Forward And Inverse Computation Of Induction Logging Based On Geometric Factor Theory In Complex Formation

Induction logging is a method for detecting the formation conductibility basedon electromagnetic induction thory. The method has good longitudinal and radialdetection characteristic due to its advantages which does not require injecting currentto formation and can used in the well of air and oil base mud, and the application ofaggregation coil system and deconvolution technology, so the method becomes animportant electrical approach for middle and low resistivity strata profile.The geometric factor theory is the most effective one for near zone field, thepaper discussed the difference resistivity logging response of Doll and Gianzero andMoran geometric factor under different influence factors with double coiled inductionlogging. In the set rang of resistivity, detection characteristic of the three geometricfacors has but little difference.When detecting the formation, the induction logging is affected by many factors,such as undisturbed formation and invaded zone and shoulder bed and mud resistivityand borehole diameter and so on, so the forward compution of induction loggingresponse under these influence factors is significance for design and environmentalcorrection of logging instrument and resistivity analysis of the actual formation.The forward compution is based on the Gianzero which considers the skin effectof formation. The formation model is proposed with variable formation parametersand gradational resistivity of transition zone. Comparing the dual induction loggingand array induction logging responses under different bed thickness and resistivityand borehole diameter and mud resistivity and existence of invaded zone, thefollowing results are obtained:Mud resistivity and borehole diameter have bigger affect on induction logging,with a higher mud resistivity and smaller borehole diameter, the response is moreclose to undisturbed formation, and also with the bed thickness becomes larger;consider the resistivity of the studied zone and its shoulder zone, when the former hasa smaller resistivity, the response is more close to real value; and same result can beobtained when the flushed zone and transition zone is thiner.As for inverse compution, resistivity distribution of different zone and parameters of the model should be known first to analyze the formation resistivityaccurately. In this paper, the least square method is used, and discussed the inversionresults of three models: radial partition model and longitudinal partition model andgrid model. When a same model is used in forward and inverse compution, the resultof the inversion is accurate. When different block uniform models with no coincidentboundaryare used, the result is intensively affected by interface position of theforword model, the result becomes more accurate form interface to a farer position.When too many blocks are divided, a small enough sample interval shoule be used togurrantee the inversion result accuracy.Using synthetical data of random noise and forward data, the inversion accuracyis discussed using least square method and damped least square method. The dampedleast square method shows good inversion accuracy with damping factor chosedartificially. What is more, inverse compution is carried out to process the dualinduction logging and the inversion result matches well with the actual loggingcurves.