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为地震成像和模型计算曾提出过不同阶次的很多近似式,其中最常用的是称为15度方程的一阶近似式,它的特点在于效率较高。然而,所有近似式都受到一个共同的约束,这就是它们都不能精确地处理大倾角反射的问题。波动方程经过某种线性变换后,可得到线性变换波动方程(LTWEQ)而不需任何近似。LTWEQ 的形式与15°方程相同,其解仍为双程波动解。对上行波(或下行波)施加约束条件后,LTWEQ 可以应用于地震成像(或模型计算)。LTWEQ以某种有限差分算法实现时,得到一个180°或全倾角的有限差分波场外推算子,用此算子可以解决常规有限差分法中的角度有限性的问题.
Many approximations of different orders have been proposed for seismic imaging and model calculations. The most common of these is the first order approximation called a 15 degree equation, which is characterized by high efficiency. However, all approximations are subject to a common constraint, which is why they can not deal with the problem of steep-dip reflection accurately. After some linear transformation of the wave equation, a linear transformation wave equation (LTWEQ) can be obtained without any approximation. The form of LTWEQ is the same as the 15 ° equation, and the solution is still a two-way fluctuation solution. LTWEQ can be applied to seismic imaging (or model calculation) after constraints have been imposed on the upgoing (or descending) wave. When LTWEQ is implemented with some kind of finite difference algorithm, a 180 ° or full dip finite difference wavefield extrapolation operator is obtained. This operator can solve the problem of the limited angle in the conventional finite difference method.