三维各向同性介质矢量波场保幅分离方法

摘要

三维各向同性介质中,基于常规散度和旋度算子分离得到的纵横波在物理意义和发生极性的反转位置上无法与原混合波场完全对应.现有的矢量波场分离方法是在波场求取散度和旋度基础上再做一次梯度和旋度运算,分离后的矢量纵横波与原波场极性反转位置一致,但不保幅.从一阶速度-应力方程出发,在波数域推导了矢量纵横波分离公式的表达形式,并结合有限差分过程给出了其在空间域的求解方法.该方法的本质是利用纵横波的传播速度对现有的矢量波场分离方法进行振幅校正,并将校正结果分别作为纵波与横波对于时间的二阶偏导.简单层状模型和SEG/EAEG盐丘模型的试算结果表明,该方法能够适应复杂波场的矢量纵横波分离,并保证分离后纵横波的波形与原混合波场保持一致,具有较好的保幅性.%In a 3D isotropic medium,P-wave and S-wave can be separated by divergence and curl operator,but the physical meaning and polarity inversion position will be inconsistent with the original mixed wavefield.The existing method of vector wavefield separation is seeking gradient to the divergence of wavefield and seeking curl to the curl of wavefield once more,which can make sure the position of the polarity is same as before,but the amplitude will be changed.The authors have deduced the formulas of vector wavefield separation in the wavenumber domain,which was based on one-order velocity-stress equation,and gave the concrete solution method combined with finite difference in space domain.The essence of the method was to correct the amplitude of existing vector wavefield separation method by P-wave and S-wave's propagation velocity,then regard the correcting result as the second derivatives of P-wave and S-wave respectively.The modeling result of simple model and SEG/EAEG salt model showed that the method could adapt to the vector P-wave and S-wave separation of complex wavefield,and could ensure the waveforms and amplitude of separated wavefield were same as before.