Inversion imaging of 3D resistivity detection using adaptive-weighted smooth constraint and PCG algorithm

Three-dimensional resistivity detection is increasingly concerned in actual projects. However, its application and extension is excessively restricted because of some key problems such as low deep resolution and low inversion efficiency. For the problem of low deep resolution, an adaptive-weighted smooth constraint is proposed, which is adjusted adaptively to the mesh size in a three-dimensional model. It improves resistivity difference tolerance of deep grids and achieves difference weighted processing of grid constraints at different depths. With the adaptive-weighted smooth constraint, the deep resolution and inversion imaging quality are improved effectively. For the problem of time-consuming and low inversion efficiency in inversion, a rapid and stable method of 3D resistivity inversion and imaging based on preconditioned conjugate gradient (PCG) algorithm is proposed. The diagonal matrix in Jacobi iteration is used as the preconditioned matrix for speeding up the convergence speed significantly. The inversion of the preconditioned matrix is convenient to be solved and doesn’t occupy memory spacing. At last, the inversion method is applied in a synthetic example and water flowing fracture detection in tunnel engineering for checking its feasibility and effectiveness. The results show that the deep resolution, calculation efficiency and inversion quality of 3D resistivity detection are improved effectively by using the adaptive-weighted smooth constraint and the PCG algorithm.