木齐小时平均值在1 000 Mm^-1以上的高值区间大于塔中地区。（2）散射系数日变化：塔中呈现单峰变化,其中最大值387.0 Mm^-1出现于凌晨02：00,最小值276.4 Mm^-1出现于午后的17：00;乌鲁木齐呈现三锋变化,3个峰值分别出现于09：00、14：00、22：00,与塔中地区存在明显差异。（3）散射系数月均值变化：塔中的月平均值最大是4月,为500.2 Mm^-1,最小是2月,为145.9 Mm^-1;乌鲁木齐月均值最大在2月,为1 086.3 Mm^-1,最小值在7月,为101.1 Mm^-1,两地区月均值变化整体呈现相反的现象。（4）散射系数季节变化：塔中地区春季>夏季>秋季>冬季;乌鲁木齐冬季>秋季>春季>夏季。     

Scattering characteristics in heterogeneously fractured reservoirs from waveform estimation

Offset-dependent characteristics of seismic scattering are useful for characterizing fractured reservoirs. We use two models that have different background medium properties and different azimuthal AVO responses to study elastic wave propagation and scattering in gas-saturated, heterogeneously fractured reservoirs. Heterogeneous fracture density distributions are built through stochastic modelling. Synthetic seismograms are generated by 3-D finite difference modelling, and waveforms along crack-normal and strike directions are considered in this paper. The multiple signal classification (MUSIC) frequency estimator is used in waveform estimation to provide frequency-domain attributes related to seismic wave scattering by fracture heterogeneity. Our results indicate that the strength of the scattering field is a function of the background medium. The strength also increases with increasing fracture scatterer density and with decreasing correlation length of spatial variations of fracture density. The scattering field is weak at the top of the fractured reservoir. The first-order results are dominated by velocity anisotropy of the mean fracture density field. However, the base of the fractured reservoir corresponds to a strong scattering field on which fracture heterogeneity has a larger effect and is characterized by the loss of coherence.     

半干旱区气溶胶散射特性研究

利用2005年1月至9月锡林浩特观象台积分浊度计的观测资料,结合同期的PM10质量浓度、能见度以及常规气象资料,分析了半干旱地区气溶胶的散射系数变化特征,讨论了它的季节变化、日变化、不同沙尘天气下气溶胶散射系数的变化情况,以及散射系数与PM10质量浓度、能见度的关系。结果表明1月至9月散射系数总体呈先下降再升高的趋势,日变化呈明显的双峰型;散射系数能很好的反映沙尘天气的强度;它与PM10质量浓度变化规律基本一致,两者之间具有很好的相关性;散射系数与能见度呈指数相关关系。     

Scattering of surface waves modelled by the integral equation method

The integral equation method is used to model the propagation of surface waves in 3-D structures. The wavefield is represented by the Fredholm integral equation, and the scattered surface waves are calculated by solving the integral equation numerically. The integration of the Green's function elements is given analytically by treating the singularity of the Hankel function at   R = 0  , based on the proper expression of the Green's function and the addition theorem of the Hankel function. No far-field and Born approximation is made. We investigate the scattering of surface waves propagating in layered reference models imbedding a heterogeneity with different density, as well as Lamé constant contrasts, both in frequency and time domains, for incident plane waves and point sources.     

Scattering of waves by a quasi-thin body of arbitrary shape

Summary. The problem of scattering of a wave with a front of arbitrary shape by a curved quasi-thin body bounded by contour L of arbitrary shape is presented. The problem is solved using the Kirchhoff approximation (KA). The reflecting (scattering) properties of the body are given in terms of the reflection (transmission) coefficients. The routine technique of computation in the KA is complemented by significant improvements. The procedure of smooth continuation of the body surface S beyond its boundary contour L is suggested. The invariant presentation of the expressions for the scattered field u _s obtained in the paper is extremely important.
The leading term in the formula for the field u _s is obtained as a product u _s= u _ray W , where u _ray is the reflected wavefield computed, according to the formulae of ray theory, as if the body surface is boundless; W is the so-called weakening function, which takes account of the modification of the ray field caused by diffraction at the edges (the contour L ).
The arguments of the weakening function are dimensionless quantities depending on the relation between the body size and the radii (half-axes) r _f^{( i )} ( i = 1, 2) of the Fresnel zones on the surface S. The values of r _f^{( i )} are obtained in the paper. The method of computation of the function W turns out to depend essentially on the reciprocal position of the Fresnel zone and body contour. When the contour L is of a complex form, the surface S is divided into simple surfaces S_i , each of which is limited by a contour L , which permits the carrying out of a single valued (in the sense of the leading part of the field) smooth continuation of S_i .     

Scattering of waves in elastic media containing passive and active cracks

Scattering of wavefields in a 3-D medium that includes passive and/or active structures, is numerically solved by using the boundary integral equation method (BIEM). The passive structures are velocity anomalies that generate scattered waves upon incidence, and the active structures contain endogenous fracture sources, which are dynamically triggered by the dynamic load due to the incident waves. Simple models are adopted to represent these structures: passive cracks act as scatterers and active cracks as fracture sources. We form cracks using circular boundaries, which consist of many boundary elements. Scattering of elastic waves by the boundaries of passive cracks is treated as an exterior problem in BIEM. In the case of active cracks, both the exterior and interior problems need to be solved, because elastic waves are generated by fracturing with stress drop, and the growing crack boundaries scatter the incident waves from the outside of the cracks. The passive cracks and/or active cracks are randomly distributed in an infinite homogeneous elastic medium. Calculations of the complete waveform considering a single scatter show that the active crack has weak influence on the attenuation of first arrivals but strong influence on the amplitudes of coda waves, as compared with those due to the passive crack. In the active structures, multiple scattering between cracks and the waves triggered by fracturing strongly affect the amplitudes of first arrivals and coda waves. Compared to the case of the passive structures, the attenuation of initial phase is weak and the coda amplitudes decrease slowly.