常速度梯度射线追踪与二维层速度反演

速度问题是勘探地震学的核心 ,可以借助常速度梯度射线追踪方法 ,从反演的角度探讨速度建模问题。在射线追踪方面 ,从程函方程出发 ,将复杂的速度场剖分成小的矩形单元 ,并假设在每个矩形单元内速度具有常速度梯度 ,由此导出的一组常速度梯度射线追踪公式 ,可实现非均匀介质的射线追踪 ,具有适应性强、精度高和快速的优点。在层速度反演方面 ,采用相干速度反演的思想 ,根据各向同性介质中 ,零偏移距射线在界面处是法向入射的原理 ,建立了合成共中心点道集与射线深度偏移的正反演关系 ,由此利用合成共中心点道集与观测的共中心点道集逼近 ,采用层剥离方法进行层速度反演。通过理论推导与模型试算得到如下的认识与结论 :常速度梯度射线追踪具有较高的计算精度与效率 ,公式采用向量形式很容易推广到三维 ;确定层速度采用的是正反演相结合的方法 ,可得到稳定的速度场 ;该方法屏弃了基于双曲时矩关系确定层速度场的假设 ,使其能适应任意的速度分布。

Ray tracing with constant velocity gradient and inversion of 2-D interval velocity

The paper discussed the building of velocity model based on ray tracing with constant velocity gradient and inversion of interval velocity. The velocity field in eikonal equation was divided into small rectangles. The velocity gradient in each rectangle was assumed to be constant, and computed by ray tracing. Theory of coherent velocity inversion was adopted in determination of velocity field. We constructed a forward-inverse relationship between synthetic CMP gather and map migration according to the principle that zero-offset rays are injected normally at interfaces in isotropic media. Inversion of interval velocity was achieved layer by layer by approaching the synthetic CMP gather to observed CMP gather. It was concluded from theory analysis and modeling that ray tracing with constant velocity gradient is high in computation precision and efficiency, and can be straightforwardly extended to 3-D space. Because it discards the assumption of time-distance relation of hyperbolic curve, the algorithm for inversion of interval velocity is suitable for arbitrary velocity distribution.