An approximate 3D computational method for real-time computation of induction logging responses

Over many years, induction logging systems have been used to create well formation logs. The major drawback for the utilization of these tools is the long simulation time for a single forward computation. We proposed an efficient computational method based on a contrast-type of integral-equation formulation, in which we applied an approximation for the 3D electromagnetic field. We assumed that the dominant contribution in the integral equation is obtained by the contribution around the singularity of Green's kernel. It is expected that the approximation yields reliable results when the (homogeneous) background conductivity around the logging tool is close to the actual conductivity at the location of the tool. We have developed a data-driven method to determine this background conductivity from the dominant part of the measured coaxial magnetic fields, which are mainly influenced by the conductivity at the tool sensors. For a synthetic model, the results were compared to the ones of a rigorous solution of the integral equation and show a good simulation response to small-scale variations in the medium. Further, the method was used to simulate the response of a realistic reservoir model. Such a model is created by a geological modeling program. We concluded that our approximate method was able to improve the approximation results in highly heterogeneous structures compared to the Born approximation and provide an effective medium-gradient around the tool. Our method, based on the wavefield approximation, also estimates the error, and hence yields a warning when the method becomes unreliable.