## Abstract

We present an algorithm to compute efficiently the propagation of nonaxially symmetric waves induced by realistic eccentered sources with a mandrel in a multicylindrically layered geometry. One of the applications of such a program is in electrical well logging, where oil exploration tools operate in a borehole drilled into the ground for geophysical subsurface sensing. The borehole surrounded by an invasion zone can be modeled as a multicylindrically layered geometry. We present an algorithm to study the effect of eccentricity (source and mandrel not in the center of the borehole) in the presence of concentric invasion zones around the borehole. The fields are decomposed into their spectral components by Fourier transforming along the z axis. For each such component, the boundary conditions between two concentric layers determines a system of 2 x 2 reflection and transmission matrices. These matrices, in turn, determine the ratio of “standing” waves to “outgoing” waves in each homogeneous region. This ratio is also a 2 x 2 matrix which can be calculated recursively [21]. Using the computed ratio for the center (borehole) region, an infinite system of equations is obtained which relates the geometry of the tool with a source, and a mandrel to that of the borehole and formation. The solution of this system of equations gives the amplitudes of the fields everywhere and, in particular, the signal measured by the receivers of the tool can be computed. We use our algorithm to study the eccentricity and invasion effects on an induction measurement and a dielectric logging measurement. In the case of dielectric logging, we find that the invasion zone may cause “resonance” effects, and that these effects remain when the tool is eccentered.

Original language | English (US) |
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Pages (from-to) | 127-136 |

Number of pages | 10 |

Journal | IEEE Transactions on Geoscience and Remote Sensing |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1990 |

Externally published | Yes |

## ASJC Scopus subject areas

- Electrical and Electronic Engineering
- General Earth and Planetary Sciences