2D Resistivity Inversion Using Spectral Parameterization

In this study, we have introduced a novel 2D electrical resistivity inversion method based on spectral parameterization that uses a complex Fourier series to image subsurface resistivity. Decomposing the resistivity into frequency components enables the efficient computation of stiffness and sensitivity matrices, which are crucial for electric field modeling and inversion. We defined a virtual current source at every model grid point to calculate the partial differentiation of the electric potential during inversion. The inversion process uses the Gauss-Newton method to update the Fourier coefficients iteratively, with a sensitivity-based weighting scheme that dynamically adjust the influence of each data point. This ensures greater resolution in high-sensitivity areas while maintaining stability in less sensitive regions. To validate the method, synthetic numerical experiments were conducted to compare it with traditional block parameterization. This simplifies the model by dividing the subsurface into homogeneous blocks. Although block parameterization offers computational efficiency, the spectral method has superior resolution and convergence in complex geological environments.