Transmission Line Method For Asimulating A Multicomponent Induction Logging Response In Transversely Isotropic Media And Its Response Characteristics

Taking the formation of layered anisotropic electromagnetic dyadic Green function as a starting point, and then basing on the theory of the transmission line (TLM) and related research, the author of this paper has first established the formula of one-dimensional layered anisotropic media magnetic current source dyadic Green function of the analytic method in this paper. Secondly, the rapid calculation of Sommerfeld integral has been studied by way of the combination of cubic spline interpolation and the Gauss-Legendre numerical integration. Making use of equipment and stratigraphic coordinate system conversed relationship in view of borehole tilt or tilt formation, the author gained the coordinate equipment magnetic current source of the magnetic field dyadic Green function. Meanwhile that multi-component induction logging extraction method is the electrical conductivity is proved. Finally, one-dimensional anisotropic layered dip hole formation, formation resistivity anisotropy coefficient, the frequency of logging work, the influence of sending and receiving coil from the line source to multi-component induction logging response.First of all, Maxwell equations of the uniform horizontal strata of the same quality is dealt with the utilizing of the techniques of Fourier transform and operator decomposition. Afterwards, the electromagnetic field in frequency domain will be broken down into two separate waves of horizontal (TE wave) and transverse magnetic (TM wave), as well as its corresponding transmission line equation. On the basis of this, TE wave and TM wave solutions are obtained through the definition of transmission line the Green function. Aso frequency domain current source and the magnetic current source of electromagnetic dyadic Green function are obtained.In the electromagnetic field in inhomogeneous media based on the results of solving, a single level of the interface transmission line Green function of current market and potential market of the reflection coefficient and transmission coefficient as well as generalized multi-layer interface and the amplitude reflection coefficient can be derived by utilizing TE wave and TM wave to satisfy the transmission line equation and boundary conditions. Thereby, the level-formed layer of anisotropic electromagnetic dyadic Green function in frequency domain is calculated with the analytical expression.In order to determine the spatial domain dyadic Green function, a fast and efficient new algorithm for Sommerfeld integral is established, which fully resolved the problem of the formation of layered anisotropic dyadic Green functions of electromagnetic field calculation. This establishment is based on the using of inverse Fourier transform formula for the space domain dyadic Green function into a series of Sommerfeld type integral, combined with the using of cubic spline interpolation theory and Gauss-Lengendre ---a combination of numerical integration.Simulation results show that the Department of coplanar coil axis of a circle is more complex than the Department which responds to a total of much. The result that low-resistant layer in a large number is in negative response, and that it is difficult to understand from the true formation of the curveσ_{a, x'x'} resistivity changes are included. However, it can effectively reflect the formation of the resistivity changes in the vertical level. The shorter is the distance of the curveσ_{a, z'z'} from the source, the bigger is the reduced vertical resolution. The causes why this phenomenon is produced are mainly due to the accumulation of the surface charge around the border so that a negative correlation is produced between the formation ofσ_{a, x'x'} and the conductivity. It is frequently seen when the strate is relatively thin. Increasing frequency will lead to a decline of the electrical conductivity as a whole and an increase in vertical resolution, which is caused by the increase of the skin effect. The changes of angle inclination have great impact on all three apparent conductivities. Evidently the larger the angle inclination with the borehole is, the larger the responseσ_{a, x'x'} andσ_{a, y'y'}of coplanar coil system is and correspondingly the less the negative response gradually is. However, in response to the gradual reduction of a total value of the axis line circle, the results show that when the angle increases the the impact of level electrical conductivity of the Department of coplanar coil increases, but the total impact to the axis line circle system reduces . At the same time we can see that angle inclination changes in borehole can affect apparently more the apparent conductivity at low resistivity zone than the apparent conductivity in resistive formation.