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Modelling of anomalous geological source from the gravity data is vital for understanding the crustal/sub-crustal interface depths and associated hazard assessment. Two-dimensional radial power spectra have usually been used to infer average depth of protuberant geological structures, which lack details of dimensional comprehension of lateral interfaces. Here in this study, we implement jointly scaled conjugate gradient-based Bayesian neural network (SCG-BNN) scheme with variogram modelling to carve out shallow and deeper interfaces of complex geological terrain of Eastern Indian Shield, India, using Bouguer gravity anomaly (BGA) and altitude variations data. Our "learner codes" uses the SCG-BNN optimization algorithm to build up a statistical model involving appropriate control parameters for the modelling of shallow and deeper interfaces. We have also compared the proposed SCG-BNN modelling results with the results of both conventional artificial neural networks (ANNs) schemes (e.g. conjugate gradient-based ANNs (CG-ANN) and SCG-ANN) and support vector regression (SVR) modelling to demonstrate the robustness of the underlying method. Comparative analysis suggests that the SCG-BNN model produced superior results than the results of CG-ANN, SCG-ANN and SVR models. The results based on SCG-BNN analysis and variogram modelling have identified the existence of three conspicuous fault structures, namely Malda–Kishanganj Fault, Munger–Saharsha Ridge Marginal Fault and Katihar Fault. The analyses also significantly minimize prediction error in three independent datasets (viz. training, validation and test), enhancing the precision of estimated shallow and deeper interface depths and thereby extenuating feasibility of "SCG-BNN" learner code. We, therefore, conclude that the underlying approach is robust to model various interface depths and generate precisely variation in the shallow and deeper interfaces with appropriate input data from altitude variation and BGA. The "SCG-BNN learner scheme" may potentially be used to exploit interface depths from several other complex tectonic regions. [ABSTRACT FROM AUTHOR]

• We propose a modeling scheme for pore pressure prediction (PP). • The scheme allows understanding the role of past PP/well log to present PP. • The scheme allows getting insight into the underlying variability and uncertainty. • The scheme could be useful to identify overpressure zones in complex geology. Pore pressure (PP) study can provide insightful information about evolution history and/or geological process taking place over a region. Conventional methods, mostly are of deterministic, and they do not allow considering underlying variability and uncertainty. Here we implement Bayesian neural networks (BNN) optimized by Scaled Conjugate Gradient (SCG) and Hybrid Monte Carlo (HMC) approach to model the PP and estimate the uncertainty in prediction from well log data of well U1343E located at Bering sea slope region of the IODP Expedition 323. In the first step, to create representative samples of well log and corresponding PP samples, Eaton's and porosity methods are employed to estimate PP empirically from well log data (e.g., gamma ray, sonic velocity, bulk density and sonic derived porosity). In the second step, in total 357 representative samples are used to build a statistical model in Bayesian framework to model the PP against depth. Prior to actual data analysis, we conducted a series of experiments combining with auto-correlation function (ACF) and/or partial autocorrelation function (PACF) analysis to fix network structure (e.g., input lag, number of hidden node) and the bounds of network hyper-parameter. In contrast to previous approach, we seek to develop a mechanism which allows to explore the link between past PP and/or well log history and present PP under rapid sedimentation rate and changing environment. The model exhibits excellent performance between predicted and computed PP with Pearson's correlation coefficient, reduction of error (RE) (RE SCG-BNN ∼ 0.99; RE HMC-BNN ∼ 0.99), and index of agreement (IA) (IA SCG-BNN ∼ 0.99; IA HMC-BNN ∼ 0.98). Comparison based on coefficient of determination, R2 , it is obtained that BNN produced superior results than the conventional artificial neural networks (ANNs). Moreover, at 530 mbsf (meter below sea floor), abrupt PP change could be linked to the transition from Pliocene to Pleistocene. The approach used here, could be useful to identify overpressure zones (OPZ) and to understand the role of past PP/well log to present PP history in many other complex geo-environmental applications. [ABSTRACT FROM AUTHOR]

A novel approach based on the concept of Bayesian neural network (BNN) has been implemented for classifying sediment boundaries using downhole log data obtained during Integrated Ocean Drilling Program (IODP) Expedition 323 in the Bering Sea slope region. The Bayesian framework in conjunction with Markov Chain Monte Carlo (MCMC)/hybrid Monte Carlo (HMC) learning paradigm has been applied to constrain the lithology boundaries using density, density porosity, gamma ray, sonic P-wave velocity and electrical resistivity at the Hole U1344A. We have demonstrated the effectiveness of our supervised classification methodology by comparing our findings with a conventional neural network and a Bayesian neural network optimized by scaled conjugate gradient method (SCG), and tested the robustness of the algorithm in the presence of red noise in the data. The Bayesian results based on the HMC algorithm (BNN.HMC) resolve detailed finer structures at certain depths in addition to main lithology such as silty clay, diatom clayey silt and sandy silt. Our method also recovers the lithology information from a depth ranging between 615 and 655 m Wireline log Matched depth below Sea Floor of no core recovery zone. Our analyses demonstrate that the BNN based approach renders robust means for the classification of complex lithology successions at the Hole U1344A, which could be very useful for other studies and understanding the oceanic crustal inhomogeneity and structural discontinuities. [ABSTRACT FROM AUTHOR]

Predictive modeling of hydrological time series is essential for groundwater resource development and management. Here, we examined the comparative merits and demerits of three modern soft computing techniques, namely, artificial neural networks (ANN) optimized by scaled conjugate gradient (SCG) (ANN.SCG), Bayesian neural networks (BNN) optimized by SCG (BNN.SCG) with evidence approximation and adaptive neuro-fuzzy inference system (ANFIS) in the predictive modeling of groundwater level fluctuations. As a first step of our analysis, a sensitivity analysis was carried out using automatic relevance determination scheme to examine the relative influence of each of the hydro-meteorological attributes on groundwater level fluctuations. Secondly, the result of stability analysis was studied by perturbing the underlying data sets with different levels of correlated red noise. Finally, guided by the ensuing theoretical experiments, the above techniques were applied to model the groundwater level fluctuation time series of six wells from a hard rock area of Dindigul in Southern India. We used four standard quantitative statistical measures to compare the robustness of the different models. These measures are (1) root mean square error, (2) reduction of error, (3) index of agreement (IA), and (4) Pearson's correlation coefficient ( R). Based on the above analyses, it is found that the ANFIS model performed better in modeling noise-free data than the BNN.SCG and ANN.SCG models. However, modeling of hydrological time series correlated with significant amount of red noise, the BNN.SCG models performed better than both the ANFIS and ANN.SCG models. Hence, appropriate care should be taken for selecting suitable methodology for modeling the complex and noisy hydrological time series. These results may be used to constrain the model of groundwater level fluctuations, which would in turn, facilitate the development and implementation of more effective sustainable groundwater management and planning strategies in semi-arid hard rock area of Dindigul, Southern India and alike. [ABSTRACT FROM AUTHOR]

Summary: Inversion of vertical electrical sounding (VES) data, especially from the crystalline hard rock area, assumes a special significance for groundwater exploration. Here we used a newly developed algorithm based on the Bayesian neural network (BNN) theory combined with Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulation scheme to invert the Direct Current (DC) VES measurements obtained from 30-locations around Tenduli-Vengurla, Sindhudurg district, Maharashtra, India. The inversion results suggest that the top layer is mostly comprised of laterites followed by mixture of clay/clayey sand and garnulites/granite as basement rocks. The source of groundwater appears to be accessible in weathered/semi-weathered layer of laterite/clayey sand that exists within the depth of 10–15m from the surface. The NW–SE trending major lineaments and its criss-crosses are also identified from the apparent and true resistivity surface map. The pseudo-section at different depths in the western part of the area, near Nivti, shows extensive influence of saltwater intrusion and its impact reaching up to the depth of 30m from the surface along the coastal area. Our results also show that intrusion of saline water decreases from the western part to the eastern part of the region. Two dimensional modeling of four resistivity profiles from the study region identified two potential groundwater reservoirs; one lying between Path-Tenduli and another in between Mat and Zaraph. The deduced true electrical resistivity section against depth correlates well with available borehole lithology in the area. The results presented here would be useful for interpreting the geological signatures like fractures, major joints and lineaments, which in turn will be helpful for identifying groundwater reservoirs and drainage pattern in the crystalline hard rock area. The newly developed HMC-based BNN method is robust and would provide insights for constraining the geophysical models and criteria for modeling resistivity data. [Copyright &y& Elsevier]

The precise classification of changes in rock boundaries/facies from well-log records is a complex problem in geophysical data processing. Observed well-log data are a complex superposition of nonstationary/nonlinear signals of varying wavelengths and frequencies, shaped by the heterogeneous composition and structural variation of rock types in the earth. This impairs our ability to use traditional statistical techniques, which in most cases fail to discriminate and/or, at best, do not precisely extract facies changes from complex well-log signals. We propose a new method, set in a Bayesian neural network (BNN) framework and using a powerful hybrid Monte Carlo simulation scheme to identify facies changes from complex well-log data. We first construct a complex, composite, synthetic time series using the data from three simple models: first-order autoregressive, logistic, and random white noise. Then we attempt to identify individual signals in the pooled synthetic time series. We use the autocorrelation and the spectral characteristics of the individual signals as input vectors for training, validating, and testing the artificial neural network model. The results show that the Bayesian separation scheme provides consistently good results, with accuracy at more than 74%. When the method was tested using well-log data from the German Continental Deep Drilling Program (KTB), it was able to discriminate boundaries of lithofacies with an accuracy of approximately 92% in validation and 93% in test samples. The efficacy of the BNN in the presence of colored noise suggests that the designed network topology is robust for up to 30% correlated noise; however, adding more noise (say, 50% or more) obscures the desired signals. Our method provides a robust means for decoding finely detailed successions of lithofacies from complex well-log data, better describing the nature of the underlying inhomogeneous crust. [ABSTRACT FROM AUTHOR]

Identification of rock boundaries and structural features from well log response is a fundamental problem in geological field studies. However, in a complex geologic situation, such as in the presence of crystalline rocks where metamorphisms lead to facies changes, it is not easy to discern accurate information from well log data using conventional artificial neural network (ANN) methods. Moreover inferences drawn by such methods are also found to be ambiguous because of the strong overlapping of well log signals, which are generally tainted with deceptive noise. Here, we have developed an alternative ANN approach based on Bayesian statistics using the concept of Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) inversion scheme for modeling the German Continental Deep Drilling Program (KTB) well log data. MCMC algorithm draws an independent and identically distributed (i.i.d) sample by Markov Chain simulation technique from posterior probability distribution using the principle of statistical mechanics in Hamiltonian dynamics. In this algorithm, each trajectory is updated by approximating the Hamiltonian differential equations through a leapfrog discrimination scheme. We examined the stability and efficiency of the HMC-based approach on “noisy” data assorted with different levels of colored noise. We also perform uncertainty analysis by estimating standard deviation (STD) error map of a posteriori covariance matrix at the network output of three types of lithofacies over the entire length of the litho section of KTB. Our analyses demonstrate that the HMC-based approach renders robust means for classification of complex lithofacies successions from the KTB borehole noisy signals, and hence may provide a useful guide for understanding the crustal inhomogeneity and structural discontinuity in many other tectonically critical and complex regions. [ABSTRACT FROM AUTHOR]

A novel approach based on the concept of super self-adapting back propagation (SSABP) neural network has been developed for classifying lithofacies boundaries from well log data. The SSABP learning paradigm has been applied to constrain the lithofacies boundaries by parameterzing three sets of well log data, that is, density, neutron porosity and gamma ray obtained from the German Continental Deep Drilling Project (KTB). A multilayer perceptron (MLP) neural networks model was generated in a supervised feed-forward mode for training the published core sample data. A total of 351 pairs of input and output examples were used for self-adaptive network learning and weight and bias values were appropriately updated during each epoch according to the gradient-descent momentum scheme. The actual data analysis suggests that the SSABP network is able to emulate the pattern of all three sets of KTB data and identify lithofacies boundaries correctly. The comparisons of the maximum likelihood geological sections with the available geological information and the existing geophysical findings over the KTB area suggest that, in addition to the known main lithofacies boundaries units, namely paragneisses, metabasites and heterogeneous series containing partly calc-silicate bearing paragneisses-metabasites and alternations of former volcano-sedimentary sequences, the SSABP neural network technique resolves more detailed finer structures embedded in bigger units at certain depths over the KTB region which seems to be of some geological significance. The efficacy of the method and stability of results was also tested in presence of different levels of coloured noise. The test results suggest that the designed network topology is considerably unwavering for up to 20 per cent correlated noise; however, adding more noise (∼50 per cent or more) degrades the results. Our analyses demonstrate that the SSABP based approach renders a robust means for the classification of complex lithofacies successions from the KTB borehole log data and thus may provide useful guide/information for understanding the crustal inhomogeneity and structural discontinuity in many other regions. [ABSTRACT FROM AUTHOR]