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全波形反演是一种利用地表或井中观测到的波场来推测地下物性参数的高精度成像方法.本文研究了频率域声波方程全波形反演的数值方法.正演用带PML边界条件的九点差分格式求解.反演是一个极小化模拟数据与观测数据之间残量的优化迭代过程,文中比较了多种数值优化方法,包括最速下降法、共轭梯度法、LBFGS方法、高斯牛顿法以及预条件方法.反演从低频到高频逐级进行,且前一个频率的反演结果作为下一个频率反演的初值,该策略有效克服了反演发散或收敛到局部极小值的情况.文中详细描述了正反演方法,并对一个简单模型和两个国际标准模型(即Marmousi模型和Overthrust模型)进行了MPI并行反演计算,结果表明牛顿方法和预条件方法能较精确地对复杂构造模型进行反演成像.
Full-wave inversion is a high-precision imaging method that uses the wave field observed from the surface or well to infer the physical parameters of the subsurface.In this paper, the numerical method of full waveform inversion of the acoustic wave equation in the frequency domain is studied. Nine-point difference format is used to solve the problem. Inversion is an iterative optimization process that minimizes the residuals between simulated data and observed data. A variety of numerical optimization methods are compared, including the steepest descent method, the conjugate gradient method, the LBFGS method, Newton method and the preconditioning method.The inversion is carried out step by step from low frequency to high frequency, and the inversion of the previous frequency is taken as the initial value of the next frequency inversion, which effectively overcomes the divergence or convergence of the inversion to the local minimum Value.In this paper, the method of forward inversion and inversion is described in detail, and MPI parallel inversion calculation is performed on a simple model and two international standard models (ie, Marmousi model and Overthrust model). The results show that the Newton method and the preconditioning method can compare Accurate inversion of complex structural models.