基于波动方程的聚焦点控制照明叠前深度偏移

Prestack depth migration by wave equation-based focus-point controlled illumination

基于波动方程的聚焦点控制照明叠前深度偏移技术借助于差分计算,把速度、密度等介质参数的影响体现在差分计算的矩阵方程中,能够自动适应速度场的任意变化,快速傅里叶变换的使用也加速了波场延拓的计算速度。因此此法兼具有限差分偏移方法和傅里叶偏移方法的优点,既可适应速度场的剧烈变化,又可保证对陡倾地层的成像效果,是目前针对复杂构造最有效的成像方法之一。对于单个聚焦点及其周围的成像步骤为:①采用矩形网格情况下绕射走时的有限差分计算方法生成合成算子;②应用合成算子来合成面炮震源和面波记录;③对合成的面炮震源和面波记录做傅里叶有限差分法波动方程叠前深度偏移,得到该聚焦点及其附近区域的成像结果。按照上述成像步骤,将震源波场和炮集记录依据相应的外推公式进行延拓,最终应用成像条件求取成像值。在地质目标处选取多个聚焦点,可以得到面向目标的控制照明偏移成像,在多个层位上选取多个聚焦点进行控制照明叠前深度偏移,可以得到整块区域的成像。通过对Marmousi模型的试算,取得了较好的效果。

With the aid of finite-difference computation,the prestack depth migration by wave equation-based focus-point controlled illumination takes the influence of the medium parameters as velocity and density into matrix equations computed by finite-difference approach,which can be automatically adapted for any changes of velocity field,and the usage of fast Fourier transform can also fasten the computational speed of the wave field continuation.Therefore,the method has superiorities of both finite-difference migration and Fourier migration,and of both being adapted for severe variation of velocity field and guaranteeing the imaging effects of steep dip strata,which is one of effective imaging method for complex structure.The imaging steps for single focus point and surroundings are as follows: using finite-difference method of diffraction travel time to compute the synthetic operator in rectangle grid; ②using synthetic operator to synthesize plane source and plane wave records; ③the Fourier finite-difference wave equation prestack depth migration is implemented by synthetic plane source and plane wave records,obtaining the imaging results of focus point and surroundings.According to abovementioned imaging steps,the continuation of source wavefield and shot-gather records is implemented according to relevant extrapolation formula and finally using imaging conditions to compute imaging value.Selecting multiple focus points at geologic targets,the target-oriented controlled illumination migration imaging can be gained,and selecting multiple focus points on multiple horizons to carry out controlled illumination prestack depth migration can result in imaging in whole area.The approach achieved good effect by the test of Marmousi model.