CAJ | 학술논문

基于经典Tikhonov正则化( classical Tikhonov regularization)的最小二乘反演是三维电阻率反演的主要方法。对于电阻率分片连续的地质体，由于光滑反演解的光滑性使得目标区域与背景区域间边界模糊，不能很好地体现异常体的形态信息和位置信息，成像效果不好。将总变分正则化( total variation regularization)与经典Tikhonov正则化结合，提出混合正则化反演方法，通过模型分析比较经典Tikhonov正则化、TV正则化、混合正则化在反演结果上的不同，证明了引入混合正则化约束的最小二乘反演既保持了经典Tikhonov正则化方法解的稳定性，又具有TV正则化方法解的保边缘性，有效地改善了三维电阻率成像效果。最后将混合正则化的反演方法应用到实际工程，验证了该方法的有效性和实用性。
기우경전Tikhonov정칙화( classical Tikhonov regularization)적최소이승반연시삼유전조솔반연적주요방법。대우전조솔분편련속적지질체，유우광활반연해적광활성사득목표구역여배경구역간변계모호，불능흔호지체현이상체적형태신식화위치신식，성상효과불호。장총변분정칙화( total variation regularization)여경전Tikhonov정칙화결합，제출혼합정칙화반연방법，통과모형분석비교경전Tikhonov정칙화、TV정칙화、혼합정칙화재반연결과상적불동，증명료인입혼합정칙화약속적최소이승반연기보지료경전Tikhonov정칙화방법해적은정성，우구유TV정칙화방법해적보변연성，유효지개선료삼유전조솔성상효과。최후장혼합정칙화적반연방법응용도실제공정，험증료해방법적유효성화실용성。
The smooth least-squares method based on the classical Tikhonov regularization method is the main method in 3D resistivity inversion. For the geological body whose resistivity is piecewise continuous, this method however fails to distin-guish the target area from the background due to the smooth nature of the solution. In order to solve this problem, the classi-cal Tikhonov regularization and the total variation regularization ( TV regularization ) were combined and introduced into the least squares inversion method. Three inversion results based on classical Tikhonov regularization, total variation regulariza-tion and the new hybrid regularization were compared. It is shown that the least square method based on hybrid regularization retains both the stability of the classical Tikhonov regularization and the edge-protected property of the total variation regulari-zation. The improvement in 3D resistivity mapping is immediate, and then the method is further verified in practical engi-neering problems.