3D magnetic inversion based on probability tomography and its GPU implement

There are two types of three-dimensional (3D) magnetic inversion methods based on the classification of the inversion result, one is the inversion approach that determines a 3D susceptibility distribution that produces a given magnetic anomaly, and the other is to inverse the source distribution in a purely probabilistic sense, in which the inversion results are equivalent physical parameters between +1 and −1. The second method is easier and more stable, but obtaining the susceptibility directly to recognize certain lithology is often more desirable. Furthermore, it is difficult to add an external geological constraint in the second method for reducing the nonuniqueness of magnetic inversion. Herein, we propose an iterative method to inverse the susceptibility based on the second method. The proposed method obtains the perturbation of susceptibility by multiplying some susceptibility with the probability tomography result of misfits in observed data and forward data given a certain susceptibility model. We present a graphic processing unit (GPU) scheme to tackle an intensive computing problem. The forward and probability function are computed in parallel on the GPU. Incorporating reasonable parallel strategies and three key optimization steps like memory optimization, execution configuration optimization and instruction optimization, the 3D magnetic inversion in this paper on a Tesla C2050 GPU shows greatly improved efficiency compared to serial code on a 2.5 GHz CPU, with a 60-fold increase in speed especially for the large volumes of data. We design a synthetic model with two prismatic susceptibility anomalies. The inversion result of this model also proves the effectiveness of the inversion method introduced in this paper.