Three dimensional Born geometrical factor of multi-component induction logging in anisotropic media

Abstract

Geometrical factor has been widely used in the design of induction tool and analysis of complex logging responses, as well as the high resolution processing of logging data. Works in this area are usually limited to two-dimensional isotropic medium and are only available to cases of coaxial transmitter and coaxial receiver coupling. For a more thorough understanding of multicomponent induction logging in the presence of transverse anisotropy, a knowledge of anisotropic geometrical factor is often necessary. In this paper, the two-dimensional and isotropic geometrical factors are extended to the anisotropic media using Born approximation, and the expressions of 3D Born geometrical factors for multicomponent induction logging are derived. Then the sensitivity and detectability of coaxial, coplanar and cross-coupling measurements are investigated. Numerical results show that with increasing coefficients of conductivity anisotropy, the spatial distribution of geometrical factors becomes increasingly complicated, and more sensitivity information can be detected by multicomponent induction tools. The multicomponent induction tool is sensitive to conductivity anisotropy at arbitrary dipping angles. In vertical wells, coplanar measurements are significantly affected by the conductivity anisotropy. Compared with coaxial and coplanar measurements, cross-coupling component offers superior sensitivity information to the conductivity anisotropy with the dipping angle being 40～ 60°. In horizontal wells, coaxial measurements are the most sensitive to the conductivity anisotropy. The extended 3D Born geometrical factor directly exhibits the anisotropy sensitivity in terms of spatial contribution, and has made up for the shortage of previous geometrical factors. The new geometrical factor will create favorable conditions for the development of new multicomponent induction tool and the interpretation of anisotropic formations.

Detection Performance Analysis of Array Dielectric Dispersion Logging Based on Sensitivity Function

“…G ( r , r ′ ) is a green function contributed to a receiving signal from an abnormal body; it can be calculated by placing a dipole source at r ′ and computing the response at r . The expression of the primary field and green function in the homogeneous formation can be derived analytically [ 35 ]. The voltage in the receivers can be expressed as follows: …”

“…Tølbøll then investigated the detection sensitivity of different dipole systems based on the Fréchet derivatives [ 34 ]. Wang et al extended the Born geometric factor to the anisotropic formation and simulated the spatial distribution characteristics of geometric factors of multicomponent induction logging [ 35 , 36 ]. The operating frequency of electromagnetic logging is generally high, and resistivity is calibrated using attenuation and phase shift.…”

Detection performance and inversion processing of logging-while-drilling extra-deep azimuthal resistivity measurements

“…As a powerful tool for the analysis of the detection performance of induction logging measurements, the geometrical factor (GF) is capable of providing the relative contributions of formation units to measured signals (Wang et al 2015). However, current GF theory is only available for the voltage signal and is not applicable to the attenuation and phase-shift signals.…”