A Fast Approximate Iterative Inversion Technique of Dual Induction Logging Data

In this paper, we advance a fast approximative iterative inversion technique (FAIIT) of dual induction tool (DIT) logs. First, we establish the fast algorithm of Fréchet derivatives of DIT logs 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 logs 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 at exploring depth, the former can obviously give shallower resistivities at 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.