波场模拟的高斯波包叠加方法

A new wave field modeling method by using Gaussian Packets

高斯波包(Gaussian Packet)是一种在高频渐进理论下描述波传播的方法,对不同高斯波包叠加可以得到给定点震源函数产生的波场。常速介质中,高斯波包按中心射线出射角度积分存在解析表达式,把该表达式与Gabor点源函数产生波场的解析式对比发现两者是等价的。基于此,利用波动方程关于震源函数的线性性,提出一种利用高斯波包叠加计算任意点源函数产生的波场的新方法。该正演方法可以应用于叠前深度偏移中。对比高斯波包叠加与有限差分法计算的点源波场结果可以看出,两者相差很小。叠前深度偏移的数值实验结果表明,该高斯波包正演的新方法有效可行。

Gaussian Packet describes the propagation of seismic wave in the high-frequency asymptotic theory whose envelopes at given time are nearly Gaussian functions.We prove that the wave field generated by a given Gabor function can be calculated by integrating Gaussian packets over take-off angles.The seismic source function can be decomposed into a series of Gabor functions,and we presented a new method which can simulate the wave field generated by any source function using Gaussian packets.Also,this method can be used in reverse time migration.Numerical experiments of prestack depth migration demonstrate the validity of Gaussian Packets modeling.