Wavelet optimized finite difference simulation for marine CSEM geophysical survey

Survey data of marine controlled source electromagnetic (CSEM) geophysical surveys is not able to proceed far without numerical modeling. Finite Difference (FD) and Finite element (FE) numerical methods are the most used techniques in geophysical modeling. These methods are reliable for complex structural media; however the computational cost is very high. The computational cost, accuracy and efficiency are reliant on sophisticated mesh structure. This paper discusses the orthogonal wavelet basis functions that give a natural framework to adapt spatial grids to localize the solution in spatial and time domain. Modeling for proper mesh structure is achieved by using wavelet basis functions called wavelet optimized finite difference (WOFD) method. In WOFD method, wavelet transform is used to determine where to coarsen/refine the grid. As a resultant, solution region will become with irregular grid point. This method will add grid points where solution is erratic and sparse where solution is smooth. Now the solution can be obtained with better accuracy and less computational cost by using finite number of terms. The efficiency of this method is assessed in terms of accuracy; computational cost and number of mesh grids for different 1D heterogeneous media. WOFD method provides new flexible numerical tool for marine CSEM geophysical modeling as discretization to local media properties. This flexibility is important and could be invaluable when the solution region is very complex.