任意方向震源二维兰姆问题的一个精确解

均匀弹性半空间表面或内部震源产生的地震波场的解析解属于Lamb问题,采用Cagniard-deHoop方法,对与水平面呈任意夹角的表面线源,求解了其作用于弹性半空间时的拉普拉斯-傅里叶双积分变换解.以δ-脉冲函数为例,给出了任意方向作用力下波场的构成,并定量解出了P波、S波、首波和Rayleigh波等各波的位移表达式,分析了不同作用方向下各波位移的相对大小.建立数值模型并进行数值模拟,模拟结果验证了理论研究的正确性.研究成果为近地表地震波场的研究提供了理论依据.

An exact solution for 2-D Lamb problem of arbitrary direction source

The analytic solution of seismic wave field caused by surface or inner seismic source in homogeneous elastic half-space belongs to Lamb problems. With the Cagniard-deHoop method, we developed a Laplace-Fourier double integral transformed solution for a surface line source which is in arbitrary angle with horizontal plane on elastic half-space. Some quantitative relations of displacements of P-wave, S-wave, head wave and Rayleigh wave under (-impulse are shown, and the relationship between amplitudes is analyzed. A digital model is built and the results of wave equation modeling are used to verify the accuracy of the theoretical achievements. Due to the particularity of near surface, the achievement on arbitrary direction source provides theoretical foundation to wave filed analysis.