(中南大学 地球科学与信息物理学院，长沙 410083)
摘 要: 在实际地下地质构造是一类多尺度的构造(如断层和褶皱等)，而传统的正则化方法多基于最小光滑策略，其反演密度模型一般不易辨识以上构造。为此在分裂Bregman迭代正则化框架下引入混合正则化方法以充分利用非光滑反演和小波多尺度反演算子的特性，引入与衰减系数无关的深度加权矩阵以更好地描述深部异常；针对非光滑反演中异常幅值易于超出现实及理论异常范围，引入密度成像中的约束以确保反演具有物理意义。通过设置两类模型，对比多类正则化反演方法。反演结果显示：混合正则化反演能有效地勾勒异常边界；在处理埋深不同的异常源时，相对于聚焦反演出现的过度聚焦现象而导致的反演深度描述不准确、异常歪斜，混合正则化反演的聚焦效应相对较弱、但深度描述准确。这表明本研究反演确实可行、有效，且具有更强的适应性。
关键字: 深度加权；密度约束；聚焦反演；混合正则化；边界识别
（School of Geosciences and Info-Physics, Central South University, Changsha 410083, China）
Abstract:Traditional regularization inversions based on minimum smooth cannot distinguish the discontinuity of the underground subsurface (such as faults and folds, etc.). Hyper-parameter regularization method was introduced under split Bregman iterative regularization framework for taking advantage of edge-preserving inversion and wavelet multiscale operator. A new depth matrix was created based on sensitive matrix for giving an exact description of deep density abnormity. Physical bounds were imposed in each inverse iteration to obtain meaningful solutions and to avoid insignificant abnormality in non-smooth inversion. The smoothness inversion, Marquardt inversion, Occam inversion and focusing inversion with two synthetic models were compared. The inversion results show that the hyper-parameter regularization inversion can preserve edge effectively and has relatively weak focusing effect when treating the designed model with different depth sources. Meanwhile, this method can avoid inaccurate depth description and obliqueness caused by over-regularization in focusing inversion. Moreover, the inversion proposed in this study is feasible, effective, and has better adaptability.
Key words: depth matrix; bound constraint; focusing inversion; hyper-parameter regularization; edge-preserving
