DETERMINATION OF EARTH RESISTIVITY PROFILE IN MULTILAYER SOIL

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1 DETERMINATION OF EARTH RESISTIVITY PROFILE IN MULTILAYER SOIL I.T.Dharmadaa, Prof.J.R.Luca, Dr.L. Udawatta, Eng.W.D.A.S Wijayapala Department of Electrical Engineering, Univerity of Moratuwa, Sri Lanka BACGROUND Reitivity i a fundamental property of a material. Thi afford an opportunity of ditinguihing one type of material from another. Main intention of Geophyical reitivity urveying i to interpret the uburface condition for engineering application. The reitivity of the oil varie widely from ite to ite and alo change eaonally. In practice, the earth exhibit a far from uniform tructure. Often, the tructure will have reitivity layer related to the phyical layer uch a topoil, ub-oil, and bedrock. Clearly thee layer or diviion in oil tructure will have a coniderable impact on both oil reitivity and earth reitance/impedance. Thi aniotropy found in platy tructure will reult in an apparent reitivity which varie from location to location. The reitivity imaging method ue tandard array developed for electrical reitivity ounding and profiling technique. Four electrode are ued in line at a time. Two inject current into the ground and two read the electrical potential between them. A et of field meaurement are obtained by varying the pacing of the electrode array. The hort pacing look at the hallow earth and the longer pacing look more deeply. Typically ued uch array are Wenner and Schlumberger array. The field data contain apparent reitivity value and geometry information. Thee data are then inverted to produce a one dimenional plot of reitivity value i.e. thickne and earth reitivity of each layer in a horizontally tratified multilayer earth tructure. Such analyi method include Graphical method requiring interpolation and judgment and computer baed iterative calculation method [1, 2]. However thee interpretation are influenced by the initial model parameter. A poor gue of initial parameter reulted in an erroneou parameter etimation. Neural Network are capable of olving everal type of problem, including parameter etimation, parameter prediction, pattern recognition, claification and optimization. Alo recently the ue of Neural Network in the Geophyic parameter etimation problem ha hown trong reult [3,4]. In the preent tudy Neural Network i propoed a the inverion tool for parameter etimation in the 1D cae. OBJECTIVES AND METHODOLOGY The objective of the preent tudy i to develop a uer friendly oftware tool with fat repone, at low cot to addre the current requirement uing Artificial Intelligence concept. The invere problem of the Geophyical Reitivity Method i olved with the Neural Network approach. Back propagation i ued a the learning rule. Two paradigm of the back propagation i.e. Scaled Conjugate Gradient(SCG) and Reilient

2 backpropagation (Rprop) are ued to evaluate on the bet performing algorithm. The MatLab7 wa ued a the oftware tool for the modeling of the Neural Network and generation of ynthetic data. Several MatLab 7 command and function available in the Neural Network Tool Box i ued for the program written. Two Neural Network are propoed in the inverion procedure. Firt Network will Identify the curve type and will pa on the input to the econd network to determine the 1D parameter. Figure 1 how the general Network tructure ued for inverion. Figure 1 General Netwrok Architecture for 1D Inverion The network are trained with ynthetic data generated by olving the forward repone equation of the apparent reitivity meaured by a wenner array for the N- layer. Given by the generalized integral form, a 1[1+ 2 FN( a) FN(2 a) where 2λh1 N1e FN ( a) 2 a J0( λa) dλ 2λh1 1 0 N1e And Jo( λ a) - Beel function of Firt kind of order zero 2 λ h2 k1 + N 2e N 1 2 λ h2 1 + k 1 N 2e 2 λ h + 1 k + N+ 1e N 2 λ h k N+ 1e N k and N k1, k, k N

3 1800 example of apparent reitivity curve are generated at 40 electrode pacing (a) of the Wenner Array ranging from 1m to 400m in ucceive tep. Anderon (1969) 801 Digital linear filter operator i ued to olve above numerical integration (Hankel Tranform) [5]. The performance of a particular network depend cruicially on the optimal network architecture. The number of input and the number of output are problem dependent, while the number of hidden layer and the hidden neuron will decide on the network generalization and abtraction capabilitie for the pecific problem. The optimal network architecture for the preent work wa finalized on monitoring the training, teting and the validation error of the network during the training phae. The network optimization reult with the network performance for the curve identification network i given in figure 2 and Figure3 below. Figure 2 Training Performance for the Training Function Trainrp and Traincg with different no of hidden node (ingle hidden layer) Figure 3 Training,validation and Tet performance of the finalized Network

4 RESULTS To evaluate the Network performance on claification of the curve type the trained network with a ingle hidden layer with 43 hidden node uing the Reilient Backpropagation i ued. Tet data point with 2 for each curve type are ued from the 150example tet data et for the performance evaluation. The network performance on the ame tet ample i evaluated with adding white Gauian noie. Curve Identification reult for Three Layer Type A curve i given in Figure4 for noiy and noiele ynthetic field data. Figure 4 Curve Identification neural Network repone for Three Layer Type A curve To evaluate the Network performance on determining three-layer parameter the trained network with two hidden layer with 50 and 35 hidden node uing the Reilient Backpropagation i ued. Parameter Etimation reult of the Three Layer oil tructure with the finalized neural network i given in Figure 5 and Table 1. Figure 5 Three Layer Type A (ample 61) Neural Network Repone and Actual Data

5 Table 1 Three layer type A network output for ample 61 Parameter Deired Value Network Repone Sample 61 P P P h h REFERENCES [1] SEEDHER, H.R., ARORA, J.., Etimation of two layer oil parameter uing finite wenner reitivity expreion, IEEE Tranaction on Power Delivery, Vol. 7 No. 3, pp [2] ]YANG, H., YUAN, J., ZONG, Y., 2001 Determination of three-layer earth model from wenner four-probe tet data,ieee Tran.Magn.,Vol. 37 No. 5,pp [3] POULTON, M.M., STERNBERG, B.., GLASS, C.E., Location of uburface target in geophyical data uing neural network, Geophyic, Vol. 57 No.12, pp [4]CALDERON-MACIAS, C., SEN, M.., STOFFA, P.L., 2000, Artificial neural network for parameter etimation in geophyic, Geophyical Propecting, Vol.48, pp [5] BRIAN BORCHERS, Department of Mathematic, New Mexico Tech Socorro, NM 87801

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