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本文从行波观点研究了小尺度三维地形对地震地面运动的影响。在数值计算中应用了三维化二维的解法和人工透射边界的处理方法,以减少计算时间和算机存贮量。主要研究结果如下:当输入水平地面运动时,孤立小山包将发生整体摇动,这一摇动的周期正是山顶和自由场地面运动振幅谱之比的峰值所对应的周期 T_0。当 H/R=1/3-2/3时(H 为山包高度,R 为山底半径),T_0=3.2R/β(β为横波速度)。这一卓越周期的存在导致山顶运动较自由场地面放大100--400%。当输入竖向地面运动时,不再出现明显的山体整体振动,山顶竖向运动较自由场地面放大40—125%。地表凹陷对水平或垂直地面运动的影响远小于具有同一尺度山包的影响,在凹陷边沿附近,地面运动稍有放大(约25%),凹陷底部的运动一般减小。比较了三维理论结果和二维模式的类似研究结果,联系地震宏观现象讨论了两者的差异。理论结果和在一个孤立山包的山顶和山底洞内取得的1975年海城地震的余震记录做了对比,结果表明两者合理地一致。最后,讨论了数值计算中遇到的几个主要问题。
This paper studies the effect of small-scale three-dimensional topography on the ground motion of the earthquake from the traveling wave point of view. Three-dimensional two-dimensional solution and artificial transmission boundary are applied in numerical calculation to reduce the calculation time and computer storage. The main results are as follows: When the input horizontal ground motion, the isolated hill package will occur the whole rocking, the period of this rocking motion is the period T_0 corresponding to the peak value of the amplitude spectrum of the ground motion and the free field. When H / R = 1 / 3-2 / 3 (H is the height of the mountain and R is the radius of the mountain bottom), T_0 = 3.2R / β (β is the shear wave velocity). The existence of this remarkable cycle leads to a 100 - 400% magnification of the summit movement over the free-field surface. When the vertical ground movement is input, the obvious mountainous overall vibration no longer appears. The vertical movement of the mountaintop is 40-125% larger than the free field ground. The effect of surface depression on horizontal or vertical ground motion is much less than that of mountain bark with the same scale. In the vicinity of the edge of the depression, the ground motion is slightly enlarged (about 25%) and the movement at the bottom of the depression generally decreases. The results of three-dimensional theory and two-dimensional model are compared, and the differences between the two are discussed in connection with the macroscopic phenomenon of earthquake. The theoretical results are compared with the aftershock records of the 1975 Haicheng earthquake taken from the top and bottom of a solitary mountain pack. The results show that the two are in reasonable agreement. Finally, several major problems encountered in numerical calculation are discussed.