Seismic Discrimination with Artificial Neural Networks: Preliminary Results with Regional Spectral Data by Farid U. Dowla,

An application of artificial neural networks (ANN) for discrimination between natural earthquakes and underground nuclear explosions has been studied using distance corrected spectral data of regional seismic phases. Pn, Pg, and Lg spectra have been analyzed from 83 western U.S. earthquakes and 87 Nevada Test Site explosions recorded at the four broadband seismic stations operated by Lawrence Livermore National Laboratory. Distance corrections are applied to the raw spectra using existing frequency-dependent Q models for the Basin and Range. The spectra are sampled logarithmically at 41 points between 0,1 and 10 Hz for each phase and checked for adequate signal-to-noise ratios (S/N > 2). The ANN was implemented on a SUN 4/110 workstation using a backpropagation-feedforward architecture. We find that, using even simple ANN architectures (82 input units, 1 hidden unit, and 2 output units), powerful discrimination systems can be designed. In order to regionalize the data characteristics, a separate neural network was assigned to each station. For this data set, the rate of correct recognition for untrained data is over 93 per cent for both earthquakes and explosions at any single station. Using a majority voting scheme with a network of four stations, the rate of correct recognition is over 97 per cent. Although the performance of the ANN is similar to that of the Fisher linear discriminant, the ANN exhibits a number of computational advantages over the conventional method. Finally, examination of the network weights suggests that, in addition to spectral shape, a criterion that the ANN utilized to discriminate between the two populations was the Lg/Pg spectral amplitude ratios. INTRODUCTION Discrimination of seismic records from natural earthquakes and underground nuclear explosions is an important problem in test ban treaty verification research (Dahlman and Israelson, 1977). Recent developments indicate that Artificial Neural Networks (ANNs) might be appropriate for solving difficult problems in signal discrimination and classification (Lippman, 1987). ANNs are computational systems consisting of a large number of simple processing units, or neurons, which are interconnected in a parallel structure. The parallel computational architecture of an ANN, besides resembling the biological brain, has potential in application areas like seismic discrimination where multiple hypotheses are pursued in parallel, where the number of input parameters is often large, and where well-defined solutions are not available. An ANN learns to solve a problem by training on examples of real data. For example, with ANNs it is not necessary to explicitly specify classification rules or algorithms. We studied ANNs in the context of a seismic discrimination problem using regional spectral data. The methodology and the results of this study are described in this paper. The problem of distinguishing underground nuclear explosions from natural earthquakes using seismic data has been studied for a long time. Currently discrimination of regional data is an important research topic and a variety of regional discriminants have been proposed by many researchers (cf. Pomeroy et al., 1982; Taylor et al., 1989). Discrimination of small magnitude events, however, is still a 1346 DISCRIMINATION WITH ARTIFICIAL NEURAL NETWORKS 1347 difficult problem. For small magnitude events (mb < 4), spectral discrimination using multiple regional phases has recently received much attention (Bennett and Murphy, 1986; Taylor et al., 1988). It is generally believed that both spectral shapes and ratios of the regional phases (Pn, Pg, and Lg) might be quite useful for distinguishing earthquakes from explosions (Pomeroy et al., 1982). Generalization and regionalization of these discriminants is, however, important for optimum performance. Since ANNs can classify populations by generating complex discriminant functions by training on real data, we used as input to the ANN the full broadband distance-corrected spectra of the regional seismic phases. During the learning phase, the ANN automatically extracted and learned the relationships among the discrete frequency components of the multiple regional phases for correct discrimination between earthquakes and explosions. The ANN was developed and tested with a large number of real seismic events, consisting of 83 earthquakes and 87 underground nuclear explosions recorded at each station of a network of four stations located in the western United States. Results of this study based on regional spectral data indicate that ANNs can indeed generate excellent discriminant functions. The rate of correct recognition for untrained data is over 93 per cent at any single station and is over 97 per cent for a network of four stations. Our primary goal at the outset of this preliminary study was to gain an understanding of the performance of neural networks for seismic event discrimination with a set of real seismic data. As the work l~rogressed, we realized that the engineering aspects of neural networks are still at an elementary stage and a number of the important issues in ANNs are unresolved. In this report we discuss some of the expertise in seismic ANNs that was developed during the course of this study. In particular, we discuss the important problems of the representation, preprocessing, normalization, and training of ANNs with a database of real seismic signals. We begin with an introductory discussion of ANNs and then discuss the problems of pre-processing and data representation. This is followed by a discussion of the seismic spectral data for discrimination and the performance of the ANN for discrimination between earthquakes and explosions. We then apply the same data to the conventional Fisher discriminant (Tj0stheim, 1981), a linear method which utilizes covariance matrix information, and compare its performance with that of the ANN. Finally, we conclude with a discussion of the implications of our results and areas of future research in seismic neural networks. ARTIFICIAL NEURAL NET FOR DISCRIMINATION The current interest in ANNs is an attempt at building a new class of powerful computers capable of solving cognitive tasks in recognition, discrimination, combinatorial optimization, and others. While these tasks are routinely performed by the human brain, they are still beyond the reach of conventional methods of computation. Part of the problem with conventional approaches is that the computational architecture might be inadequate (Rumelhart et al., 1986). Conventional computers simply do not have the power of a massive interconnected network of nonlinear processing nodes, or neurons, which might be necessary for cognitive tasks (Hopfield, 1982). From this viewpoint, researchers are considering information processing techniques and devices, such as neural networks, which approximately resemble the brain. 1348 F. U. DOWLA, S. R. TAYLOR, AND R. W. ANDERSON In this study we have used a type of ANN called the Multi-Layered Perceptron (MLP) (also called the backpropagation network). The MLP has proven to be most useful in engineering applications (see, for example, DARPA Neural Network Study, 1988). However, because ANNs are quite new to the seismological community, we provide a tutorial on MLPs in this section. Because there are many different types of ANNs, an adequate discussion of all these networks is beyond the scope of this paper. For a more complete treatment of ANNs, interested readers are referred to the popular journal article by Lippman (1987) and the book by Rumelhart et al. (1986). The Basic Model for Discrimination: Discriminant Functions In order to motivate the structure of a MLP, we begin by considering a general two-category discrimination problem: suppose we need to classify a given real vector x -[xl, x2, . . . , XN], as belonging to either class A or class B. The discrimination problem is then to map any given point in R N into one of two classes according to some desired criterion. As an example, consider the mapping shown in Figure la, where any point in R 2 plane is mapped into class A or class B according to its membership. How can we construct discriminant function, D(x), that, given x, D (x) would correctly classify x as either belonging to class A or to class B? If we construct two functions DA (x) and DB (x) with properties DA(X) > DB(X) if X belongs to class A Ds(x) > DA(X) if X belongs to class B, then, as shown in Figure lb, we have a basic model for a discrimination system. Given x we simply need to compute the output of D(x) = DA(X) -DB(X). The following discrimination rule is sufficient: if D(x) is positive then x belongs to class A, else x belongs to class B. For example, it is useful to view DA(') and DB (') as elemental functions with maximum values of 1 when the input vectors are from class A and class B, respectively. From a conventional detection theory viewpoint, the discrimination function is an interconnection of matched filters and a threshold decision system. Using the basic model of Figure lb, we see that the essential problem for a discrimination system is the specification of the discrimination function D (.) using an interconnection of elemental functions, DA(') and DB(-). The discrimination function constitutes a mapping from the input data to the output decision space. An example of a form of linear discriminant function is D(x) = wATx -wBTx where WA and WB are weight vectors of length two. The major limitation of such a linear discrimination system is that it can only discriminate between classes of objects that are linearly separable; i.e., only when the two classes can be separated by a hyperplane in R N (Rumelhart et al., 1986). On the other hand, the MLPs with multiple nonlinear discriminant functions cascaded together can generate arbitrarily complex discrimination functions (Lippman, 1987). In other words, because the architecture of multi-layered perceptrons allows construction of discriminant functions for arbitrary mapping from the input data to the output decision space, these systems are quite powerful in pattern recognition and discrimination problems. Terminology The elemental functions of an ANN are the artificial neurons (also called units, processing elements, or nodes). The structure of a neuron is shown in Figure 2. DISCRIMINATION WITH ARTIFICIAL NEURAL NETWORKS