Estimation of depth and shape of subsurface cavities via Multi Adaptive Neuro-Fuzzy Interference System using Gravity data

In common classical methods of cavity depth estimation through microgravity data, usually when a pre-geometrical model is considered for the cavity shape, the simple geometrical models of sphere, vertical cylinder and horizontal cylinder are commonly used. It is obviously an important fact that in real conditions the shapes of the cavities are not exactly sphere, horizontal cylinder or vertical cylinder but are near or to some extent near to these simple models. The linguistic variables “near to” or “to some extent near to” are consisting of fuzzy concepts and can be described as “fuzzy” variables. The membership degree of each fuzzy variable shows how much the variable is near to the mentioned simple shapes. Using the fuzzy variables leads to better results with more accuracy because in real conditions the nature of the cavities shape is “fuzzy” so that their shape is not exactly but near to the mentioned simple shapes. Consequently, in this paper in order to help the gravity data interpreter to enhance the accuracy of his/her interpretation a neuro-fuzzy model namely Multi Adaptive Neuro-Fuzzy Interference System (MANFIS) is used. When the neural network alone is used the challenge is its black-box operation so that there is no possibility for sensitive analysis but neuro-fuzzy networks consist of the sensitive analysis via the if-then fuzzy rules achieved during the training process. In Multi Adaptive Neuro-Fuzzy Interference System, the network output before the de-fuzzification stage, shows the interpreter how much the cavity shape is near to sphere, horizontal cylinder or vertical cylinder. In this research, two Adaptive Neuro-Fuzzy Interference System (ANFIS) models were paralleled to configure a Multi Adaptive Neuro-Fuzzy Interference System (MANFIS) so that one output of the designed MANFIS is the shape factor and the other is the depth of the cavity. The inputs of the MANFIS are some of the important features selected from the gravity signal along the selected principle profiles of the residual gravity map. In order to evaluate the designed MANFIS in the presence of noise in gravity data, the method was tested for synthetic data with 5% and 10% level of noise. The results showed that the joint neural networks and fuzzy logic makes it a suitable tool to help the interpreter to improve the accuracy of shape and depth estimation of cavities. Furthermore, the method is more robust to noise which were tested for two different noise levels one with low level of noise and other with medium level of noise added to the synthetic gravity data. Despite the available classical methods or net neural methods, here without any pre-assumption about the shape of the cavity, both the shape factor and depth are estimated. In is necessary to mention that the value of the estimated shape factor implies that which of the geometrical models among sphere, vertical cylinder or horizontal cylinder are better fitted to the real shape of the subsurface cavity. After checking and confirming the accuracy of the designed MANFIS for synthetic data, the method was tested for real data through micro-gravity data over a gravity site located in Great Bahama Free Port, west of North America. The results are very near to the available borehole and extracted data.