Use of wavelets in marine controlled source electromagnetic method for geophysical modeling

Wavelets gained significant attention in science and engineering disciplines due to their remarkable data analyzing capabilities. Wavelets are also used for finding numerical solution of various engineering and geophysical problems. Marine controlled source electromagnetic (CSEM) method is a relatively new geophysical technique used to explore petroleum reserves from shallow and deep water. This work attempts to use periodic and non-periodic wavelets in CSEM for modeling of geophysical problem. This is results in a solution with multi-scale approximations using multiresolution analysis (MRA) algorithm. In this work, Daubechies wavelets are used, as the basis functions for solving the wave equation of marine CSEM, because of their orthonormality and compact support. Accuracy of the proposed method for marine CSEM is determined by comparing the results with the analytical solution for isotropic problem as well as those obtained using finite element (FE) method. Numerical results show that the governing equations for aforementioned geophysical method yield less obscure results than that of finite element method, for both bounded and unbounded domains. Furthermore, the proposed wavelet based numerical method produces multi-scale approximation that would prove useful for further analysis and data processing.