Amplitude ratio average method in frequency domain for Q estimation of extrinsic attenuation based on Taylor series expansion with different orders
ZHANG Jin1,2, WANG Yanguo2,3, LAN Huitian4, ZHANG Guoshu5, PAN Yeli2
1. Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province, Nanchang, Jiangxi 330013, China; 2. School of Geophysics and Measurement-Control Technology, East China University of Technology, Nanchang, Jiangxi 330013, China; 3. State Key Laboratory of Nuclear Resources and Environment, East China University of Technology, Nanchang, Jiangxi 330013, China; 4. Exploration and Development Research Institute of Daqing Oilfield Company, Daqing, Heilongjiang 163712, China; 5. School of Nuclear Science and Engineering, East China University of Technology, Nanchang, Jiangxi 330013, China
摘要 在估计实际品质因子Q值时，因受频段选择、子波叠加、噪声干扰、非本征衰减等因素影响，容易导致Q值估计误差偏大。为此，提出基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法（Amplitude ratio average in frequency domain， FARA法）。该算法首先利用参考频段内振幅比的连乘消除非本征衰减的影响；然后基于振幅因子在参考频点处的1~4阶泰勒级数展开表达式，推导适用于含非本征衰减地震记录的单频点Q值计算公式；其次，采用高、低频双参考频段结合方式削弱参考频段的影响；最后，采用主值频段内所有频点的平均化处理提高算法的稳定性。模型试验表明，采用高、低参考频段结合的模式可以显著提高所提方法的Q值估计精度，相对于对数谱面积双差值（LSADD）法，新方法受时差、时窗及噪声等因素的影响更小。实例应用表明，不同阶次的FARA法Q估计值的一致性较好，且整体大于LSADD法的Q估计值，与模型试验结果吻合，表明由新方法获得的Q值更可靠。
Abstract：In the actual quality factor Q estimation， it is prone to have a large estimation error due to factors such as frequency band selection， wavelet superposition， noise interference， and extrinsic attenuation. Thus， the amplitude ratio average method in the frequency domain （FARA） for Q estimation based on Taylor series expansion with different orders considering extrinsic attenuation is presented. Firstly， the continuous multiplication of the amplitude ratio in the reference frequency band is utilized to eliminate the effect of extrinsic attenuation. Then， based on the 1st-4th order Taylor series expansion expression of the amplitude factor at the reference frequency point， the single-frequency point Q estimation formula for the seismic records with extrinsic attenuation is derived. Secondly， the combination of high and low reference frequency bands is adopted to weaken the impact of reference frequency bands. Finally， the average processing of all frequency points average in dominant frequency bands is leveraged to improve the algorithm’s stability. The model test shows that the combination of high and low reference frequency bands can significantly improve the Q estimation accuracy of this method， and the proposed method is less sensitive to the time difference， time window， and noise interference than the logarithmic spectral area double difference （LSADD） method. The example application shows that the Q value estimated by the FARA method with different orders has good consistency， with greater overall Q value than that of the LSADD method. This is consistent with the model test results， indicating that the Q value estimated by the FARA method is more reliable.
张瑾, 王彦国, 兰慧田, 张国书, 潘耶莉. 基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法[J]. 石油地球物理勘探, 2023, 58(6): 1423-1435.
ZHANG Jin, WANG Yanguo, LAN Huitian, ZHANG Guoshu, PAN Yeli. Amplitude ratio average method in frequency domain for Q estimation of extrinsic attenuation based on Taylor series expansion with different orders. Oil Geophysical Prospecting, 2023, 58(6): 1423-1435.
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