輻射半徑基底函數網路於井測資料之反推

Abstract

我們採用監督式的輻射半徑基底函數網路(Radial basis function network, RBF)，而且提出改良式兩層RBF 與改良式三層RBF 於井測資料的反推。網路的 輸入是井測的視導電率(apparent conductivity, Ca)，而輸出是真實地層導電率(true formation conductivity, Ct)，由於做井測反推，所以輸入與輸出的特徵值數目是相 同的。在實驗的部份，分為模擬資料的實驗與實際的井測資料的應用。在模擬的 實驗，共有31 組模擬的井測資料，其中25 組做訓練，6 組做測試。 在改良式兩層RBF 中，第一層為對訓練樣本做非監督式的分群，我們以 K-means 分群法與pseudo F-statistic test 來決定最佳的分群數，成為第一層的節點 數。第二層為一個單層的監督式的perceptron，我們以s-形的轉換函數代替線性的 轉換函數，則 delta 的學習法則取代Widrow-Hoff 的學習法則，這樣的改良式RBF 具有非線性對應的特性。經由模擬的實驗，我們將不同長度的輸入做比較，結果 10-27-10 RBF 得到最小的測試誤差，也成為兩層RBF 中最佳的網路。 我們將最佳的10-27-10 兩層RBF 擴充為三層RBF，將兩層RBF 的第二層擴 展為一個兩層的perceptron，成為改良式三層RBF，以得到更佳的非線性對映。並 且以Mirchandani 與Cao 提出的理論，決定改良式三層RBF 中的隱藏層節點個數。 由模擬的實驗結果得出10-27-9-10 為最佳的改良式三層RBF。而且10-27-9-10 的 改良式三層RBF 較10-27-10 改良式兩層RBF 有較小的測試誤差。 我們將最佳的 10-27-9-10 改良式三層RBF 經過模擬的資料訓練後，應用於實 際井測資料的反推，得出的結果是可以接受的，這表示我們所提出的改良式RBF 可以用於井測資料的反推。

We adopt the supervised radial basis function network (RBF), and propose the modified two-layer RBF and the modified three-layer RBF for well log data inversion. The input of the network is the apparent conductivity (Ca), and the output is the true formation conductivity (Ct). For the well log data inversion, the number of input nodes is the same as the number of output nodes. We have experiments in simulation and real data application. In simulation, there are 31 sets of simulated well log data. 25 sets are used for training, and 6 sets are used for testing. In the modified two-layer RBF, the first layer is the unsupervised clustering for the training samples. We use K-means clustering algorithm with pseudo F-statistics test to determine the optimal number of clusters that becomes the node number. The second layer is the supervised perceptron. We use the sigmoidal activation function instead of the linear activation function. The delta learning rule replaces the Widrow-Hoff learning rule. It becomes non-linear mapping. Comparing the testing results of different input data length, 10-27-10 can get the smallest error in two-layer RBF. The best 10-27-10 two-layer RBF is expanded to three-layer RBF. We expand the one-layer perceptron to a two-layer perceptron. That can get more non-linear mapping. The number of hidden node is determined by the theorem of Mirchandani and Cao. The best 10-27-9-10 RBF can get the smallest error in the testing. Also, 10-27-9-10 three-layer RBF has smaller error than 10-27-10 two-layer RBF. After the training of the best 10-27-9-10 modified three-layer RBF, we apply it for the inversion of the real field well log data, and the result is acceptable. It shows that the proposed RBF can perform the task of well log data inversion.