模擬退火、基因演算、與類神經網路於震測速度選取之研究

Abstract

速度選取是震測資料處理中的一個重要步驟，即在時間與速度的semblance圖中挑選出適當的時間與速度序對 (time-velocity pairs) 來表示地層間時間與速度的關係函式。傳統藉由地球物理專家進行速度選取的方法過程耗時，因此吾人把速度選取轉化為組合最佳化問題，即從區域峰值點的集合中尋找一個代表最佳折線的組合。我們建立能量的目標函式，此函式包括被選取點的semblance (energy) 總和，及限制條件，包含選取點的數量、間隔速度 (interval velocity)、速度斜率 (velocity slope) 的限制，我們利用三種最佳化演算法包含模擬退火、基因演算、與霍普菲爾類神經網路求取目標函式的最佳化，來尋找一個由峰值點的集合所組成的最佳折線，即最佳時間與速度的關係函式。 在模擬退火過程中，每一次的系統隨機狀態代表一個解，而具較高能量的新系統隨機狀態有一定的機率被接受。系統降溫後的最低能量狀態即為所求最佳折線，是一個全域的最佳解。在基因演算中，每一個個體代表一個解，數個個體會演化數個世代。最後一個世代中最高適應值個體即為所求最佳折線，也是一個全域最佳解。在霍普菲爾網路中，系統狀態代表一個解。我們由能量的目標函式推導得出系統的運動方程式，藉由非同步更新使能量下降到最後網路收斂，並到達一個代表最佳折線的穩定狀態。在基因演算，我們求目標函式的最大值。在模擬退火與霍普菲爾類神經網路為求目標函式的最小值，故在實作時我們對目標函式轉為負數，而求最小值。 在模擬退火與基因演算法的參數設定中，我們藉由循序式的每次決定一個參數的數值，找出最佳的參數。我們有模擬與實際的震測資料的實驗，我們使用模擬的二十二個同中點的震測圖(commom midpoint gather)與實際的Nankai的十五個同中點的震測圖做實驗。我們將所得到的折線與人工選取的折線計算誤差，作為結果評量指標，結果顯示在模擬與實際的震測資料中，基因演算法都能有最好的結果。另外，我們將三種方法所得到的最佳化折線進一步運用於動態修正(normal move-out correction)及共中點疊加(stacking)，結果顯示由三種方法所得的最佳化折線皆能強化模擬與實際的震測資料的訊號。我們的速度選取最佳化的研究有助於震測資料的進一步處理與解釋。

Velocity picking is an important step for seismic data processing. It is to pick several time-velocity pairs forming a polyline in a semblance image to represent the time and velocity relation in layers. Conventionally the geophysicists did it, but it took much time. We transfer it to a combinatorial problem which is finding the best combination from the set of candidate points. We define an objective function of energy that includes total semblance value of picked points, and constraints on the number of picked points, interval velocity, and velocity slope. We adopt three optimization methods: simulated annealing (SA), genetic algorithm (GA), and Hopfield neural network (HNN), to find the optimal solution of objective function and obtain the best polyline consisting of picked peak points respectively. In SA, the random system state represents a solution, and the higher energy random system state has a certain probability to be accepted and skip the local minimum. After annealing, the lowest energy system state is the best polyline. It is a global optimal solution. In GA, an individual represents a solution. Several individuals evolve many generations. The highest fitness individual in the last generation is the best polyline. It is also a global optimal solution. In HNN, the neurons of network represent a solution. We derive the equation of motion from the objective function and use asynchronous updating to renew the neurons of network. Finally, the network converges. The stable network state represents the best polyline. In GA, we find the maximum of the objective function. In SA and HNN, we find the minimum of the objective function. In the implementations of SA and HNN, we change the objective function to a negative function and find the minimum. In the parameter settings of SA and GA, we find the best parameter settings by sequential method. We have experiments on simulation data and Nankai real seismic data. We have 22 common midpoint gathers (CMP gathers) of simulated seismic data and 15 CMP gathers of Nankai real seismic data for experiments. We evaluate the performance by comparing the mean difference between the picking result of each adopted method and that of human. The experiments show that GA has the best result on the simulated and real seismic data experiments. The best picking results by three methods are further used to do normal move-out (NMO) correction and stacking. The results show that both of the signals of the simulated and real seismic data are enhanced. The results of velocity picking by three optimization methods will be helpful for further seismic data processing and interpretation.