基于经验模态分解字典的自适应匹配追踪谱分解方法及其在油气检测中的应用

利用地震信号的瞬时属性确定时频原子动态参数的扫描范围，获得的瞬时频率稳定性较差且存在负值。利用连续相位求取瞬时频率易受噪声影响，并存在频率异常值。为此，首次将经验模态分解（EMD）引入匹配追踪（MP）算法，提出了基于EMD字典的自适应MP谱分解方法。将EMD视为一种基于过完备时频字典的稀疏分解方法，在计算匹配原子主频的过程中，引进基于连续相位的阻尼最小二乘反演求解瞬时频率，并加入整形正则化算子对数据进行平滑处理，利用整形正则化平滑算子的阻尼最小二乘法有效避免了频率异常值，得到的瞬时频率曲线更平滑、真实，且更突显高频成分。将基于EMD字典的快速MP方法应用于储层含油气性预测，对比不同尺度瞬时谱剖面可以清楚地看到明显的低频阴影现象，且提高了分解效率，从而进一步验证了方法可行性。

Spectral decomposition method of adaptive matching pursuit based on empirical mode decomposition dictionary and its application in oil and gas detection

When the instantaneous properties of seismic signals are used to determine the sweep range of the atomic dynamic time-frequency parameters, the obtained instantaneous frequency has poor stability and negative values. The calculation of instanta-neous frequency with the help of continuous phase is vulnerable to noise and abnormal frequencies can be found. For these reasons, the empirical mode decomposition (EMD) is introduced into the ma-tching pursuit (MP) algorithm for the first time, and a spectral decomposition method of adaptive MP based on the EMD dictionary is proposed. EMD is regarded as a sparse decomposition method on the basis of an over-complete time-frequency dictionary. In the process of calculating the dominant frequency of the matching atom, the continuous phase-based damped least squares inversion is employed to solve the instantaneous frequency, and a shaping regularization operator is introduced for data smoothing. This method avoids abnormal frequencies, and the obtained instantaneous frequency curve is smoother and more realistic with more prominent high-frequency components. The fast MP method based on the EMD dictionary is applied to the prediction of oil and gas content of the reservoir. In the comparison of instantaneous spectrum profiles of different scales, the low-frequency shadow phenomenon is obvious, and the decomposition efficiency is improved, which further verify the feasibility of the method.