地震数据反演中的Monte－Carlo算法、模拟退火算法（SA）及遗传算法（GA）

Analysis of Monte-Carlo Algorithm,Simulated Annealing Algorithm and Genetic Algorethm Used in Seismic Data Inversion

Ｍｏｎｔｅ－Ｃａｒｌｏ反演方法不是从方程出发直接求反问题，而是在可行解空间中随机产生一系列搜索点，通过检验各搜索点得到反问题的解，该方法具有很强的抗噪音能力，不需对问题作任何线性近似．模拟退火技术是把最优化问题与统计力学中热平衡问题进行类比得来的，它是一种最优化技术，把我们要找极值的函数看成是整个系统的能量函数，任一时制的系统状态则看成是模型空间的一个点．其优点是可避免陷入局部极小值，缺点是计算量很大。遗传算法（ＧＡ）这种新的“全局优化”算法的出现早于模拟退火十多年。ＧＡ的实质是应用于一个模型群体的一组运算，使我们得到一个新的群体，它比上一代成员有更大的期望平均拟合度。上述三种用于反演问题求解的算法已广泛地应用在地球物理求解中，已成为求解非线性反问题的有力数学工具。

Monte-Carlo inversion method does not solve inverse problem by way of equations,but through the inspection of a series of searching points randomly generated in solvablemodel space. This method has strong antinoise ability, and needs no linearizing assumptions.Simulated annealing (SA) technique is produced by comparing the optimum problemswith the thermal balance problens in statistical mechanics, and therefore,is an optimizationtechnique which regards the function erquired to find its extreme value as an energy functionof the whole system, and the system state at any time as a point in the model space. Thetechnique has the advantage of avoiding local minimization, but ilas the drawback of muchcalculation. Genetic algorithm (GA), a global optimization technique, appeared ten yearsearlier than SA.GA is in fact a group of operations applied to a model population to producea new model population that has higher values of average fitness than the antecedent members. The three algorithms mentioned above have been widely used in the solving of geo physical problems and are a powerful mathematical tool for nonlinear inversion problems.