High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Wide-Band Numerical Solution and Examples

Abstract

We present a new, accurate, high-performance, wide-band three-dimensional (3-D) solver for the electromagnetic (EM) field scattering problem in an isotropic earth. The solver relates to those based on the volume integral equation (IE) approach and exploits a modified Neumann series (MNS) technique to solve Maxwell's equations. The solver allows for the conduction, polarization and displacement currents to be taken into account and admits for 3-D earth excitation by arbitrary electric or/and magnetic sources. We estimate the solver efficiency for scatterers discretized into Nx × Ny × Nz prisms, where it requires only about 6NxNyNz (log2(2Nx) log2(2Ny) + 6Nz) multiplications to get one term of the MNS expansion and about 200 NxNyNz2 bytes of memory. Our experience show that the number of terms N which are to be summed up to get the solution to 1% accuracy doesn't exceed fifty for the models with the conductivity contrast of up to 100. We demonstrate the solver versatility for magnetotellurics (MT) and controlled-source simulations. EM fields arising from a 3-D model with two high-contrast thin layers residing in layered earth were simulated due to a 10 Hz electric dipole located at the surface. When the layers were discretized into 16, 384 prisms our code on a Pentium-100 MHz took T ∼ 58 minutes, M ∼ 7 Mbytes and N ∼ 280. We also modeled the 0.1 Hz and 0.01 Hz MT responses within 3-D model with 1 Ω·m and 100 Ω·m blocks. When the blocks were discretized into 8, 000 prisms the code took T ∼ 5 minutes, M ∼ 8 Mbytes, and N ∼ 25. Finally fields for a crosswell model including a 3-D conducting target were simulated for 0.1 kHz and 10 kHz electric and magnetic dipoles in the wellbores. While the target was discretized into 6, 250 prisms the code took T ∼ 16 minutes, M ∼ 13 Mbytes, and N ∼ 24. All simulations showed from very good to excellent agreement with those of the other 3-D solvers.