Fast 3D Imaging from a Single Borehole Using Tensor Induction Logging Data

There is growing interest in the development of new borehole electromagnetic (EM) induction methods capable of characterizing the conductivity distribution in the space surrounding the borehole. The main goal of this paper is to develop a method of three-dimensional (3-D) imaging from a single borehole using a tri-axial (tensor) induction instrument. The tensor instrument has a directional sensitivity, which allows finding the correct location of the 3-D resistive and conductive targets from single-hole data. Our method is based on the novel localized quasi-linear (LQL) approximation. The LQL approximation is specially designed for modeling the electromagnetic field generated with a moving transmitter, which is the case for borehole induction logging. The traditional approach to electromagnetic modeling and inversion requires multiple solutions for different transmitter positions. The LQL approximation makes it possible to run the forward and inverse problem at once for all the transmitters, which makes the inversion of the well-logging data much more efficient. Our study demonstrates that this method can be effectively used for 3-D imaging from a single borehole.