201071164112_f029

72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010 Barcelona, Spain, 14 - 17 June 2010

F029Semi-automatic Determination of the Number ofSeismic Facies in Waveform ClassificationW. Xiong* (CNPC-BGP), Z.H. Wan (CNPC-BGP), M.S. Chen (CNPC-BGP) & H.Y. Zhang (CNPC-BGP)

SUMMARYWaveform classification is a popular method in seismic facies analysis. It has been successfully applied tooil and gas reservoir prediction. However, the decision of the number of seismically-determined facies infield applications is not straightforward. Generally the task is performed by trial and error of a subjectiveuser, which consequently increases the workload of the interpreter and the uncertainty of reservoir faciesprediction. This problem is addressed here by proposing a self-organizing neural network in which thestructure of the output layer is one-dimensional. Using this technique, the number of seismic facies can besemi-automatically determined. This method is applied to a synthetic example and a field example. It isshown that the proposed method is capable of estimating the number of classes effectively and enhancingthe discrimination of seismic facies in an efficient way.

Introduction

In waveform classification, seismic waveforms are classified using clustering analysis technology. In this method, the number of classes is a key parameter. Choosing this parameter is difficult as the geological characters vary from field to field. In fact, a good understanding of geology and seismic data is required to correctly determine the number of seismic facies. In field application, the number of classes usually varies 5 to 15 depending on the complexity of the seismic signal and the time thickness of the reservoir. The result of classification would be too smooth if the number of classes is very small. On the contrary, the result would be too detailed to be interpreted if the number of classes is too great. Stratimagic is one of the most commonly used software packages for waveform classification. In this software, the user should try at least three times to determine the number of seismic facies, where (1) the number of classes is equal to the target thickness divided by six, (2) the number of classes is the previously calculated value divided by two, and (3) the number of classes is the first calculated value multiplied by 1.5 (Stratimagic training manual, 2002). This is the routine approach to obtaining the number of classes using commercial software at present. It is a trial and error task by the user, which consequently increases the workload of the interpreter and the uncertainty of reservoir facies prediction. This problem is addressed here by adopting a self-organizing neural network in which the output layer is one-dimensional. The number of seismic facies can be semi-automatically determined using this technique.

Method

Kohnen’s Self-Organizing Map (SOM) is one of the most promising techniques for waveform classification. It was initially proposed by Finnish professor T. Kohonen in 1984. It is an unsupervised and self-leaning network containing two layers. It is composed of many input nodes and output nodes. Each input node is connected with all the output nodes by the weights, and each output node is connected with the local output nodes (the neighbourhood) by the weights as well. Normally, there are many nodes in the input layer and the structure of the output layer is two-dimensional. The convergence of the Kohonen method is very slow and it is sensitive to the initial input condition and the sequence of the input samples. Chen Z.D. (1997) and Luo L.M. et al. (1997) improved this method by setting initial weights and adjusting the learning rate, the convergence criterion and the adjustment of classification patterns. The improved algorithm converges faster and provides enhanced accuracy in the result of seismic facies. Based on this method, we propose two improvements aimed to find a more efficient way to determine the number of classes.

Kohonen’s one-dimensional SOM

The 2D output nodes need to be further interpreted before the result of Kohonen’s SOM can be finally used. For example, Matos et al. (2007) proposed a method to estimate the number of classes by combining 2D SOM and the K-mean method, i.e. the number of classes is calculated by the K-mean method based on the 2D U-matrix from the SOM. For Kohonen’s SOM, in which the output layer is 2D, the same seismic facies is often mapped by multiple neurons, which makes the network so large that it is difficult to interpret the final result. Actually, the neural network in which the output layer is one-dimensional (Figure 1) can meet the requirements for seismic facies classification. In this network, there are less neurons in the output space than in 2D. The structure of the 1D output layer is different from the 2D output layer. It is a linear topology and the number of nodes in the output layer is equal to the number of classes. This network is still capable of adjusting the weights of the neurons in the output layer within the neighborhood according to their response to the neurons in the input layer. Because of our improvement to the network structure of the output layer, the following equation can be used to determine the number of classes.



The formula of estimating the number of classes

Regardless of pattern recognition or neural network, the result is better if the distances between clusters are larger and the distances between samples in each cluster are smaller. This criterion is used to determine the number of classes in our method. Suppose the number of classes varies from 2 to M, the sum of the distances (ERRK) between the samples in each cluster is expressed by the following equations when the number of classes is equal to K:

)(1)))(((1 1

2)( i,...,njiwxERRK

i

n(i)

j

ijK

and NinK

i

1

)(

Where xj(i) is the jth sample in the ith cluster, w(i) is the weight for the ith cluster, n(i) is the number of

samples of the ith cluster and N is the total numbers of samples. The EER is minimized when the

number of classes is correct.

Figure 1 One-dimensional SOM: X1, X2 ,…, XN are the input nodes; Y1, Y2,…, YN are the output

nodes; W11 is the weight connected with X1 and Y1. Nc is the neighbourhood.

A test on a synthetic data

A 3D synthetic model (Matos, 2007) was used to validate the introduced method. The velocity model is shown in Figure 2a. The synthetic seismic signal generated with this velocity model is shown in Figure 2b. The reservoir is represented by three different seismic facies characterized by the their velocities of 3100m/s, 3200m/s, and 3300m/s. We use the seismic amplitudes within a 32-millisecond window around the chosen seismic horizon (the blue dotted line), i.e., the marked area between red dotted lines in Figure 2c. The use of the contiguous seismic trace amplitudes as input attributes is equivalent to a waveform classification in the area of interest. The classified results with the proposed algorithm are shown in Figure 3. In the example in Figure 3a, the ERR is constant when the number of classes is greater than three. So the number of the classes is determined to be three. Figure 3b shows the seismic facies map when the number of classes is three. From this map, we can easily know that there are three facies in this example. With our method, the number of classes can be correctly determined using the ERR curve and the seismic facies map matches the true model well.

Application to real data

Our method was applied to 3D observed seismic data. The seismic data along a crossline is shown in Figure 4. In this figure, the yellow line is the seismic horizon. The waveforms near line 370 and line 580 are the zone of study. A 50-ms window along the seismic horizon (10 ms above and 40 ms below the yellow line) is used to analyse the seismic facies. Figure 5a shows the ERR versus the number of classes. The ERR decreases gradually as the number of classes increases. The change in ERR appears to be less when the number of classes is greater than eight. Hence the number of classes is set to eight

Y1 Y2 . . . YM Output Nc

X1 X2 … XN Input

W11 WNM


for the waveform classification. Eight model traces used in this example are shown in Figure 5b. Figure 5c is the result of the waveform classification (seismic facies) using the above parameters. The white solid line is the location of the crossline shown in Figure 4. The fluvial channel can be clearly seen from the map, which is delineated by a white dotted line. From the figures, we can see that the fluvial facies in Figure 5c correspond to the first model trace in Figure 5b. Figure 5d is the seismic facies map when the number of classes is equal to four. The fluvial channel in this figure is not as obvious as in Figure 5c. It is more difficult to identify the channel, especially the part in the centre. Therefore, the fluvial channel is better delineated when the number of classes is eight. This proves that our method is an efficient approach for determining the number of facies and produces reliable results.

Conclusions

We proposed a method by which the number of facies can be efficiently determined. Compared with the traditional method that based on trial and error, our method reduces the user’s workload and the uncertainty in the result caused by the subjective user. The method introduced here determines the appropriate number of facies from the cross-plot of the ERR versus the number of classes. Theoretically, the best number of classes corresponds to the point where the ERR value is minimized. However, it might be difficult to find this point in practice. In general, the number of classes corresponding to the point where the ERR curve becomes flat is best.

References

Chen, Z.D. [1997]. Reservoir seismic attribute optimization. Oil industry publishing house, China. Luo, L.M. and Wang, Y.C. [1997]. Improvement of self-organizing mapping neural network and the application in reservoir prediction. Oil Geophysical Prospecting, 32,237-245. Matos, M.C. Osorio, P.L.M. and Johann, P.R.S. [2007]. Unsupervised seismic facies analysis using wavelet transform and self-organizing maps. Geophysics, 72, 9-21. Paradigm. [2002]. Stratimagic training manual. Paradigm geophysical corporation.

Figure 2 The synthetic model. a) The velocity model. b) The synthetic seismic. c) The picked horizon (in blue dotted line) and the time window (between red dotted lines).

Tw

o-w

ay ti

me

(s)

Distance (m)

a)

Trace Number (trace spacing is 50m)

TW

T (

ms)

b)

TW

T (

ms)

Trace number (trace spacing is 50m)

c)


Figure 3 The result of wavelet classification. a) The crossplot of ERR versus the number of classes. b) The seismic facies map.

Figure 4 The seismic profile along a crossline (displayed with wiggles and variable density colour). The yellow line is picked seismic horizon. Colour bar is amplitude.

Figure 5 The result of waveform classification. a) The crossplot of the ERR versus the number of classes. b) The model traces c) The seismic facies map when the number of classes is 8. d) The seismic facies map when the number of classes is 4.

ER

R

The number of classes

a) 0

b) 10

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40Cro

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ne

0 10 20 30 40 50 60 70 80 90

Inline

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Inline100 200 300 400 500 600

400

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700

Cro

ssli

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c)

The number of classes

ER

R

a)

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d)b)

The number of model trace

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of s

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201071164112_f029

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