Adaptive Homopoty Method Using Conjugate Gradient Algorithm For Inversion Of Two-dimensional Wave Equation With Well Log Constraint

Inversion of wave equations is a branch of the study of inverse problems and plays an important role in it. It has wide application not only in many areas such as pattern recognition, measurement, image processing, and quantum mechanics, but also in a geophysical exploration areas. As the scientific and technological progress, the use of computers and the corresponding computational capabilities have been strengthened. The study of inversion of wave equations has been attracted by more and more people. Because of important development in theory and wide application of inversion of wave equations, various ways are carried out by many researchers from different angles.In order to effectively overcome the main difficulty of inversion of wave equation such as nonlinear and ill-posedness, the paper combines Tikhonov regularization, Tomotopy method with conjugate gradient methods, and designs a practical and effective Tomotopy conjugate gradient method. The method is not only be effective to overcome ill-posedness of the inverse problem, but also promote computational speed and efficiency, etc. The paper also applies the new method to logs data and designs a Regularization Tomotopy logs-constraint conjugate gradient method, which applies to ill-posed, strong noisy, many-minima geophysical exploration inverse problems.The paper carries various methods on numerical simulations, by using point source to the even, layered and abnormal media. The comparative analysis of results on three kinds model indicates convergence and efficiency of constructed methods, which indicate theory meaning and strong application of the constructed methods.