双感应测井资料的快速近似迭代反演

A fast approximate iterative inversion technique of dual induction logging data

本文给出一种双感应资料快速近似迭代反演技术.首先建立Fréchet导数的快速算法,保证在反演过程中能够同时获得测井响应相对于地层电阻率和层界面的偏导数,并给出用规范化处理与奇异值分解技术进行迭代反演的具体过程.为了对理论模拟和井场实际资料进行反演,利用综合分层技术从双感应曲线中提取层界面初始位置和地层电阻率初值,通过单独迭代反演中感应资料,修改层界面和地层电阻率实现中感应资料的最佳拟合,得到探测深度相对较浅的地层电阻率,然后固定层界面位置,再迭代反演深感应资料,得到另一组探测深度相对较深的地层电阻率.理论和实际资料处理结果证明,两个不同探测深度的电阻率反演结果的相对大小能够准确地反映地层真实的侵入特征.此外,由于深感应仪器具有较深的探测深度,不论在高侵或低侵地层上,深感应反演结果与地层原状电阻率的差异大大小于视电阻率的差异,所以利用反演结果也能得到更好的地层原状电阻率的估计值.

In this paper, we advance a fast approximate iterative inversion technique （FAIIT）of dual induction tool logs （DIT）. First, we establish the fast algorithm of Fréchet derivatives of DIT with respect to bed interfaces and formation resistivities simultaneously, and give the process of the iterative inversion by use of normalization and singular value decomposition （SVD）. The initial model parameters including interface and resistivities per bed must be extracted by comprehensively blocking of DIT for realization of the inversion of both synthetic and field logs. After the initial model is obtained, the bed resistivity and interface per bed are iteratively revised through the inversion of the medium induction log （IM） only. Then, deep induction log （ID） is only used to reconstruct other bed resistivities. Due to the difference of ID and IM in exploring depth, the former can obviously give shallower resistivities in exploring depth than the later. The inversion results of both synthetic and field logs clearly prove that the inversion results from ID and IM respectively can demonstrate the exact characteristics of formation invasion. Besides, because of ID with deeper exploring depth, inversion results of ID are largely closer to formation virgin resistivities than apparent resistivity of ID in beds of either deep or shallow invasion, so the better estimation of formation virgin resistivity is also obtained.