基于自适应优化有限差分方法的全波VSP逆时偏移

与地面地震资料相比,VSP资料具有分辨率高、环境噪声小及能更好地反映井旁信息等优点.常规VSP偏移主要对上行反射波进行成像,存在照明度低、成像范围受限等问题.为了增加照明度、拓宽成像范围、提高成像精度,本文采用直达波除外的所有声波波场数据(全波),包括一次反射波、多次反射波等进行叠前逆时偏移成像.针对逆时偏移中的四个关键问题,即波场延拓、吸收边界条件、成像条件及低频噪声的压制,本文分别采用自适应变空间差分算子长度的优化有限差分方法(自适应优化有限差分方法)求解二维声波波动方程以实现高精度、高效率的波场延拓,采用混合吸收边界条件压制因计算区域有限所引起的人工边界反射,采用震源归一化零延迟互相关成像条件进行成像,采用拉普拉斯滤波方法压制逆时偏移中产生的低频噪声.本文对VSP模型数据的逆时偏移成像进行了分析,结果表明:自适应优化有限差分方法比传统有限差分方法具有更高的模拟精度与计算效率,适用于VSP逆时偏移成像;全波场VSP逆时偏移成像比上行波VSP逆时偏移的成像范围大、成像效果好;相对于反褶积成像条件,震源归一化零延迟互相关成像条件具有稳定性好、计算效率高等优点.将本文方法应用于某实际VSP资料的逆时偏移成像,进一步验证了本文方法的正确性和有效性.

Full-wavefield VSP reverse-time migration based on the adaptive optimal finite-difference scheme

Vertical seismic profiling (VSP) data provides higher resolution information, lower environmental noise and better information beside wells than surface seismic data. Meanwhile, reverse-time migration (RTM) based on two-way wave equation has no dip limitations on the image. It is significant to implement the RTM on VSP data.#br#The four key factors of RTM are wavefield extrapolation, absorbing boundary conditions (ABC), imaging condition and noise suppressing. For the first factor, the paper compares the finite-difference (FD) method based on optimal scheme (optimal-based FD method) with the FD method based on space Taylor series expansion (space TE-based FD method) and the FD method based on time-space Taylor series expansion (time-space TE-based FD method) to indicate the accuracy of the optimal-based FD method. Moreover, to improve the efficiency, the adaptive variable-length spatial operators method is introduced into the optimal-based FD method (adaptive optimal-based FD method). The adaptive optimal-based FD method is adopted to solve the acoustic wave equation and thus implements the wavefield extrapolation of RTM efficiently and accurately. Second, the hybrid ABC is used to suppress artificial reflections from the model boundaries caused by the limited computational boundaries. Then the paper compares normalized cross-correlation imaging condition with deconvolution imaging condition for imaging, which indicates the prior is more stable and efficient. Finally, the Laplace operator filtering is applied to remove the low frequency noises.#br#The conventional migration from VSP data using only up-going primary wavefield often suffers from poor illumination and limited migration scope. To enhance the illumination, enlarge the migration scope and improve the accuracy, the analysis of VSP RTM imaging with direct wave, primary wave, first-order multiple, second-order multiple and higher-order multiples implies that the full-wavefield (complete acoustic wavefield data without direct wave) can be treated as effective wave to implement prestack RTM.#br#RTM test on VSP model data shows that the adaptive optimal-based FD method is more efficient and accurate than the fixed-length TE-based FD method, and suitable to VSP RTM. VSP RTM result using full-wavefield is clearer and images a larger area than VSP RTM only using up-going field. Imaging test on VSP field data demonstrates the efficiency and accuracy of our method.