Towards Real-Time 3D Modeling of Induction Logs Using an Integral Equation Method

Real-time 3D imaging of the induction log is essential for improving the decision-making process in geosteering. To fulfill this need, we investigated various strategies for reducing the computational cost for 3D modelling of induction logs using the integral equation (IE) method, including the use of iterative Krylov solver, convolution with FFT algorithm, contraction IE formulation, computation acceleration with GPUs, and domain decomposition. We present two cases example to demonstrate the implementation of IE with these strategies. In the first case, we show that the application of domain decomposition allows one to only discretize the inhomogeneous domain and save the computation cost in the case of isolated domains. We present a logging while drilling scenario on a complex model for the second case. Our implementation of the efficient IE on GPUs enables significant acceleration and allows the computation of 3D forward modelling within less than two minutes for each local 3D simulation domain with approximately two million grid cells on a laptop. The implementation of domain decomposition formulation shows a different arrangement of solving IE by decomposing the domain.