双平方根波动方程偏移速度分析

传统的剩余校正（RMO）偏移速度分析方法基于走时原理，在陡倾角和欠照明地区，因为不能得到充分的角度域信息而失效.本文将展示一种基于波场延拓理论的偏移速度分析方法，即波动方程偏移速度分析（WEMVA）.这种方法先利用成像优化方法获得剩余成像，再利用剩余成像反演剩余速度.此类方法继承了波动方程偏移方法的优点和缺点.波动方程偏移速度分析是一种线性反演方法，它要求对Born近似的展开序列作一阶截断.高阶部分的丢失必然带来巨大的截断误差，因此剩余成像必须也进行线性化，以适应大速度扰动和大延拓步长.因此，在此类算法中，剩余成像的获取和线性化是偏移速度分析的关键.在叠前偏移算子中，因为双平方根算子的数学表达式更为简洁，所以本文基于对波动方程偏移速度分析初步讨论，并通过模型验证其原理.

Wave-equation migration velocity analysis by Double Square Root method

The traditional RMO Migration Velocity Analysis (MVA) is based on travel time theory. However, it fails in steep or under illumination events, because of the scarcity of angle information. We present a new MVA method based on wave continuation theory, called wave equation migration velocity analysis (WEMVA). First, image perturbations generated by image enhancing methods. Then, velocity perturbations are inversed with image perturbations. WEMVA methods also inherit both the advantage and disadvantage from wave equation migration.Wave equation migration velocity analysis is a linearized inverse problem. It truncates the Born scattering serial to the first order term which bring divergence. The image perturbations must be linearized to the same order. The linearization of image perturbations is the key to WEMVA.In this paper we will generally discuss the WEMVA method by Double Square Root (DSR) for the convenience of mathematic expression, and demonstrate how it works in numerical model.