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Fig. 3. Comparison of the measured/predicted R; values from the model ANN-2 for a) training samples, and b) testing and validation samples In this study, apart from RMSE, the performance indices (i.e., variance account for, VAF, which is represented by Eq. (10), mean absolute error, MAE, determination coefficient, R?) were also computed to assess the performance of the developed models 29,61-64]. In Eq. (10), var denotes the variance, y is the measured Multiple regression analysis (MRA) was performed to predict Re from its Rr and its saturation state (S;). To achieve this, two MRA models (MRA-1 and MRA-2) were developed by using SPSS 8.0.0. The experimental data for the onshore and offshore samples (refer Tables 1 and 2) and the data reported by Sreedeep et al. [18] and

Figure 3 Comparison of the measured/predicted R; values from the model ANN-2 for a) training samples, and b) testing and validation samples In this study, apart from RMSE, the performance indices (i.e., variance account for, VAF, which is represented by Eq. (10), mean absolute error, MAE, determination coefficient, R?) were also computed to assess the performance of the developed models 29,61-64]. In Eq. (10), var denotes the variance, y is the measured Multiple regression analysis (MRA) was performed to predict Re from its Rr and its saturation state (S;). To achieve this, two MRA models (MRA-1 and MRA-2) were developed by using SPSS 8.0.0. The experimental data for the onshore and offshore samples (refer Tables 1 and 2) and the data reported by Sreedeep et al. [18] and

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Details of the onshore samples.
Details of the onshore samples.
distribution characteristics of these samples, dry-sieving, and whenever required hydrometer analysis, was conducted [52]. The specific gravity G of these materials was determined by using an Ultra-pycnometer (Quantachrome®, USA), which employs Helium gas [53]. For the sake of generality, six tests were conducted on each soil sample and the average value was considered as the repre- sentative G, as listed in Tables 1 and 2 for the onshore and offshore samples, respectively. The sulphite and chloride contents of onshore samples are found to be 5-10 ppm, and 25-50 ppm, respectively. However, for the offshore samples the sulphite and chloride contents are quite high (5-10 ppm, and 500-1000 ppm), respectively. These samples were also tested for Re and Ry, respectively, as described in the following, and the results are presented in Table 1 and Table 2, respectively. Fig. 1. The setup used for determining electrical resistivity of the soil sample.
distribution characteristics of these samples, dry-sieving, and whenever required hydrometer analysis, was conducted [52]. The specific gravity G of these materials was determined by using an Ultra-pycnometer (Quantachrome®, USA), which employs Helium gas [53]. For the sake of generality, six tests were conducted on each soil sample and the average value was considered as the repre- sentative G, as listed in Tables 1 and 2 for the onshore and offshore samples, respectively. The sulphite and chloride contents of onshore samples are found to be 5-10 ppm, and 25-50 ppm, respectively. However, for the offshore samples the sulphite and chloride contents are quite high (5-10 ppm, and 500-1000 ppm), respectively. These samples were also tested for Re and Ry, respectively, as described in the following, and the results are presented in Table 1 and Table 2, respectively. Fig. 1. The setup used for determining electrical resistivity of the soil sample.
Table 1 (continued ) analysis (MRA). In ANN models, network training was accom- plished with the neural network toolbox written in Matlat environment [50]. While, the Levenberg-Marquardt [50] and the Scaled Conjugate [51] learning algorithms were used in the training stage. Details of the experimental investigations, whict have yielded the data used in both models, are presented in the following section.
Table 1 (continued ) analysis (MRA). In ANN models, network training was accom- plished with the neural network toolbox written in Matlat environment [50]. While, the Levenberg-Marquardt [50] and the Scaled Conjugate [51] learning algorithms were used in the training stage. Details of the experimental investigations, whict have yielded the data used in both models, are presented in the following section.
Details of the offshore samples. Table 2
Details of the offshore samples. Table 2
Rg and Rr of the soils used by Sreedeep et al. [18] and Abu-Hassanein [11].
Rg and Rr of the soils used by Sreedeep et al. [18] and Abu-Hassanein [11].
Table 3 (continued ) -: Data not available.
Table 3 (continued ) -: Data not available.
Boundaries of the parameters used for the models developed. Table 4
Boundaries of the parameters used for the models developed. Table 4
The details of the optimal performance of the ANN-1 model. Table 5
The details of the optimal performance of the ANN-1 model. Table 5
The details of the optimal performance of the ANN-2 model. Table 6
The details of the optimal performance of the ANN-2 model. Table 6
Connection weights and biases of the best ANN models selected. Table 7
Connection weights and biases of the best ANN models selected. Table 7
Fig. 2. Comparison of the measured/predicted R_ values from the model ANN-1 for a) training samples, and b) testing and validation samples.
Fig. 2. Comparison of the measured/predicted R_ values from the model ANN-1 for a) training samples, and b) testing and validation samples.
Fig. 4. a) Comparison of the measured/predicted Re values from the model ANN-1 for onshore samples and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11], and b) offshore samples.
Fig. 4. a) Comparison of the measured/predicted Re values from the model ANN-1 for onshore samples and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11], and b) offshore samples.
Fig. 5. Comparison of the measured/predicted R_ values from the model ANN-2 for a) onshore samples and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11] , and | offshore samples. Details of the optimal performance of the ANN-1 and ANN-2 models are presented in Tables 5 and 6, respectively. Tables 5 and € show that the optimal performance of testing data set for ANN-1 and ANN-2 models are better than the training data set. This is possibly due to the cross validation technique [56] used as the stopping criterion to overcome over fitting. As mentioned earlier, in this technique, the training is stopped when the error on the As mentioned earlier, a network with one hidden layer can approximate any continuous function, provided that sufficient connection weights are used [57]. Hence, to be in line with this assumption, one hidden layer was used in this study. It can be noted from Tables 5 and 6 that ANNs with one hidden layer and adequate number of hidden neurons are found to be quite useful as observed by earlier researchers [29,46,47].
Fig. 5. Comparison of the measured/predicted R_ values from the model ANN-2 for a) onshore samples and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11] , and | offshore samples. Details of the optimal performance of the ANN-1 and ANN-2 models are presented in Tables 5 and 6, respectively. Tables 5 and € show that the optimal performance of testing data set for ANN-1 and ANN-2 models are better than the training data set. This is possibly due to the cross validation technique [56] used as the stopping criterion to overcome over fitting. As mentioned earlier, in this technique, the training is stopped when the error on the As mentioned earlier, a network with one hidden layer can approximate any continuous function, provided that sufficient connection weights are used [57]. Hence, to be in line with this assumption, one hidden layer was used in this study. It can be noted from Tables 5 and 6 that ANNs with one hidden layer and adequate number of hidden neurons are found to be quite useful as observed by earlier researchers [29,46,47].
Fig. 6. Comparison of the measured/predicted R_ values from a) MRA-1, and b) MRA-2 for all samples.
Fig. 6. Comparison of the measured/predicted R_ values from a) MRA-1, and b) MRA-2 for all samples.
Fig. 7. Comparison of the measured/predicted R; values from a) Eq. (2), and b) Eq. (3) for all samples. A comparison of the experimental results vis-a-vis those obtained from both ANN models, for training, validation, and testing samples, is depicted in Figs. 2 and 3. It can be noted from In addition, the measured Rg values were compared vis-a-vis with those obtained from both ANN models based on the soil types. To achieve this, samples used were categorized into two groups such as (a) onshore soils and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11], and (b) offshore soils. The comparison of measured versus predicted Rg values from ANN-1 model is depicted in Fig. 4 for the first and second group samples, respectively. Similarly, the comparison of measured versus predicted Re values from ANN-2 model is depicted in Fig. 5 for the first and second
Fig. 7. Comparison of the measured/predicted R; values from a) Eq. (2), and b) Eq. (3) for all samples. A comparison of the experimental results vis-a-vis those obtained from both ANN models, for training, validation, and testing samples, is depicted in Figs. 2 and 3. It can be noted from In addition, the measured Rg values were compared vis-a-vis with those obtained from both ANN models based on the soil types. To achieve this, samples used were categorized into two groups such as (a) onshore soils and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11], and (b) offshore soils. The comparison of measured versus predicted Rg values from ANN-1 model is depicted in Fig. 4 for the first and second group samples, respectively. Similarly, the comparison of measured versus predicted Re values from ANN-2 model is depicted in Fig. 5 for the first and second
Performance indices for ANN, MRA and generalized models. Table 8 group samples, respectively. Figs. 4 and 5 show that both ANN models yield good predictions for onshore samples and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11]. However, both ANN models yield poor predictions for offshore soils. This may be attributed to the fact that less data, only 18 data sets for offshore soils, were used in the development of both ANN models. It must also be appreciated that (refer Tables 1 and 2) Rg values for offshore samples is much lower, due to their high chloride content (>500 ppm). In general, for these samples, Cr reported by Eq. (3) should be multiplied by a factor 0.7.
Performance indices for ANN, MRA and generalized models. Table 8 group samples, respectively. Figs. 4 and 5 show that both ANN models yield good predictions for onshore samples and the soils used by Sreedeep et al. [18] and Abu-Hassanein [11]. However, both ANN models yield poor predictions for offshore soils. This may be attributed to the fact that less data, only 18 data sets for offshore soils, were used in the development of both ANN models. It must also be appreciated that (refer Tables 1 and 2) Rg values for offshore samples is much lower, due to their high chloride content (>500 ppm). In general, for these samples, Cr reported by Eq. (3) should be multiplied by a factor 0.7.
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