石油科学通报2024，Vol.9Issue(4)：549-562,14.DOI:10.3969/j.issn.2096-1693.2024.04.041
基于微分超拉普拉斯块约束的改进弹性阻抗反演方法
A modified inversion method for elastic impedance based on the differentiable hyper-Laplacian blocky constraint
摘要
Abstract
The introduction of rock physics models allows us to fully utilize pre-stack seismic data for inversion,thereby obtaining more comprehensive information about the subsurface media.However,the increase in the number of parameters to be inverted in the elastic impedance equation,which is based on the reflection coefficient equation,as well as the varying contri-butions of different parameters to the reflection coefficient,have also increased the difficulty of the inversion.Consequently,to ensure the stability of multi-parameter inversion,the two-step inversion method has been widely applied.That is,firstly,perform elastic impedance inversion to obtain elastic impedance information under different incident angles and azimuthal angles,and then use elastic impedance as input for the next step of multi-parameter inversion.Elastic impedance,as an extension of acoustic impedance inversion technology,has become very mature,but there are still problems such as non-uniqueness of solutions,insufficient resolution,and insufficient sparsity of the solution.This article introduces the hyper-Laplacian blocky constraint into the inversion process.This is commonly used in the field of signal and image processing.It can avoid the issue of 0-norm differentiation and also allow for the selection of the optimal p-value according to the characteristics of the data itself,ensuring a certain degree of stability while obtaining higher resolution in the inversion results.At the same time,a linearized approximate PP wave reflection coefficient equation is introduced to obtain the inversion results of elastic impedance directly from the seismic data.First,the derivation of a linearized elastic impedance approximation equation is carried out,and its accuracy is analyzed.Subsequently,based on the Bayesian theory,the objective function of elastic impedance inversion with the introduction of the differentiable hyper-Laplacian blocky constraint is derived.The iterative reweighted least squares method is chosen to solve the objective function to obtain the elastic impedance inversion results.Finally,the results of the new method are compared with those obtained by traditional methods to verify the accuracy and stability of the method.Both the correlation coefficient and the comparison of elastic impedance curves effectively demonstrate that the inversion results obtained by the proposed method are better than those of the traditional inversion results constrained by L1 norm and L2 norm.By applying the new method to the inversion of both synthetic data and real data,its effectiveness and feasibility have been proved.Therefore it can be widely applied in the inversion process of elastic impedance,providing more reliable and comprehensive information for subsequent multi-parameter inversion.关键词
弹性阻抗/叠前反演/微分超拉普拉斯/贝叶斯框架/分辨率Key words
elastic impedance/pre-stack inversion/differentiable hyper-Laplacian blocky constraint/Bayesian-based inversion framework/resolution分类
天文与地球科学引用本文复制引用
侯斯允,李景叶,耿伟恒,韩磊,王永平..基于微分超拉普拉斯块约束的改进弹性阻抗反演方法[J].石油科学通报,2024,9(4):549-562,14.基金项目
中国石油天然气集团有限公司项目"物探应用基础实验和前沿理论方法研究"(编号:2022DQ0604-04)资助 （编号:2022DQ0604-04）
