3-D resistivity inversion by the least-squares QR factorization method under improved smoothness constraint condition
用改进的光滑约束最小二乘正交分解法实现电阻率三维反演

In this paper, we have deeply studied 3-D resistivity inversion, providing a practical algorithm of \{3-D\} inversion. Using the finite difference method to solve the 3-D forward problem, we have properly improved the elements of roughness matrix in order to form the roughness matrix in different cases, setting up the inversion equation under the condition that the total roughness of the model is minimum. It is fast and stable that using the least-squares QR factorization(LSQR) algorithm to solve inversion equations. The LSQR algorithm only requires the result of the derivative matrix and its transpose multiplying vectors, therefore we avoid direct and complicated computations of the derivative matrix. The above approach reduces the need for computer memory, and speeds up the inversion calculation. Two different calculation examples show that the above approach is efficacious for solving large scale 3-D resistivity inversion.