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这里我们描述了两种基于非线性优化法的层速度估算法:甚快模拟退火法(VFSA)和遗传算法(GA)。目标函数是利用深度偏移后的叠前地震数据定义的该反演问题涉及到两相邻的偏移后的炮记录之间反射界面的横向一致性的优化问题。事实上,速度分析中的正常时差校正被叠前深度偏移所取代。当每一对偏移后的炮记录之间的最小平方差为最小时,就求得了真速度模型。我们的模型是利用分布在一个矩形网格上的三次B样条进行参数化。利用偏移后数据的主要优点是:不需要拾取旅行时、不需要知道震源子波、不需要为了评价数据与模型之间的拟合程度而对合成波形数据进行成本昂贵的计算。利用非线性方法,可自动确定全局最小,而与目标函数的梯度估算值和起始模型无关,也不用对目标函数本身的特点进行假设。不管是对二维合成数据,还是对构造复杂的墨西哥湾实际数据,对速度估算问题用甚快模拟退火法比用遗传算法收敛要快4～5倍。尽管计算量大,但该问题所需模型参数不多,加之利用基尔霍夫偏移的快速旅行时程序,就使得该算法易于用来处理实际地质问题。
Here we describe two layer velocity estimation methods based on nonlinear optimization: VFSA and GA. The objective function is the inversion problem defined by the pre-stack seismic data after the depth migration. It involves the optimization of the lateral consistency of the reflective interface between two adjacent offset shot records. In fact, normal time difference correction in velocity analysis is replaced by prestack depth migration. The true velocity model is obtained when the minimum square error between each pair of offset shots is the smallest. Our model is parameterized using cubic B-splines distributed over a rectangular grid. The main advantage of using offset data is that it is not necessary to know the source wavelet when it is not necessary to pick up a trip and there is no need to make costly calculations of the synthesized waveform data in order to evaluate the fit between the data and the model. The non-linear method automatically determines the global minimum without regard to the gradient estimation of the objective function and the initial model, nor does it assume the characteristics of the objective function itself. Whether it is for two-dimensional composition data or for the complex data of the Gulf of Mexico, the speed estimation problem is simulated by the fast simulated annealing algorithm 4 to 5 times faster than the genetic algorithm. Although computationally intensive, the model requires few model parameters, combined with the fast travel time program using Kirchhoff migration, making the algorithm easy to handle for practical geologic issues.