Examples of the use of shallow neural networks are used here to demonstrate the power of shallow neural networks and to provide some indications of what needs to be considered in successful applications of any neural network for exploration. The first example is from an attempt to test the power of neural networks to locate deposits whereas the second example represents a test of what might be possible with the correct kinds of information.
An early study of neural networks in exploration used a multiple-layer feedforward network to predict possible locations of undiscovered mineral deposits (Singer and Kouda, 1996). The goal was to locate possible kuroko massive sulfide deposits using the data from 20 years of drilling in the largely concealed Hokuroku District of Japan (Fig. 2). The data used were from X-ray analyses of gypsum, sericite and pyrite in 152 drill holes in the approximately 40×40 km2 district. Average amounts per hole of pyrite, sericite, and gypsum plus anhydrite as measured by X-rays in 69 drill holes were used to train the net. Mainly drill holes near and between the Fukazawa, Furutobe, and Shakanai mines were used to train the network with the output neuron being the logarithm of distance to a deposit. Five neurons were used in the hidden layer. The training data were selected carefully to represent well-explored areas where confidence of the distance to ore was assured. The validation consisted of testing the trained network on the total available dataset, including the 69 drill holes used for training. The network succeeded in identifying all known deposits and pointed to an area in the northeast part of the District where an independently discovered a kuroko deposit had been found (Fig. 2). Such drill hole data is not commonly available in exploration for mineral deposits in concealed settings, so the nature of the data limited the network's applicability elsewhere. In addition, the training of the network was mostly based on one deposit which limits their application for other deposits even of the same type.
Figure 2. Neural network output in the Hokuroku district, Japan. Based on X-ray data of gypsum, sericite, and pyrite in drill holes. One hidden layer, 5 neurons (from Singer and Kouda, 1996).
Commonly in exploration for undiscovered deposits, the information that might be useful is widely scattered and often some samples contain missing data for some of the variables. To test one way to deal with missing information, an artificial example of 800 points was generated with three kinds of alteration and a geophysical variable. The alteration was assumed to be zoned around the deposit but with some irregularities. The alteration variables were coded as 1 if present in the sample, -1 if not present, and 0 if no information was available on alteration such as when the sample was located where possible altered rocks were covered by younger sediments. The geophysical variable was available in all samples and had higher values in an annulus around the deposit. All simulated data were located in X-Y space in kilometers from the center of the deposit. A probabilistic neural network (Masters, 1993) was trained on a randomly selected subset of 360 points into one of four distance classes of 0–1 km, 1–3, 3–5 and 5–10+ km (Table 1). The rows in Table 1 that have 0 for all three alteration variables represent samples located where rocks that could have been altered were covered—that is no alteration could have been observed even if it existed.
PNN INPUT PNN OUTPUT PROB. PNN PNN X Y Dist. Group Alt1 Alt2 Alt3 Geoph. Gp1 Gp2 Gp3 Gp4 Group Distance 0.88 0.32 0.94 1 1 -1 -1 0.305 1.00 0.00 0.00 0.00 1 0.5 2.45 1.63 2.95 2 -1 1 -1 0.689 0.00 1.00 0.00 0.00 2 2 2.18 -0.96 2.38 2 0 0 0 0.727 0.21 0.35 0.08 0.35 4 8 -0.94 3.06 3.20 3 -1 -1 1 1.129 0.00 0.00 1.00 0.00 3 4 2.38 2.85 3.72 3 0 0 0 1.495 0.00 0.54 0.41 0.05 2 2 -1.68 4.63 4.93 3 -1 -1 1 1.402 0.00 0.00 1.00 0.00 3 4 4.94 0.72 4.99 3 0 0 0 1.902 0.00 0.14 0.85 0.00 3 4 6.82 1.55 6.99 4 0 0 0 0.865 0.10 0.47 0.13 0.30 2 2 2.82 4.42 5.25 4 -1 -1 -1 0.675 0.00 0.00 0.00 1.00 4 8
Table 1. Example input and output of three alteration and one geophysical variables. X and Y are distances of sample in km from deposit, Group is distance group, PNN INPUT is the input alteration and geophysical variables. PNN OUTPUT are the probabilistic neural network probabilities and the median distances
Figure 3 shows roughly contoured distances of the output of the probabilistic neural network using both training and test samples. The plot demonstrates that samples with some missing variables can be coded so that they can be used to point to the location of a mineral deposit. With only 360 training points this shallow neural network was powerful enough to learn reasonable estimates of distance to a deposit.
Figure 3. Contours of maximum estimated probability distance classes to center of deposit from 800 artificial samples of geophysics and alteration around a porphyry copper deposit.
These two examples show both the power of even shallow neural networks and point to some significant issues that need to be addressed in order for these networks to successfully generalize for discovering new mineral deposits.