Fast Numerical Calculation Method Of Array Induction Logging Response

Induction logging plays an important role in the resistivity logging field. With the development of logging technology, the array induction logging tool, which can provide higher resolution, deeper depth of investigation, clearer invasion indications and richer formation information, has become the primary tool of resistive logging. This dissersation will apply the numerical mode matching method (NMM), which is a fast forward tool for calculating the electric logging response, to calculate the response of the array induction logging. A fast forward code is developed by making use of the characteristic of multi-array and multi-frequency of the array induction logging. The result has an important practical significance in many aspects of the array induction logging response. Such as fast calculating and interpreting of the logging response, fast inversion based the fast forward data. The contents include the follow three aspects.Firstly, according to the rotational symmetry of the vertical borehole formation, beginning from the Maxwell equation, the two-dimensional electric field distribution generated by a transmitter coil and all the formula of NMM method are derived. According to theory of induction logging, the electric field distribution of the receiver coil is converted to the formation conductivity, that is the tool response.Secondly, the selection of basis functions in NMM and the formation and solution of the eigenvalue equation are discussed. Based on the eigenvalue equation the forming and assembling of matrix Am&Bm are derived. How to use the already formed matrix to solve the symmetric matrix eigenvalue problem is given. It can use the known method. For example, the Jacobian matrix method can be used to solve the eigenvalue and eigenvectors.Finally, the NMM is applied to the array induction logging to analyze the basic response characteristics of the array induction logging in the inhomogenous formation. The formation includes borehole, invade, and shoulder. The results have the theoretical significance on the logging response analysis and tool design. When the NMM is used to the case that there is high resistivity contrast between invasion and formation due to the low resistivity mud invasion, the problems of deviation or even error of the results are studied in detail. The answer is attributed to three factors:the form of radial meshing grid, the number of basis functions established under a certain precision, and the radial grid node position. For the above three factors, we propose the improving method and program the computer code. The results show the all array responses calculated by the improving way are reasonable, reflect accurately the formation conductivity distribution information. It provides the correct data for the study of response characteristics and data process in the array induction logging. In addition, in the new code the features of the multi-array and the multi-frequency are taken into account. It improves the computing speed.