As a first step towards the fast inversion of geophysical data, in this work we focus on the rapid simulations of 2.5D logging-while-drilling (LWD) borehole resistivity measurements. Given a commercial logging instrument configuration, we calibrate the FE method offline with respect to (i) the element sizes via non-uniform tensor product grids; (ii) the arbitrary polynomial order of approximation on each element; and (iii) the interpolation of certain Fourier modes. This leads to the design of proper FE discretizations to simulate measurements acquired in an arbitrary 2D formation.Numerical results show that we accurately simulate on a sequential computer any field component at a rate faster than one second per logging position.

The Marie Sklodowska-Curie grant agreement No 644602 MTM2013-40824-P SEV-2013-0323 BERC 2014-2017