矩形网格三维显式差分偏移

Explicit 3D migration on rectangular grids

(CGGVeritas公司，新加坡577177)

CGGVeritas, 577177, Singapore

由Hale提出的基于McClellan变换的三维显式差分偏移算法能够对速度横向变化剧烈的陡倾角复杂介质偏移成像，该算法计算效率高，但只适用于方形网格上采集的资料。对于矩形网格的地震记录，通常需将其先插值到方形网格上，然后再应用基于McClellan变换的三维显式差分偏移算法进行偏移成像，这样既降低了计算效率，又增加了对内存的需求。为此，提出了一种修正McClellan变换的三维显式差分偏移算法，即将插值嵌于外推算子中，无需对数据重采样，可以直接对矩形网格资料进行偏移成像。理论分析与数值实验结果表明，应用修正方法偏移成像的结果与基于数据插值的显式偏移算法结果相吻合，但计算量显著降低。

Explicit 3D migration based on McClellan transform proposed by Hale is capable of imaging efficiently the steep complicated medium with vigorous change in lateral velocity. Although this method is high in computation efficiency, it is only suitable for the data acquired from square grids. As for the data acquired form rectangular grids, the data is firstly interpolated onto square grids and then goes on migration imaging based on Hale’s scheme, greatly increasing the computation cost and the demand for memory. Therefore, an explicit 3D differential migration algorithm based on a modified McClellan transform was proposed, which handles unequal sampling intervals in the inline and crossline directions and no resample is needed. The modified McClellan transformation matrix can directly image data from a square grid. Theoretical analysis and numerical examples show that our explicit 3D differential migration algorithm can effectively provide high quality of wave equation migration results which agree very well with the results from standard Hale’s scheme with data interpolation.