多波多分量高斯束叠前深度偏移

Multimode and multicomponent Gaussian beam prestack depth migration

本文对基于弹性波动理论的多波多分量高斯束偏移进行了完整且详细的分析和公式推导,实现了3D空间多分量(矢量)波场的直接成像.由于当前多数基于弹性波动方程的偏移方法只是假设应力边界条件为自由地表边界条件,这种假设不符合垂直地震剖面(VSP)和海底电缆(OBC)等地震数据.为此本文详细分析了实际应用中常见的三种弹性各向同性介质模型的应力边界条件:自由空间、海底和自由地表模型.在上行传播假设情况下,获得了应力边界条件与位移边界条件的关系式.在此基础上,准确推导了3D多波多分量高斯束波场延拓和偏移成像公式,并在偏移过程中实现了完整的多波型自动分离.由于常规的互相关成像条件不适用于矢量波场成像,本文引用了散度/旋度互相关成像条件.通过约定PS转换波的正向旋转方向解决了3D空间PS成像极性翻转问题.利用2D和3D模型数据偏移成像验证了我们所提出的多波多分量高斯束偏移方法的可行性.

Conventional migration methods based on the elastic wave equation assume that the boundary is a free surface, where the normal and shear stresses are all zero. This assumption is not consistent with many kinds of seismic data, such as VSP （Vertical Seismic Profile） and OBC （Ocean Bottom Cable）. In this paper, we analyze the stress boundary conditions for three kinds of models,including free-space, ocean-bottom and free-surface models. Under the assumption of up-going propagation, the relationships between the stress boundary condition and displacement boundary condition in the three models are established. Based on these relationships we derive the multimode and multicomponent Gaussian beam＇s continuation and migration equations accurately. The complete decomposition of wave modes is implemented automatically during the migration. Since the conventional cross-correlation image condition is not suitable for vector wave field imaging, we use cross-correlation of divergence and curl of vector wave fields. By setting the positive rotation direction of PS converted waves we solve the polarity reversal problem in a 3D space. Synthetic data from 2D and 3D models are used to validate the feasibility of the approach we propose.