【摘要】 地震勘探所面对的地下介质中常包括低速体、起伏地表、高陡构造、孔缝单元等,对这些区域进行地震波场模拟时,为保证模拟精度和计算稳定性,网格间距需要取得很小,从而导致基于笛卡尔坐标系的常规有限差分正演模拟方法的局部过采样问题。为此,本文在前人研究成果的基础上,将伪深度思想引入到正演模拟中,利用曲线坐标系下的梯度、散度公式推导出伪深度域一阶速度—应力方程,实现了伪深度域地震正演模拟。同时,鉴于横向过采样问题没有得到有效解决的实际情况,采用自适应变差分算子计算横向空间导数,提出了伪深度域自适应变差分算子算法,综合考虑了纵、横向的空间采样问题,进一步提高了计算效率。最后,将算子扩展到逆时偏移中,实现了伪深度域自适应逆时偏移算法。模型试算结果表明:相比常规正演模拟算法,伪深度域自适应变差分算子算法在保证精度的前提下,计算效率提高了约25%,存储占用降低了近30%。更多还原

【Abstract】 Surface seismic exploration usually meets challenges like low-velocity bodies,surface topography,steep structures,fractures and so on.Seismic wavefield simulation with conventional Cartesian finite difference forward modeling method in these areas often needs very small grid spacing to ensure the accuracy and stability.So it leads local oversampling problem.To overcome this problem,we introduce the idea of pseudo-depth to the forward modeling.Using the gradient and divergence formula in curvilinear coordinates,we derive the first-order velocity-stress equation in pseudo-depth domain and implement the pseudo-depth domain seismic modeling algorithm.Meanwhile,considering uneven horizontal sampling,we introduce adaptive variable-length spatial operators to calculate the horizontal spatial derivatives and propose seismic forward modeling method with adaptive variable-length spatial operators in the pseudodepth domain.Finally,by extending the forward operator to reverse time migration,we implement pseudo-depth domain reverse time migration with adaptive variable-length spatial operators.Model test results show that our pseudo-depth domain method with adaptive variable-length spatial operators can reduce about 25%of computer time consuming and nearly 30% of the storage without influencing the accuracy of the results.更多还原