(中南大學(xué) 地球科學(xué)與信息物理學(xué)院，長沙 410083)
摘 要: 在實際地下地質(zhì)構(gòu)造是一類多尺度的構(gòu)造(如斷層和褶皺等)，而傳統(tǒng)的正則化方法多基于最小光滑策略，其反演密度模型一般不易辨識以上構(gòu)造。為此在分裂Bregman迭代正則化框架下引入混合正則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，引入與衰減系數(shù)無關(guān)的深度加權(quán)矩陣以更好地描述深部異常；針對非光滑反演中異常幅值易于超出現(xiàn)實及理論異常范圍，引入密度成像中的約束以確保反演具有物理意義。通過設(shè)置兩類模型，對比多類正則化反演方法。反演結(jié)果顯示：混合正則化反演能有效地勾勒異常邊界；在處理埋深不同的異常源時，相對于聚焦反演出現(xiàn)的過度聚焦現(xiàn)象而導(dǎo)致的反演深度描述不準(zhǔn)確、異常歪斜，混合正則化反演的聚焦效應(yīng)相對較弱、但深度描述準(zhǔn)確。這表明本研究反演確實可行、有效，且具有更強(qiáng)的適應(yīng)性。
關(guān)鍵字: 深度加權(quán)；密度約束；聚焦反演；混合正則化；邊界識別
（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
