基于黏滞声波方程解析解的AVF反演

纵波衰减与频散是PP波地震记录衰减的主要原因，因此理论上只需利用PP波叠后地震资料即可反演振幅随频率的变化关系（AVF），以获取纵波频散因子指示流体。但基于传统单界面的AVF反演方法并不令人满意且在很多方面仍然存在争议。为此，提出基于零炮检距黏滞声波方程解析解的AVF反演方法，其流程为：①利用时频谱方法等计算地震记录的时频谱； ②基于地震记录提取子波，消除地震数据中子波叠印获取反射系数的时频谱； ③基于黏滞声波方程进行波阻抗反演，获得更准确的阻抗参数计算Fréchet导数； ④根据导数矩阵建立AVF反演方程，选取合适的参考频率点以及参与计算的频率点反演高精度频散属性。数值模拟和实际数据测试表明：界面频散对地震记录的影响很小，且传播过程的AVF效应远大于界面频散造成的AVF效应；新方法的精度和分辨率明显高于传统单界面AVF反演。

AVF inversion based on analytical solution of viscous acoustic equation

The P-wave attenuation and dispersion are the main reasons for the attenuation of PP wave seismic records. Therefore, in theory, only the post-stack seismic data of the PP wave is required for AVF inversion and the subsequent acquisition of P-wave dispersion factor that can indicate the fluid area. However, the AVF inversion method based on the traditional single-interface assumption is not satisfactory and is controversial in many aspects. So, an AVF inversion method based on the analytical solution of the zero-offset viscous acoustic equation is proposed. The process is as follows:①The time-frequency spectra of seismic records are calculated by a time-frequency spectrum method. ②With seismic records, wavelets are extracted to eliminate the wavelet overprints in seismic data and thereby obtain the time-frequency spectra of the reflection coefficients. ③According to the viscous acoustic equation, wave impedance inversion is carried out to obtain more accurate impedance parameters and thus to calculate the Fréchet derivative. ④An AVF inversion equation is formulated in view of the derivative matrix. Then, appropriate reference frequency points and frequency points involved in the calculation are selected to acquire the high-precision dispersion attributes through inversion. Numerical simulation and actual data tests show that interface dispersion has little effect on seismic records and the AVF effect of the propagation process is much greater than that caused by interface dispersion. The accuracy and resolution of the proposed method are significantly higher than those of the traditional single-interface AVF inversion.