泥质砂岩激发极化弛豫时间谱的正则化反演

The regularization inversion of induced polarization relaxation time spectrum of agrillaceous sand

激发极化衰减谱是一系列单指数衰减的线性叠加，因此可以对衰减谱进行多指数反演，得到的弛豫时间谱可用于储层孔隙结构和渗透性评价，是一种非常有前途的技术。由于实际测井的信噪比相对较低，常规的奇异值分解方法难以获得合理的弛豫时间谱，为此，采用正则化约束，结合奇异值分解，对合成数据和实际测量的衰减谱进行反演，得到连续的弛豫时间谱；同时，讨论了弛豫时间谱的时间常数分布、正则化因子以及信噪比对反演结果的影响。研究结果表明：该方法适用于信噪比较低的实际测量结果的反演，弛豫时间常数的分布点数为32～64较为合适；随着正则化因子的增加，反演结果逐渐变得平滑，存在一个最优的正则化因子，用于获得最为合理的弛豫时间谱；在双对数图中，最优正则化因子随着信噪比的增加而线性降低，因此通过测量结果的信噪比，可以求取最优正则化因子，进而将该技术应用于实际。

The time-domain induced polarization （IP） decay curve is a linear superposition of IP signal from individual pores. It can be transformed to relaxation time spectrum related to the pore structure and can be used to estimate the permeability of the argillaceous sand. So the IP logging is a useful tool for reservoir characterizing. The singular value decomposition （SVD） method can be used to ex-tract the relaxation time spectra from the decay data with high signal-to-noise ratio （ SNR） . This method is unstable and invalid for the practical downhole use because of the noisy decay data. In this study, a method of regularization was applied to extracting continuous IP relaxation time spectra from simulated and real decay data. Influence of the regularization factor, SNR and relaxation time arrangement on the spectra was also discussed. Firstly, for the simulated decay data with noise, the spectra become smoother with increasing regu-larization factor. There is an optimal value which can be used to get the most reasonable spectrum. The optimal factor decreases linearly with increasing SNR on a log-log scale. This relationship can be used to predict the optimal factor from a known SNR. Secondly, the in-fluence of relaxation time arrangement on the spectra shows that the suitable relaxation distribution point ranges from 32 to 64. Finally, the developed algorithm and the prediction of the optimal factor are very suitable for the inversion of the spectra of the real data.