| With the increasing demand for oil and gas resources,how to effectively identify and evaluate the complicated reservoirs such as thin interactive reservoirs,fractured reservoirs,and shale oil and gas has become an urgent research topic.As these reservoirs usually exhibits anisotropy,it is difficult to obtain correct conductivity information using the conventional coaxial induction logging techniques.The new multi-component induction logging(MCIL)tool consisting of a triaxial transmitting coil system and a triaxial receiving coil system can provides tensor-type measurements,offering an important tool for the exploration and evaluation of anisotropic reservoirs.It is possible to extract information such as anisotropic conductivity and stratigraphic dip from the tensor-type measurements provided by this tool.In the ideal case,many formations can be approximated as uniaxially anisotropic(also called laterally isotropic)formation,characterized by horizontal and vertical conductivity components.For the MCIL tool,both the forward modeling and inversion based on the uniaxial anisotropy assumption have been well studied.However,due to the complexity of the subsurface environment,some formations(for example,thin interacting layers with fractures crossing the layer plane)exhibit biaxial anisotropy.Such formations need to be characterized by three independent conductivity components.In the past two decades,researchers in China and abroad have investigated MCIL in biaxial anisotropic formation,but it is mainly limited to forward modeling and analysis of response characteristics.There are still many challenges to extract the biaxial anisotropic conductivity information from the original tensor type logging data.One-dimensional layered model is a simplified model commonly used in geophysical research,in which the EM field can be solved quickly using the analytical method.Formations that ignore boreholes and intrusion zones can usually be approximated as onedimensional layered models,which are often used for preliminary interpretation of measured data and selection of initial models for high-dimensional inversion.Thus,this model is important in both theoretical studies and practical applications.In this thesis,a full-parameter regularization iterative inversion algorithm of multi-component induction logging data is established based on the one-dimensional layered biaxial anisotropic formation model,in which the biaxial anisotropic conductivity of each layer and the layer interface are the parameters to be solved.Since forward modeling and sensitivity calculation is the foundation of iterative inversion,we systematically studies three parts in order: forward modeling,sensitivity calculation and inversion.In the first part(see Chapter 2 and Chapter 3),we first establish the analytical formulation for computing the electromagnetic(EM)field excited by a magnetic dipole in the layered biaxial anisotropic model using the propagation matrix method.This algorithm is then used to simulate the MCIL response in the layered crossbedding model,which can be regarded as a degenerate biaxial anisotropy model.The effects of azimuth and dip angles of the crossbedding plane on the logging response are investigated.The analytical formulation provided in this part are applicable to the case where the source and field points are in arbitrary layers,will also be used in the subsequent solution for sensitivity.In the second part(see Chapter 4 and Chapter 5),we give a fast algorithm for computing the sensitivities of the MCIL responses with respect to the formation conductivity components and the layer interfaces.The computation of sensitivity(also known as Fréchet derivative)is one of the essential steps in iterative inversion,and efficient inversion algorithms need to be based on fast computation of sensitivity.The commonly used methods based on difference approximation cannot meet the requirements of fast inversion.Therefore,an analytical solution of the MCIL response with respect to the biaxial anisotropy conductivity sensitivity of each layer is derived.Firstly,according to the perturbation analysis of Maxwell’s equation and reciprocity theorem of the EM fields,sensitivities with respect to the conductivity components are expressed as volume integrals,while sensitivities with respect to the layer interfaces are expressed surface integrals.The integrands of the two types of integrals contain two sets of electric fields.Secondly,the analytical expressions of the electric fields are substituted into the above integral expression of the sensitivities.Both sensitivities with respect to conductivity components and those with respect to interfaces can be simplified to the two-fold Fourier integral by analytical manipulation.Fourier integrals similar to the forward simulation.Finally,the Fourier integrals are calculated by numerical integration method to obtain the two types of sensitivities.A comparison with the numerical results of the difference approximation verifies the correctness of the analytical expressions of sensitivities proposed in this paper.The results also show that the analytical method is several times more efficient than the difference approximation,and the more layers the more significant the advantage.In the third part(see Chapter 6),we present the Tikhonov regularization one-dimensional full-parameter inversion algorithm to reconstruct the formation information from the MCIL data.The inversion algorithm is based on the layered biaxial anisotropic model,where the parameters to be inverted contains the biaxial anisotropic conductivity components and the interfaces.Firstly,an iterative inversion algorithm based on the basic Gauss-Newton method is developed,where the Jacobian matrix consists of the sensitivities with respect to conductivity components and the interfaces.Secondly,the Tikhonov regularization technique is introduced to ensure the stability of the iterative inversion.Finally,according to the concept of the quasi-solution,the regularization factor is selected.The value of the regularization factor is automatically adjusted during the iterative process,so that a larger regularization factor is used at the initial stage of the iterative process to enhance the stability of the inversion,and a smaller value(or a zero value)is used when the iterative process is close to convergence to speed up the convergence.The inversion results of several theoretical models show that when the appropriate initial model is selected,both the biaxial anisotropic conductivity components and interfaces can be reconstructed accurately by the Tikhonov regularization inversion algorithm. |
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