波数域等价波动方程三维弹性波波场分离

Wave field separation based on 3D equivalent elastic wave equation in wave number domain

将基于传统弹性波波动方程正演模拟或者反向外推得到的波场作为纵横波耦合的混合波场,利用亥姆霍兹分解方法对混合波场进行分离,可得到纯纵波波场和纯横波波场,但是用这种方法分离后的波场和原波场相比产生了振幅畸变。为了消除这一现象,笔者从亥姆霍兹分解方程入手,利用纵波波场旋度为零、横波波场散度为零的特性,在波数域将传统波动方程分解为无旋部分和无散部分,得到波动方程的一种等价表示。数值实例表明,该方法既能获得混合波场、纯纵波波场和纯横波波场,又能使分离前后的波场振幅无畸变。

The mixed wave field including P wave and S wave can be obtained after forward modeling or extrapolating based on the conventional elastic wave equation. The coupling wave field can be separated into pure P wave and S wave via Helmholtz decomposition. But the previous method produces amplitude distortion. To eliminate this phenomenon, a new equivalent elastic wave equation was presented in wave number domain taking advantage of the features that the curl of P wave is zero and divergence of S wave is zero. The neo-equation derives from separating the conventional wave equation into two portions contained curl-free and divergence-free. The numerical results show that the method can simultaneously produce the mixed wave field, pure P wave field and S wave field. The amplitude distortion was removed