2D wavelets Galerkin method for the computation of EM field on seafloor excited by a point source

Wavelet-based numerical method for solution of partial differential equations (PDE) is more efficient and accurate than the conventional finite difference (FD) and finite element (FE) techniques. The application of wavelet for solving the governing field equations of marine controlled source electromagnetic (CSEM) method is considered to be relatively new. Among the important properties of wavelet includes locality in space, compact support, adaptivity and orthogonality. These properties allow the wavelet-based numerical solution to provide an accurate, efficient and powerful numerical solution to PDE. In this work, a wavelet Galerkin (WG) method is proposed for the computation of EM field in two dimensional stratified layered media that is radiated by a mobile point source. The proposed method solves the wave equation of marine CSEM by using compactly supported Daubechies wavelets which are differentiable according to the requirement. The results generated are verified against with solution obtained by FD and FE methods. The distinctive features of the proposed method shows that the obtained results are close enough and it effectively approximate the solution with very less computational time as well as elapsed memory.