Three-dimensional gravity inversion based on improved FCM clustering algorithm

In gravity inversion, traditional inversion methods usually generate smooth inversion results, that is, there are no obvious boundaries between different geological units. Fuzzy C-Means (FCM) algorithm is introduced into the inversion to solve the problem mentioned above to improve the accuracy and spatial resolution of inversion results. However, when the volume of an anomalous body is much smaller than that of the surrounding rock, and the weight coefficient of the FCM clustering term in the objective function is not selected properly, the algorithm is prone to cause uniform shrinkage of the anomaly inversion results, resulting in lower inversion accuracy, or even failure of the inversion.The main reason for the inversion failure is usually because the total volume of the anomalous bodies is much smaller than the volume of the surrounding rock.For this reason, in this paper, the scaling factor is introduced into the FCM clustering term of the objective function to balance the membership degree of the model parameters to each cluster, so as to reduce the influence of small anomalous body volume compared with the surrounding rock volume. By establishing a simple positive correlation between the scaling exponent e_k and the distance s_normal from the normalized clustering center and the real clustering center, the scaling factor ρ_k is continuously updated during the inversion process, which significantly reduces the difficulty in selecting the weight coefficient of the FCM clustering term in the objective function, and avoids the problem of volume shrinkage of the inverted anomalous bodies, thus enhancing the stability of the inversion. The numerical experiments of inversion with theoretical gravity anomaly data and actual data inversion show that the improved algorithm has higher inversion stability and accuracy compared with the previous FCM method.