The construction of stochastic facies-based models conditioned to ground penetrating radar images

Transcription

1 Calibration and Reliability in Groundwater Modelling: A Few Steps Closer to Reality (Proceedings of ModelCARE'2002, Prague. Czech Republic June 2002). IAHS Publ. no The construction of stochastic facies-based models conditioned to ground penetrating radar images STEPHEN MOYSEY, ROSEMARY KNIGHT Department of Geophysics, Stanford University, Stanford, California 94305, USA movsey@stanford.edii RICHELLE M. ALLEN-KING Department of Geology, Washington Stale University, Pullman, Washington 99164, USA JEF CAERS Department of Petroleum Engineering, Stanford University, Stanford, California 94305, USA Abstract Neural networks are used to estimate radar facies probabilities from ground penetrating radar (GPR) images, yielding stochastic facies-based models that honour the large-scale architecture of the subsurface. For synthetic GPR images, a neural network was able to correctly identify radar facies with an accuracy of over 80%. Manual interpretation of a set of 450 MHz GPR field data from the Borden aquifer resulted in the identification of four radar facies. Of these, a neural network was able to identify two with an accuracy of near 80%, one with an accuracy of 44%, and was not able to identify the fourth. Key words estimation facies; ground penetrating radar (GPR); neural network; radar; stochastic INTRODUCTION Capturing the large-scale architecture of the subsurface is a critical step in the development of groundwater models when processes such as contaminant fate and transport are of interest. If direct hydrogeological measurements are limited, it is common to rely on stochastic methods to enforce subsurface structure. However, these methods are typically poor at preserving realistic geological continuity when data are sparse. An alternative approach is to impose the large-scale structure by considering a data source that can map the facies architecture of a study area. Ground penetrating radar (GPR) is a geophysical tool that can provide "images" of the subsurface over large areal extents (refer to Knight (2001) for a recent review on the use of GPR in environmental applications). These images can be interpreted to provide subsurface models of radar facies, which are defined as regions within a radar image that have similar characteristics. The primary characteristics used to identify radar facies are: (a) reflection amplitude, (b) reflection continuity, (c) reflection configuration, and (d) external form (i.e. geometry) (van Overmeeren, 1998). It is often possible to associate radar facies with particular geological environments (Overmeeren, 1998) or correlate them to specific sedimentary facies (Beres & Haeni, 1991; van Heteren et al, 1994). Under the assumption that radar and hydrogeological facies are equivalent, Rauber et al. (1998) used radar facies as hard data for generating

2 396 Stephen Moysey et ai. conditional groundwater transport models. The assumption of equivalence between hydrogeological and radar facies has not yet been fully investigated; however, in certain environments it is likely to be a good approximation. The manual interpretation of facies from radar images has three distinct disadvantages: (a) a large amount of time and expertise is required to interpret an extensive GPR data set; (b) facies interpretations made by an expert are deterministic and lack a quantitative estimate of uncertainty; and (c) the expert may introduce unquantifiable bias into an interpretation due to personal experience or skill. To overcome these disadvantages, we propose the use of artificial neural networks as an automated tool for radar facies recognition in large GPR data sets. Neural networks are regression models that provide a general way of nonlinearly relating two sets of variables (Bishop, 1995), where one set of variables is considered to be an input to the network and the other is a network output. For the problem of facies identification from radar data, we use the neural network as a pattern recognition device. In our approach, we assume that information encoding facies in the radar image can be extracted to locally identify particular facies types (Fig. 1). Specifically, we select a window of radar data at any spatial location for which the facies type needs to be determined. This window of radar data, which is a "multiple point" data event implicitly containing information on the amplitude, continuity and configuration of reflections near the point of interest, is fed as an input vector to the neural network. The output of the neural network is designed to be a vector where each element is the probability of the occurrence for each of a pre-defined set of facies types. Before it is used for estimation of facies probabilities, the neural network is first "trained", by nonlinear optimization, to recognize characteristic facies patterns using a set of manually interpreted data. In the data set used for training, outputs are specified by a 1-of-c coding (Bishop, 1995, p. 225); for a given spatial location, the element of the output vector corresponding to the manually identified facies type is assigned the value 1 and all other elements are set to 0. A similar methodology has recently been used by Caers & Ma (2002) for the automated interpretation of facies from seismic data. This work should be referred to for details regarding design of the neural network and methods of training required to enforce network outputs to be facies probabilities. Radar Image Input Neural Network Facies Facies Interpretation Vector (Window Input) Probabilities (Point Output) Fig. 1 Schematic diagram of the neural network approach. A window of radar data, centred on location u, is given to the neural network as input (x; u). The outputs are the set of facies probabilities for location u {P(F ), P(F 2 ), P(F 3 ); u). These facies probabilities can be used to generate facies models of the subsurface.

3 The construction of stochastic facies-based models conditioned to GPR images 397 Fig. 2 Facies architecture used for synthetic examples. SYNTHETIC EXAMPLES To illustrate the feasibility of the automated facies identification concept, two synthetic models (Examples 1 and 2) based on a common facies architecture (Fig. 2) are presented. To generate the model, each of the facies is populated, by stochastic simulation, with a different set of hydrological properties that are transformed using petrophysical relationships to construct a map of the dielectric constant. This geophysical property map is used in a simplified (convolutional) radar forward model to obtain the radar response for the system. Prior to applying the neural network to the synthetic model, it must be trained to recognize the character of the radar reflections for each of the facies. Training data sets for each of the facies types were generated in a manner analogous to that used for creating the synthetic model. The synthetic radar response for Example 1 is shown in Fig. 3(a). For this case, property values were chosen such that the contrast in radar response between the two facies is clearly distinguishable by eye; reflections in Facies 1 have higher amplitudes and are less continuous than those in Facies 2. A window of 7 x 7 pixels scanned over the image was used as input to the neural network. The probability of the occurrence of Facies 1 is given in Fig. 3(b). The network output probabilities shown have been smoothed to compensate for local inconsistencies made by the network. The probability of Facies 2 can be obtained as 1 - P(Fi), where P(Fi) is the probability of Facies 1. The performance of the neural network was assessed by comparing the facies (a) (b) m (C) I I Facies 1 I Facies 2 Fig. 3 Synthetic Example 1 : (a) radar response, (b) probability of the occurrence of Facies 1 estimated by the neural network, and (c) facies classification.

4 398 Stephen Moysey et al. Fig. 4 Synthetic Example 2: (a) radar response, (b) probability of the occurrence of Facies 1 estimated by the neural network, and (c) facies classification. model obtained by classification using a maximum likelihood criterion (Fig. 3(c)) against the true model (Fig. 2). Locally, the neural network correctly classified 93% of Facies 1 and 86% of Facies 2. More importantly, geological facies continuity was preserved in the final facies model. The second synthetic model, Example 2, was generated such that the two facies have similar reflection characteristics and amplitudes, but that the orientation of the reflections is different. The facies are much more difficult to identify by eye in the radar image for Example 2 (Fig. 4(a)) than for Example 1 (Fig. 3(a)). As before, a 7x7 pixel window was used as input data to the neural network. The probabilities for Facies 1 are given in Fig. 4(b) and maximum likelihood classifications in Fig. 4(c). Local misclassification increased for this more complex model compared to that in Example 1, but the network was still able to correctly identify 85% of Facies 1 and 88% of Facies 2. As before, geological continuity is preserved. FIELD EXAMPLE: BORDEN AQUIFER As a test of the automated facies classification technique using an actual radar image, a 20 m line of 450 MHz GPR data obtained from the Borden Aquifer (CFB Borden, Ontario, Canada), was considered. The radar data were processed using standard techniques (dewow, trace stacking and AGC gain). A synthetic aperture image reconstruction technique was applied to minimize the presence of diffraction hyperbolae in the image, caused by energy scattering from localized anomalies such as large rocks. All radar processing was performed using Sensors & Software's pulseekko Tools (version no. 2.0). Figure 5(a) shows the section of radar data used for the testing of the network and the radar facies model obtained by manual interpretation. Four radar facies types were identified by manual interpretation: (1) flat-lying reflectors, (2) dipping reflectors, (3) massive (distinct reflectors are absent or signal was lost due to attenuation), and (4) complex or reverse dip reflectors.

5 The construction of stochastic facies-based models conditioned to GPR images 399 Position, m Fig. 5 Borden Aquifer example: (a) radar response and manual facies interpretation, Facies 1: flat reflectors, Facies 2: dipping reflectors, Facies 3: massive, Facies 4: complex reflectors; (b) facies probabilities estimated by the neural network; and (c) facies classification. A window of 7 x 7 pixels (1.4 ns x 35 cm) was used as input to the neural network. Unlike the synthetic cases, an independent radar image was not available for training of the neural network. For the purposes of the test, the training set was therefore generated by randomly selecting samples from the image that reflect approximately 5% of the total radar data. After training on this limited data set, the network was used to classify the entire radar image. The resulting probability maps for each facies type are given in Fig. 5(b) and the maximum likelihood classification in Fig. 5(c). The Bayesian confusion matrix in Table 1 gives a summary of classification accuracy.

6 400 Stephen Moysey et al. Table 1 Bayesian confusion matrix summarizing facies misclassiftcation for the Borden radar section. For example, the entry in row 1 and column 3 is the percentage of Facies 1 that are classified as Facies 3, i.e. 13%. Ideally this matrix should be diagonally dominant, indicating that all facies are correctly identified. Facies 1 Facies 2 Facies 3 Facies 4 Facies Facies Facies Facies Both Facies 1 (i.e. flat-lying reflectors) and Facies 3 (i.e. massive regions) were identified with reasonable accuracy. For many of the areas where misclassification of these two facies occurred, re-inspection of the radar image indicates that the error may be related to inconsistencies in the original manual interpretation, rather than the interpretation produced by the neural network. The classification accuracy for Facies 2 was relatively low, especially considering the distinctive dipping characteristic observed in the reflectors. It is possible that the window size used in this example was too small to clearly distinguish the orientation of these reflectors from the flat-lying reflectors of Facies 2. Alternatively, the fact that the majority of the diffraction hyperbolae, which were removed from the image by preprocessing, occur in this facies is a piece of information that was not used to aid in the automated classification but was available to the manual interpreter. To determine whether the diffraction hyperbolae are important characteristics defining Facies 2, the classification was repeated using the original radar data to which the synthetic aperture image reconstruction process had not been applied. Correct identification of Facies 2 increased from 44%, without diffractions, to 55% when the diffractions were retained. This increase emphasizes that the specific characteristics important for defining particular radar facies, e.g. diffractions, are facies specific. The neural network did not distinguish the complex/reverse dip reflectors in Facies 4 from the flat-lying reflectors of Facies 1. Possible explanations may be related to underrepresentation of this facies in the training set, since it composes a relatively small fraction of the overall image, or it may simply be that a better choice of characteristics which define this facies must be given if it is to be distinguished from Facies 1. CONCLUSIONS Neural networks offer a method to model the conditional probability distributions of facies types subject to radar data. Preliminary testing on synthetic and field radar data sets indicates that a neural network can identify radar facies types with acceptable accuracy. In the current examples, the input to the neural network was a window of the radar image. Further work is required to identify what particular characteristics of a radar facies would act as the optimal inputs for automated identification of that facies. Investigation of the relation between radar and hydrogeological facies in various geological environments is another line of research that must be addressed.

7 The construction of stochastic facies-based models conditioned to GPR images 401 Obtaining quantitative estimates of uncertainty in radar facies interpretation is a significant advantage of the proposed technique over manual interpretation. The stochastic facies model, i.e. facies probabilities, returned by the neural network can be integrated with other data types to obtain subsurface models conditioned to all available data. Using such an approach, radar data will help to provide the geological framework when hard data is sparse. Acknowledgements This work was supported by funding to R. Knight under Grant no. DE-FG07-00ER15118-A000, Environmental Management Science Program, Office of Science and Technology, Office of Environment Management, United States Department of Energy (DOE). However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect views of DOE. Further support was provided by a Stanford Graduate Fellowship. The authors would also like to thank James Irving for his assistance with processing of the radar data. REFERENCES Beres, M. Jr & Haeni, F. P. (1991) Application of ground-penetrating-radar methods in hydrogeologic studies. Groundwater 29(3), Bishop, C. M. (1995) Neural Networks for Pattern Recognition. Oxford University Press, Oxford, UK. Caers, J. & Ma, X. (2002) Modeling conditional distributions of facies from seismic using neural nets. Mailt Geol. 34(2), Knight, R. J. (2001) Ground penetrating radar for environmental applications. Ann. Rev. Earth Planet. Sci. 34(9), Rauber, M., Stauffer, F., Huggenberger, P. & Dracos, T. (1998) A numerical three-dimensional conditioned/unconditioned stochastic facies type model applied to a remediation wed system. Water Resour. Res. 34(9), Van Fleteren, S., FitzGerald, D. M. & McKinlay, P. A. (1994) Application of ground-penetrating radar in coastal stratigraphie studies. In: Proc. Fifth Int. Conf. on Ground Penetrating Radar (Kitchener, Canada, June 1994), Waterloo Centre for Groundwater Research, Canada. Van Overmeeren, R. A. (1998) Radar facies of unconsolidated sediments in The Netherlands: a radar stratigraphy interpretation method for hydrogeology. J. Appl. Geophys. 40, 1-18.