Studying On3D FV Algorithm Of The Response Of Array Induction Well Logging Tool In Inhomogeneously Isotropic Layered Formation And Its Response Characters

Array induction logging tools utilize single transmitting coil, many of thereceiving coils consist of array coil system. Moreover, the coil uses low、medium andhigh operating frequency. so we can obtain a series of logging curves with differentspacing and frequency. these logging curves have different vertical resolution andlateral surveying depth. In order to obtain the correct stratigraphic informationthrough these curves reasonably, we must study these curves’ variation with differentvertical resolution and lateral surveying depth in detail.We have established the numerical simulation algorithm of array inductionlogging response based above. First of all, in order to overcome the problems oflow-frequency induction numbers, we decompose the electric field into asuperposition of vector potential and scalar potential. so that we can establish theHelmholtz equation of vector potential and scalar potential; Secondly, we can discretethe finite volume for the Helmholtz equation based on the Yee’s staggered grid ofvector potential and scalar potential. so we can establish large discrete equations withvector potential and scalar potential. Because the stiffness matrix which consists ofequations is large sparse matrix, we use the stable bi-conjugate gradient method ofincomplete LU decomposition preconditioning to achieve the fast solving of thediscrete equations. Then we can transform the magnetic tensor what we havecalculated into the apparent conductivity tensor. Finally, we can use the simulationsoftware of array induction logging response to examine the influence of arrayinduction logging response which come from the mutative instrumental frequency、spacing and variation of borehole radius mud resistivity in vertical wells model, andwe can summarize their variation. This paper provides a theoretical basis for the studyof array induction logging instrumental parameter design and the inversion in the future.