基于一阶速度-胀缩-旋转方程的多分量联合逆时偏移

摘要

Elastic reverse time migration (RTM) is an important technology in multi-component seismic exploration.In order to suppress noise in RTM and correct polarization of S-wave,the propagation directions of P-wave and S-wave have to be calculated accurately.The propagation direction of seismic wave is generally indicated by Poynting vector.The conventional first-order velocity-stress equations could only calculate a Poynting vector which indicates the propagation direction of the mixed wavefield rather than that of the P-or S-wavefield.Therefore,it is unable to accurately suppress noise or correct S-wave polarity by using the conventional Poynting vector.Theoretically,the first-order velocity-dilatation-rotation equations could calculate Poynting vectors of pure P-and S-wavefield,which indicate the propagation directions of P-and S-wave,respectively.Therefore,the problems in the conventional method could be avoided by using the Poynting vectors calculated by the first-order velocity-dilatation-rotation equations.This paper focuses on the elastic RTM which is based on the first order velocity-dilatation-rotation equations.Firstly,the authors derived a reverse-time propagation scheme in staggered-grid with 2-order time difference accuracy and 2 N-order space difference accuracy.The authors also derived the stability condition of the scheme.Secondly,the authors calculated the P-and Swave Poynting vectors to indicate the propagation directions of pure P-and S-wavefield,respectively.Then,the elastic RTM could be implemented by utilizing a cross-correlation imaging condition in the wavefield which is separated by propagation directions.The numerical tests show the elastic RTM based on the first-order velocity-dilatation-rotation equations can accurately correct S-wave polarization.In addition,the migrated sections obtained by this method could suppress noise better than the conventional method which is based on the first-order velocity-stress equations.%弹性波逆时偏移是多分量地震勘探领域的重要研究内容,逆时偏移过程中纵、横波传播方向的准确求取是实现纵、横波偏移噪声压制和横波极性校正的前提,坡印廷矢量是指示纵横波传播方向的重要依据.常规一阶速度-应力方程只能求取纵、横波混合波场的坡印廷矢量,其指示的波场传播方向也只是混合波场的传播方向而非单纯纵波或横波的传播方向,故无法准确解决偏移噪声压制和横波极性校正等问题.理论上,一阶速度-胀缩-旋转方程能够求取纯纵波或纯横波的坡印廷矢量,获得单一类型波的传播方向信息,从而克服常规方法的局限.基于一阶速度-胀缩-旋转方程的弹性波逆时偏移技术,首先给出了该方程逆时延拓的交错网格时间2阶、空间2N阶差分格式和稳定性条件,其次在波场延拓过程中通过求取纵、横波的坡印廷矢量获得了单一类型波的传播方向,并利用基于行波分离的互相关成像条件实现了该方程的多分量联合逆时偏移.模型试算表明:基于一阶速度-胀缩-旋转方程的弹性波逆时偏移能够准确解决横波的极性校正问题,并取得优于常规算法的偏移噪声压制效果.