Depth and shape estimation of salt domes via interpretation of gravity data using Multi Layer Perceptron Neural Networks



In applied geophysics especially in potential methods like gravity generalized bodies are often used to represent the distribution of underground masses, as sphere, vertical cylinders, vertical prisms, horizontal cylinders, vertical faults, anticlines and synclines. In this paper Multi Layer Perceptron (MLP) Artificial Neural Networks are used to find the most probable model for a given gravity anomaly of a salt dome. Therefore a neural network is trained with anomalies produced by two different kinds of distributing bodies, producing similar anomalies. These simple models which are the most common used shapes for modelling of salt domes are Sphere and Vertical Cylinder. The trained Multi Layer Percetron Artificial Neural Network is then able to recognize the kind of body that is producing the given gravity anomaly .Throught neural networks technique the ambiguity between similar anomalies generated by different disturbing bodies can be solved without using densities. There is no classical interpretation method available, which can, for example discriminate between an anticline and a syncline without any hypotheses about the shape or density contrast of the target.It is shown here that this can be done by applying Multi layer perceptron Artificial Neural Networks for qualitative gravity interpretation. By using of this kind of Artificial Neural Networks the gravity data interpreter can do qualitative and gravity quantitative interpretation. Qualitative interpretation means to solve the ambiguity between two bodies that produce similar anomalies. In quantitative interpretation with multi layer perceptron Artificial Neural Networks, the model parameters (include depth, radius) can be achived. Sphere and vertical cylinder are the models to representing the salt domes. Therefore, as we use data gravity of humble salt dome, as a real test of the method, we will use these models for training of the neural network. By using of sphere and vertical cylinder models, we prepared, normalized and used a set of suitable features as inputs of the network. Because there is no certain rule for defining the suitable number of the neurons of hidden layer, by changing the number of neurons in hidden layer, and comparing the Sum Squared Errors in every state, we received best number for neurons for this layer. After defining these neurons, by synthetic data from artificial sphere and cylinder models, trained the network.
It is necessary to mention that the neural network was trained in the relatred domain of thre probable depth, especially for the real data that we know the geological prior information and so the approximation of the depth domain is possible.Also the training data are all normalized both inputs and outputs. The index used to evaluate the errors was sum squared error for both validation and test data. Finally by using outputs of the network used for recognition of the shape of the anomaly, and the network used for defining model parameters, we defined the shape and parameters of humble salt dome. The results for real and synthetic gravity data showed very good ability of the multi layer perceptron neural networks for estimation of shape and depth of salt domes.        


Main Subjects

- حاجیان، ع.ابراهیم زاده اردستانی،و.، لوکس،ک.، سقاییان نژاد، م.،1388، اکتشاف قنات‌های زیرزمینی مدفون از طریق شبکه‌های عصبی مصنوعی و با استفاده از داده‌های میکروگرانی‌سنجی، فیزیک زمین و فضا 35(1)، 9-15.
- حاجیان، ع.، ابراهیم زاده اردستانی،و.، ضیایی، ز.،1383، تخمین عمق بی‌هنجاری‌های گرانی با استفاده از شبکه‌های عصبی مصنوعی، کنفرانس مهندسی معدن ایران، دانشگاه تربیت مدرس.
- منهاج، م.، مبانی شبکه‌های عصبی، انتشارات دانشگاه صنعتی امیرکبیر(پلی تکنیک)، چاپ سوم 1384.
-Aghajani, H., Moradzadeh, A., and Zeng, H.,2009, Normalizd full gradient of gravity
anomaly method and its application to the Mobrunsulfide body, Canada. World Applied
Science Journal 6(3), 392-400.
-Aghajani, H. Moradzadeh, A. and Zeng, H., 2009 “Estimation of Depth to Anomalous Body from Normalized Full Gradient of Gravity Anomaly” Journal of Earth Science, 20(6),1012–1016.
- Albora A.M., Uçan O.M., Özmen A., Özkan T., 2001,Separation of Bouguer Anomaly Map Using Cellular Neural Network, Journal of Applied Geophysics,46,129-142.
- Burr, D. J., 1987, experiments with a connectionist text reader, in proceedings of a first international conference on neural networks, San Diego, CA., 4, 717-724.
- Cottrel G. W., Munro, p., and Zipser, D., 1987, image compression by backpropagation, an example of extensional programing. Advances in cognitive science, 3, 78-89.
- Gret, A. A., Klingele, E. E., 1998, Application of Artificial Neural Networks for Gravity Interpretation in Two Dimension, Report No.279, Institute of Geodesy and Photogrammetery, Swiss Federal Institute of Technology, Zurich.
- HajianA., Ardestani V.E., Lucas C. 2011, Depth estimation of gravity anomalies using Hopfield Neural Networks, journal of the earth & space physics,37(2),1-9.
- McCuloch, W., and Pitts, W., 1943, A logical calculus of the ideas immanent in nervous activity, Bulletin of Mathematical Biophysics., 5, 115-133.
- Menhaj, M.B., 1999, Application of computational intelligence in control, first edition, professor Hesabi publishers, 236, (in Persian).
-Nabighian, M. N..GrauchV. J. S, HansenR. O. , LafehrT. R. , Li1,Y. PeirceJ. W. ,
PhillipsJ. D., and RuderM. E., 2005, The historical development of the magnetic method in exploration, Geophysics, 70(6), 33–61.
- Osman O., 2006, A new approach for residual gravity anomaly profile interpretations: Forced Neural Networks (FNN), Annals of Geophysics, 49(6).
- Osman O., AlboraA. M., UcanO. N.,2007, Forward Modelling with Forced Neural Networks for Gravity Anomaly Profile, Journal of Mathematical Geology, 39,593-605.
- Parker, R. L., 1977, Linear inference and under parameterized models, ReviewGeophysics, 15, 446-456.
- Parker, D. B., 1982, Learning logic: invention report, office of technology licensing, Stanford University, 1, 64-81.
- Parker, D. B., 1987, Second order back propagation. Implementing an optimal O(n) approgsimation to newton's method as an artificial neural network: MIT Press, 1, 318-362.
- Rumelhart, D. E., Hinton, G. E., and Williams, R. J., 1986, Learning internal representations by error propagations: Parallel distributed processing, MIT Press, 1, 318-362.
- Salem, A., and Ushijima, K., 2001, Detection of cavities and tunnels from gravity data using a neural network, exploration geophysics,32, 204-208.
- Sejnovski, T. J., and Rosenberg, C. R., 1987, Parallel networks that learn to pronounce English text: Complex systems 3., 145-168.
- Salem A., 2011, Multi-deconvolution analysis of potential field data, Journal of Applied Geophysics, vol. 74, p. 151-156.
- Salem, A. and Elawadi, E., and K. Ushijima2003, Short note: Depth determination from residual gravity anomaly using a simple formula; Computer and Geosciences, 29, 801-804.
- Werbos, P. J., 1974, Beyond regression: New tools for prediction and analysis in the behavioural sciences, Master thesis, Harvard University.