A Hybrid Monte Carlo Method Based Artificial Neural Networks Approach for Rock Boundaries Identification: A Case Study from the KTB Bore Hole

Abstract

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.

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

“…There are, however, several limitations in conventional neural network approaches also (Bishop, 1995;Maiti and Tiwari, 2009). One of the major limitations is that the network is trained by maximizing a likelihood function of the parameters or equivalently minimizing an error function in order to obtain the best set of parameters starting with an initial random set of parameters.…”

Application of dimensionality reduction technique to improve geophysical log data classification performance in crystalline rocks

“…These occur in a range of continental and oceanic settings, where a number of boreholes have been and continued to be drilled in order to provide information of the Earth's crust by means of geophysical surveys and geological mapping (Harvey et al, 2005). Several studies have been reported by geophysicists based on crystalline rocks using well logging data (see for example Pratsone et al, 1992;Pechnig et al,1997Pechnig et al, , 2005Bartetzko et al, 2005;Maiti and Tiwari, 2009;Luo and Pan, 2010;. The general understanding collected from these studies show that, the well logging data from crystalline rocks are not simple to analyze because of their complicated geological characteristics and the difficulty in understanding and using the intensive information content in these data.…”

ANN based inversion of DC resistivity data for groundwater exploration in hard rock terrain of western Maharashtra (India)

“…For example: (1) for seismic event classification (Dystart and Pulli, 1990), (2) well log analysis (Aristodemou et al, 2005;Maiti et al, 2007;Tiwari, 2009, 2010b), (3) first arrival picking (Murat and Rudman, 1993), (4) earthquake time series modeling (Feng et al, 1997), (5) inversion (Raiche, 1991;Devilee et al, 1999), (6) parameter estimation in geophysics (Macias et al, 2000), (7) prediction of aquifer water level (Coppola et al, 2005;Tsanis et al, 2008), (8) magneto-telluric data inversion (Spichak and Popova, 2000), (9) magnetic interpretations (Bescoby et al, 2006), (10) signal discrimination (Maiti and Tiwari, 2010a), (11) DC resistivity inversion (Qady and Ushijima, 2001;Singh et al, 2010;Maiti et al, 2011). There are, however, several limitations in conventional neural network approaches (Bishop, 1995;Maiti and Tiwari, 2009). One of the main problems is that the network is trained by maximizing a likelihood function of the connection weights or equivalently minimizing an error function in order to obtain the best set of connection weights starting with an initial random set of connection weights.…”