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Some remarks on the Gaussian beam summation method 总被引：1，自引：0，他引：1
Summary. Recently, a method using superposition of Gaussian beams has been proposed for the solution of high-frequency wave problems. The method is a potentially useful approach when the more usual techniques of ray theory fail: it gives answers which are finite at caustics, computes a nonzero field in shadow zones, and exhibits critical angle phenomena, including head waves. Subsequent tests by several authors have been encouraging, although some reported solutions show an unexplained dependence on the 'free' complex parameter ε which specifies the initial widths and phases of the Gaussian beams.
We use methods of uniform asymptotic expansions to explain the behaviour of the Gaussian beam method. We show how it computes correctly the entire caustic boundary layer of a caustic of arbitrary complexity, and computes correctly in a region of critical reflection. However, the beam solution for head waves and in edge-diffracted shadow zones are shown to have the correct asymptotic form, but with governing parameters that are explicitly ε-dependent. We also explain the mechanism by which the beam solution degrades when there are strong lateral inhomogeneities. We compare numerically our predictions for some representative, model problems, with exact solutions obtained by other means. 相似文献
We use methods of uniform asymptotic expansions to explain the behaviour of the Gaussian beam method. We show how it computes correctly the entire caustic boundary layer of a caustic of arbitrary complexity, and computes correctly in a region of critical reflection. However, the beam solution for head waves and in edge-diffracted shadow zones are shown to have the correct asymptotic form, but with governing parameters that are explicitly ε-dependent. We also explain the mechanism by which the beam solution degrades when there are strong lateral inhomogeneities. We compare numerically our predictions for some representative, model problems, with exact solutions obtained by other means. 相似文献
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Summary. The largest earthquake-induced acceleration yet recorded occurred at the United States Geological Survey's (USGS) Strong Motion Array Station 6 during the 1979 October 15, Imperial Valley, California earthquake. This large acceleration (1.74 g, vertical component) is anomalously strong considering the low magnitude of the event ( M = 6.4), and the fact that receivers in the immediate neighbourhood of Station 6 recorded much lower accelerations. Previous studies of the records by other investigators have suggested a number of explanations for the anomaly, several of which implicate the near-receiver geological structure.
We present a detailed time and frequency domain analysis of the acceleration records at Stations 6, 5, 7, 8 and Diff Array to suggest that the anomalous acceleration is the consequence of the focusing of the incoming body waves by the lens-like effect of the sedimentary wedge between Imperial Valley and Brawley faults. The analyses include a detailed comparison of observed particle motions between neighbouring stations. Narrow band-pass filtered particle motions at Station 6 reveal the interaction of multipath arrivals as well as the frequency-dependent interference between them. Three-dimensional ray tracing experiments confirm the fact that the faulted sedimentary wedge is capable of focusing P -waves near Station 6. The interpretation that best combines theoretical and observed results is that amplification was due to the formation of an elliptic umbilic caustic with focus near the surface. 相似文献
We present a detailed time and frequency domain analysis of the acceleration records at Stations 6, 5, 7, 8 and Diff Array to suggest that the anomalous acceleration is the consequence of the focusing of the incoming body waves by the lens-like effect of the sedimentary wedge between Imperial Valley and Brawley faults. The analyses include a detailed comparison of observed particle motions between neighbouring stations. Narrow band-pass filtered particle motions at Station 6 reveal the interaction of multipath arrivals as well as the frequency-dependent interference between them. Three-dimensional ray tracing experiments confirm the fact that the faulted sedimentary wedge is capable of focusing P -waves near Station 6. The interpretation that best combines theoretical and observed results is that amplification was due to the formation of an elliptic umbilic caustic with focus near the surface. 相似文献
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爆炸应力波作用下缺陷介质裂纹扩展的动态分析 总被引：2，自引：0，他引：2
采用透射式焦散线测试系统,进行爆炸应力波作用下缺陷介质裂纹扩展试验,研究了含与炮孔共线的预制裂隙介质裂纹扩展速度、加速度、裂纹尖端动态应力强度因子和动态能量释放率的变化规律以及它们之间的变化关系。试验结果表明,在爆炸应力波作用下裂隙两端产生了两条翼裂纹A、B,翼裂纹A的长度较翼裂纹B长,两条翼裂纹向相反的方向扩展;在翼裂纹扩展过程中,存在着加速与减速的过程,扩展速度瞬间达到峰值,其后逐渐振荡下降;动态应力强度因子也呈现瞬间达最大值到逐渐减小连续振荡变化的趋势,动态应力强度因子 > ;翼裂纹尖端的动态能量释放率对裂纹扩展具有驱动作用。 相似文献
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