Development of the Multi-resolution Grid Modelling for CSEM

We present a new multi-resolution (MR) approach to 3D electromagnetic (EM) modelling. Initially, the approach was developed for plain wave assumption. Current work is a further extension of the MR solver for controlled-source applications. Modelling with controlled-source requires the finer grid discretization in the near source location to accurately model the rapidly varying EM fields in the vicinity of the source. On the other hand, the EM field propagates in a diffusive manner and can be sufficiently well described on a grid that becomes gradually coarser with depth. We implement a MR finite-difference scheme that allows us to decrease the horizontal grid resolution with depth. MR approach, therefore, provides a means to significantly decrease the number of degrees of freedom and hence improve on computational efficiency without significantly compromising the accuracy of the solution. In MR implementation, the full grid is represented as a vertical stack of sub-grids, each of which is a standard staggered grid. Therefore, operators and functions already developed for a simpler standard structured grid can be applied for each sub-grid. The major difficulty lies in discretizing the operators around interfaces between varying cell sizes.