Anticlinal Structure Modeling with Feed Forward Neural Networks for Residual Gravity Anomaly Profile Ata Eshaghzadeh1* , Roghayeh Sadat kalantari2 1) 2) Graduate student of geophysics, Institute of Geophysics, University of Tehran, Iran (eshagh@ut.ac.ir) Graduate student of geophysics, Institute of Geophysics, University of Tehran, Iran (rskalantar_eng@yahoo.com) Introduction Geologically, Anticlines are the most important geological structures amongst regional studies and hydrocarbon exploration methods. In general, inversion of gravity anomalies is non-unique in the sense that the observed gravity anomalies in a survey can be explained by a variety of density distributions. To resolve such an ambiguity, the anomalous mass should be estimated by a suitable geometry with a defined density contrast. Several forward gravity modeling schemes have been proposed for anticlinal structure. Although the exhibited methods differ in the definition of the density changes in proportion to depth, the normal isosceles triangular model is generally used to describe the geometry of this structure to analyze gravity anomalies. Since anticlinal structures have mostly two non-isocline skirt, therefore utilization of the isosceles triangular model will be accompanied by a large error in the forward modeling. We have proposed using two adjoining right triangle for resolving mentioned problem. The density has been assumed constant. In this paper, a new method for anticline structure modeling based on feed forward neural network is presented. Neural networks have been employed for interpreting well logs (Huang et al.,1996), recognizing seismic wave forms (Ashida,1996) and automatic detection of buried utilities and solid objects from GPR data (Al- Niamey et al.,2000). In addition, application of the magnetic data interpretation has been reported. In these cases, the back propagation network was used for structural interpretation of aeromagnetic data (Pearson et al.,1990), classification of buried objects from their magnetic signatures (Brown, et al.,1995) and more recently detection of tunnels from gravity data (Salem et al.2001). The network is trained by synthetic data as input and output. For feed forward neural network training we have used the back-propagation algorithm. The results indicate that feed forward neural networks, if adequately trained, can predict the 2D form of anticline structure. The proposed method was applied to gravity data from Korand in Iran. The modeling results show high similarity with the attained results from seismic operation. Method The 2D geometry of anticlinal structure is shown in figure 1. The Z-axis is positive downward and the X-axis is transverse to the strike of the respective model. d1 and d2 are the depths to the top and bottom of the model. I and j are the angles of the fold limb. The gravity anomaly g(x) at any point P(x‘, 0) on the x-axis can be deduced from the fundamental equation of a gravity anomaly due to a 2D source with cross-sectional area s (Rao and Murthy 1978) :  zdvdz s r2 g ( x)  2G  (1) 8th Congress of the Balkan Geophysical Society 5-8 October 2015, Chania, Greece Here, G is the universal gravitational constant, dv dz is the cross-sectional area of a line mass, Δρ is the density contrast and r is the radial distance from the element dv dz to the point P(x‘, 0). Substituting limits for the gravity anomalies due to each right triangle can be expressed as g ( x)  2G  d2  ( d2  d1 )cot Z  d1 v  0 zdvdz . z  (v  x)2 2 (2) Here, ψ=i and j are rightmost side right triangle and left-hand side right triangle, respectively. and x=x’-S, S is the distance of the origin of the model from the reference point, R (figure 1). The gravity anomaly based on anticlinal structure at any point on the earth is the sum of the gravity effect of the two right triangle models. Figure 1 Geometys of anticlinal structure. In this study, Feed Forward Neural Network (FNN) is used for the gravity anomaly modeling. Neural Networks are being increasingly used in prediction, estimation, and optimization problems. The method can estimate the geometric parameters of the anticline structure, including d 1, d2, i and j. Figure 2 presents simple feed forward topology where information flows from inputs to outputs in only one direction. We used a three - layer FNN; consisting of 7 neurons in the input layer, 20 neurons in the hidden layer and 4 neurons in the output layer. While sigmoid is used for the first and hidden layers, linear activation functions are used for the last layer. As for the FNN to recognize the pattern of the profile data, some parameters are defined as the input of the FNN. To train the neural network with gravity data, the point is that if all the data is applied as inputs of the network, it will have a lot of inputs, and be time consuming in training .To prevent this problem, some features (parameters) , separated first, are selected from gravity data. In other words, there must be a relation with the geometrical parameters of the anticline. These parameters or features are obtained from the gravity anomaly curve. 8th Congress of the Balkan Geophysical Society 5-8 October 2015, Chania, Greece Figure 2 Feed-forward (FNN) topology of an artificial neural network We have spot 7 parameters; the coordinate of the maximum gravity value point from the reference point, the point coordinate where the gravity value is 75% of the maximum gravity value and width of curve in these points, the point coordinate in which the gravity value is 50% of the maximum gravity value and width of curve in these points, the point coordinate in which the gravity value is 25% of the maximum gravity value and width of curve in these points (figure 3). Since there are 7 defined parameters, input layer in neural network includes 7 neurons. The outputs are geometric parameters of the anticline structure, which consists of d1, d2, i and j, so hence the output layer of the neural network contains 4 neurons. Figure 3 Defined parameters for the anticlinal structure gravity anomaly curve Artificial neural networks can be categorized into two main categories: unsupervised recurrent and supervised feed-forward networks. In the unsupervised recurrent type, the networks allow information 8th Congress of the Balkan Geophysical Society 5-8 October 2015, Chania, Greece to flow in both directions. These models are called unsupervised given the fact that there was no supervision on the set-out of the input-output mapping relation during the learning phase. In the supervised model, though, and through a set of correct input-output pairs, called the training set, the network learns the relation between the input-output pairs has been used in the back propagation algorithm for network training. Conclusions The method of artificial neural network is used as a suitable tool for intelligent interpretation of gravity data. For the first time, we have designed a feed forward neural network to estimate the gravity curve parameters based on the anticlinal structure as an innovative phenomenon. Also, a new method for the 2D gravity field computing of the anticlinal structure with various slopes has been presented. Geological information plays an important role in training data production. We have used a data set of 12800 points to train and test the neural network. From this, 8960 points (about 70% of the total data) were randomly selected for network training and the remaining 30% of the data was used for testing the network. Each data point is a vector of seven input values as described earlier. The designed network was tested by both synthetic and real data. The validity of this method was tested using noise-free and noise-corrupted synthetic models and satisfactory results were obtained. In this paper the gravity data from Korand region, Northeast of Iran, is analyzed based on 2D modeling accomplished for the gravity anomaly as for 12 profiles. The obtained 2D models of the anticlinal structure juxtaposed and accordingly attained 3D model of anticlinal structure in the study region. The modeling results with feed forward neural network method conform to the seismic data interpretation results as well. References Al-Nuaimy, W., Huang, Y., Nakhkash, M. and Eriksen, A., 2000, Automatic detection of buried utilities and solid objects with GPR using neural networks and pattern recognition, Journal of applied Geophysics, 43, 157-165. Ashida, Y., 1996, Data processing of reflection seismic data by use of neural network, Journal of applied Geophysics,35, 89-98. Brown, M. P. and Poulton, M. M., 1996, Locating buried objects for environmental site investigations using Neural Networks, JEEG, 1, 179-188. Chakravarthi, V., Sundararajan, N., 2007. Marquardt optimization of gravity anomalies of anticlinal and synclinal structures with prescribed depth dependent density. Geophysical Prospecting 55, 571– 587. Chakravarthi, V., Sundararajan, N.,2007. TODGINV—A code for optimization of gravity anomalies due to anticlinal and synclinal structures with parabolic density contrast. Computers & Geosciences 34 (2008) 955–966 Huang, Z., Shimeld, J., Williamson, M. and Katsube, J., 1996, Permeability prediction with artificial neural network modeling in the venture gas field ,offshore eastern Canada, Geophysics, 61, 422-436. Kenji Suzuki., 2011. Artificial Neural Networks Methodological Advances and Biomedical Applications. InTech. Osman, O., Albora, A. M., and Ucan, O. U., 2007, Forward modeling with forced Neural networks for gravity anomaly profile: Math. Geol., 39, 593-605. 8th Congress of the Balkan Geophysical Society 5-8 October 2015, Chania, Greece Pearson, W., Wiener, J. and Moll, R., 1990, Aeromagnetic structural interpretation using neural networks” A case study from the northern Denver-Julesberg Basin”, Ann International Meeting, Soc. Expl.Geophysics, Expanded abstract, 587-590. Rao, B.S.R., Murty, I.V.R., 1978. Gravity and Magnetic Methods of Prospecting. Arnold-Heinemann Publishers, New Delhi, India, 390pp. Salem, A., Elawadi, E., Abdelaziz, A., Ushijima, K., 2001, Imaging subsurface cavities from microgravity data using Hopfield neural network, Proceeding of the 5 th SEGJ International Symposium,Totyo, 199-205. 8th Congress of the Balkan Geophysical Society 5-8 October 2015, Chania, Greece