Study on 3-D resistivity inversion using conjugate gradient method

We present a 3-D minimum structure inversion algorithm for d.c. resistivity data, using conjugate gradient (CG) relaxation techniques. Firstly, the mi nimum structure inverse equations are solved. In doing so, the CG relaxatio n technique only requires the results of derivative matrix G and its transp ose G(T) multipled by a vectors, i.e. Gx and G(T)y, respectively. Then the Rodi method is introduced to compute, and the Jcobian matrix G, Gx and G(T) y can be got after one forward calculation in each inverse iteration. There fore, only one forward calculation is required in each inversion iteration, the inversion is computed much quickly. Additionally, we are able to bypas s the actual computation of the derivative matrix G and the inversion of G( T)G, also to avoid the huge storage for G and G(T)G. On the other hand, sin ce there are so many inversion parameters, we impose a smoothness constrain t on the model in minimum structure inversion to solve the smoothest soluti on which effectively erases unnecessary structures, obtains trustworthy res ults close to true model. We firstly merge these methods and techniques int o 3-D resistivity inversion and obtain very promising results, which have b een tested on 3-D synthetic data. A new iterative technique is also, develo ped to deal with the problem of very slow convergence rate in traditional m inimum structure inversion, it shows that only about ten iterations or less are required to reach the convergence.