基于重加权TL1范数的非稳态谱反演算法

Nonstationary spectral inversion algorithm based on reweighted TL_(1) norm

地震数据反射系数反演是联结地下储层和地震数据的桥梁,一直是研究的热点。目前反射系数反演大多基于L_(1)范数约束的稀疏脉冲反褶积。近年来,奇偶分解算法的出现使得子波间调谐效应减弱,这使得基于L_(1)范数约束的谱反演得到进一步应用。稀疏约束的能力关系到待求解反射系数的准确性,本文针对常用的L_(1)范数和Lp范数稀疏能力约束度不足的问题,引入TL_(1)范数(Transformed L_(1)Norm)稀疏约束,有利于获得更准确的反演反射系数;同时考虑反射系数较大的位置拟合能力需要增强,提出重加权TL_(1)范数(Reweighted Transformed L_(1)Norm,RTL_(1))进一步提高稀疏约束能力。参数测试结果证明了重加权类范数重建能力强于未重加权类范数,RTL_(1)在稀疏重建上的有效性。模型和实际数据处理结果证明RTL_(1)相比于常用的稀疏约束项更有利于提高谱反演的反射系数精度。

Seismic data reflectivity inversion is a critical step to connect reservoir parameters and seismic data,which remains a research hotspot.At present,reflectivity inversion is mostly in the form of the sparse-spike deconvolution based on the L_(1)-norm constraint.In recent years,the emergence of the odd-even decomposition algorithm has weakened the inter-wavelet tuning effect,which makes the spectral inversion based on the L_(1)-norm constraint receive further applications.The sparse constraint ability is related to the accuracy of the inversion reflectivity remaining to be solved.Because of the insufficient sparsity constraint ability of the L_(1)-norm and the Lp norm,this paper introduce the transformed L_(1)(TL_(1))sparse constraint,which is conducive to the obtainment of a more accurate inversion reflectivity.Meanwhile,given that the fitting ability of the large reflectivity needs to be enhanced,this paper propose the reweighted TL_(1)(RTL_(1)) norm to further enhance the sparse constraint ability.Parameter tests show that the reconstruction ability of the reweighted norm is better than that of the non-reweighted norm,which proves the effectiveness of the RTL_(1) norm in sparse reconstruction.Models and field data processing demonstrate that the RTL_(1) norm is more effective in enhancing the accuracy of reflectivity inversion in spectral inversion compared to conventional sparse constraints.