3D Gauss-Newton Inversion of CSEM Data with Grid Shaking

The best 3D CSEM inversion codes, like Gauss-Newton, solve the normal equations at each iteration. This is very numerically intensive. The memory requirements and number of numerical operations can be reduced by model compression, where interpolators are used to link the model grid to a reduced number of parameters. Rather than keeping the interpolators constant, we allow them to change at each iteration. In our case, compression is obtained by using an inversion grid much coarser than the model grid, and the change of interpolator simply consists in changing the position of the corner of the coarse grid. We call that approach grid shaking. It allows to increase the degree of compression without affecting resolution. We show an example of 3D inversion of CSEM data where the size of the inversion cells is multiplied by 3 in all directions. This reduces the number of parameters with a factor 27. The memory requirements are divided by about 27 and the number of numerical operations by about 40 because solving the normal equations requires less conjugate gradient iterations. Despite these high gains in numerical performance the quality of the inversion is rather increased than degraded.