Nonlinear Forward And Inversion Of Induction Well Logging With Geological Constraint

The formation resistivity, which can be used to distinguish the oil, gas and waterlayers qualitatively and to evaluate the oil saturation quantitatively, is the main basisfor logging interpretation and evaluation of the oil and gas reservoirs. The inductionlogging tools can be used for measuring the formation resistivity in the boreholes andoil-based mud wells. We can analysis the logging response characteristics of differentformation by forward modeling, and can obtain the formation resistivity from theinduction logging directly by inversion.In this dissertation, the finite difference frequency-domain method is employedfor modeling the induction logging in 2D and 3D isotropic formation. The scatteredfield formulation is used because transmitter coils and receiver coils are often locatedvery close in well logging application. This dissertation employs the LIN preconditiontechnique to decompose the scattered field into curl-free and divergence-freeprojection. After finite-differencing the equations for the scattered field, the linearsystem (Ax=b) is assembled, and it is solved with Bi-Conjugate Gradient Stabilized(BICGSTAB) methods with incomplete LU factorization and incomplete Choleskyfactorization preconditioning. When the total electromagnetic field is determined, theinduction logging response is calculated based on the induction logging theorem. Theforward algorithm is verified by contrasting the numerical results with those of theanalytical solution and numerical mode-match method.In this dissertation, the influencing factors of the convergence speed and globalsearch capacity of the differential evolution (DE) and particle swarm optimization(PSO) algorithm are studied and several improvements of the DE and PSO algorithmare proposed, after studying the principle of the DE and PSO algorithm. A novel DEand PSO hybrid algorithm (DEPSO) is developed considering the advantages anddisadvantages of both DE and PSO. The DEPSO algorithm is evaluated on severalbenchmark functions. The numerical results indicate that the DEPSO algorithm hasthe advantages of fast convergence and fine global search capacity, and it is suitablefor the multi-modal function optimization. Based on the DEPSO algorithm which has the advantage of fine global searchcapacity, an inversion algorithm for induction logging is developed which employsthe regularization method to stabilize the inversion with the prior geologicalinformation. The numerical results show that with this inversion algorithm, the modelparameters can be inversed accurately from the noise free induction logging data, andwhen the unknown parameters and the noise of observed data increase, the inversionaccuracy decreases. The inversion results of the synthetic data indicate that theDEPSO inversion algorithm has the advantages of independence of the initial valuesand fine global search capacity. It can overcome the ill-posed problem caused by theinsufficiency and mistake of the observed data, and can be applied to solve thenonlinear multi-parameters multi-modal geophysics inversion problems. Theinversion results of field induction logging data indicate that the real conductivitymodel of the formation can be obtained with the DEPSO inversion algorithm. Themodel accords to the actual subsurface situation and can be used as the basis of thewell logging interpretation and evaluation.