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我们建立了一阶单程波方程,该方程以声波方程的特征分析和优化分散关系为基础。我们证明了上述方程等价于三阶标量偏微分方程。对于均匀介质,这一标量方程可简化为类似于45°旁轴波动方程的形式。在二维不均匀介质中,这一体系精确描述了入射角小于75°的波传播过程。 修正逆时偏移方法采用表示下行波的单程波方程。作为偏移中的波场外推算子,下行波方程能将反射同相轴归位到其相应的反射面上,不具有在速度模型中不连续处的散射。因此,根据上述的偏移技术,可以得到振幅与反射率成比例的成像。我们给出一个将这种新的偏移方法应用于合成地震记录的实例,该地震记录中包含了P—P反射和P—SV转换波。 采用单程波方程来建立吸收边界条件,它对于生成合成地震图是很有用的。这些边界能有效地吸收很宽入射角范围内的波。
We establish a first-order one-way wave equation that is based on the characterization and optimization of the acoustic wave equation. We show that the above equation is equivalent to third-order scalar partial differential equations. For homogeneous media, this scalar equation can be reduced to a form similar to the 45 ° paraxial wave equation. In a two-dimensional inhomogeneous medium, this system accurately describes wave propagation at angles of incidence of less than 75 °. The modified inverse time migration method uses a one-way wave equation that represents the descending wave. As a wave field extrapolation operator in the migration, the down-going wave equation can direct the reflection events to its corresponding reflection surface without scattering at discontinuities in the velocity model. Therefore, according to the above-described offset technique, imaging can be obtained in which the amplitude is proportional to the reflectance. We present an example of applying this new migration method to synthetic seismograms that contain P-P reflections and P-SV converted waves. The one-way wave equation is used to establish the absorption boundary condition, which is useful for generating synthetic seismograms. These boundaries effectively absorb waves over a wide range of incident angles.