We implement a parallel algorithm with the advantage of MPI （Message Passing Interface） to speed up the rapid relaxation inversion for 3D magnetotelluric data. We test the parallel rapid relaxation algorithm with synthetic and real data. The execution efficiency of the algorithm for several different situations is also compared. The results indicate that the parallel rapid relaxation algorithm for 3D magnetotelluric inversion is effective. This parallel algorithm implemented on a common PC promotes the practical application of 3D magnetotelluric inversion and can be suitable for the other geophysical 3D modeling and inversion.
The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the data in the frequency domain, which is very suitable for parallel computation. With the advantage of MPI and based on an analysis of the flow of the 3D magnetotelluric serial forward algorithm, we suggest the idea of parallel computation and apply it. Three theoretical models are tested and the execution efficiency is compared in different situations. The results indicate that the parallel 3D forward modeling computation is correct and the efficiency is greatly improved. This method is suitable for large size geophysical computations.
Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional （3D） conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjugate gradient inversion algorithm doesn＇ t need to compute and store the Jacobian matrix but directly updates the model from the computation of the Jacobian matrix. Requiring only one forward and four pseudo-forward modeling applications per frequency to produce the model update at each iteration, this algorithm efficiently reduces the computation of the inversion. From a trial inversion with synthetic magnetotelluric data, the validity and stability of the 3D conjugate gradient inversion algorithm is verified.
