2D inverse modeling of residual gravity field using modular feed forward neural network: A case study; a chromite mine

One of the most important aspects of mineral deposit exploration is depth estimation values of the mineral masses. Gravity method is used widespread for detection of mineral deposits. A new approach is presented in order to interpret residual gravity anomalies due to simple geometrically shaped bodies such as horizontal cylinder, vertical cylinder, and sphere. This approach is mainly based on using feed forward modular neural network (MNN) inversion for estimating the shape factor, depth, and the amplitude coefficient. The sigmoid function has been used as the activation function in the MNN inversion. The new approach has been tested first on synthetic data from different models using only one well-trained network. The results of this approach show that the parameter values estimated by the modular inversion are almost identical to the true parameters. Furthermore, noise analysis has been made. The inversion of noisy data produces satisfactory results for the data up to 5% of random noise. The reliability of this approach is demonstrated for real gravity field anomalies taken over a chromite deposit near Sabzevar City, Khorasan Province, Iran.

Forward modeling plays an important role in gravity data interpretation. Gravity data interpretation aims mainly to estimate the depth and location of the causative target. It is known that the gravity data interpretation is non-unique where different subsurface causative targets may yield the same gravity response (anomaly); however, a priori information about the geometry of the causative target may lead to a unique solution (Roy et al., 2000; Aboud et al., 2004). Neural networks (NNs) provide means to build mathematical models that relate input data to desired output data. The neural networks do not know the physics of the forward problem; they have only catalogs of the input/output pairs of the forward mapping that have been fed to it. In this paper, MNN inversion is used mainly to compute the depth and the shape factor of the causative target from a gravity anomaly. NNs can offer a unique solution, especially for noisy data, when acknowledge of a task is not available or unknown nonlinearity between input and output may exist (Bhatt and Helle, 2002; Al-Garni, 2010).

NNs can be considered as universal approximation which can approximate any function in terms of its variables. Generally, a NN is fed by a training set of a group of examples from which it learns to estimate the mapping function described by the example patterns. NNs algorithms may be divided into two main groups, which are supervised (associative) learning and unsupervised (self-organization) learning. The supervised learning is based on desired outputs. During the training, the NN tries to match the outputs with the desired values. In unsupervised learning, the method is not given any target value where the desired output of the network is unknown. During the training, the network performs some kind of data compression such as dimensionality reduction or clustering. The NN inversion that has been used for training is based on the MNN architecture. A MNN is characterized by a series of independent NNs moderated by some intermediary. Each independent NN serves as a module (local expert) and operates on separate inputs to accomplish some subtask of the task that the network wishes to implement (Azam, 2000). The outputs of the modules are mediated by an integrated unit called gating network, which does not permit to feed information back to modules.

NN inversion of gravity data over simple geometric shaped bodies such as sphere, horizontal cylinder, and vertical cylinder has been investigated in this paper. MNN inversion has been used in order to obtain three parameters: shape factor, depth, and amplitude coefficient. This approach has been tested first on synthetic data using only one welltrained network, and then, on a field example taken from Sabzevar area, Iran. The results show the upper and bottom depths of the ore body are about 8 m and 32 m, respectively.