一维波动方程小波逐版本反演

通过将波动方程中的密度及弹性模量参数（函数）投影到一系列波数有上限的Ｌ_２（Ｒ）的子空间Ｖｉ上，并在该子空间（而不是Ｌ_２（Ｒ））中寻找尽量满足条件的密度和弹性模量函数，令Ｊ→－∞．并充分利用小波技术的优越性，相当于对反演指标实施了一系列低通滤波，对解决传统反演问题中局部极值问题是很有希望的途径．逐版本反演不仅可用于波动方程，同样可用于解其他类型的微分方程反问题．

ONE DIMENSIONAL LADDER INVERSION OF WAVEEQUATION BY WAVELET REPRESENTATION

A ladder inversion is presented in which the density and bulk modules are projected onto a ladder of subspaces with wavenumbers limited from above.By apPlying the Daubechies'wavelet technique,this decomposition makes it more stable and efficient to calculate the low wavenumber components of the parameters. The stability is due to the nonexistence of high wavenumber components in the index during the low wavenumber ladder inversion.The problem brought by most other methods using similar techniques has been solved,i.e.the ladder inversiondoes notsped the system with high wavenumber components after extracting the low wavenumber components stably.The method presents high efficiency because a largeand often illposed problem has been decomposed into a ladder of smaller,more stable,independent problems which need much less iterations because of the striking datum compression effect of the wavelet coefficients.Moreover,since the dominant wavenumber of the current ladder is always clear,we can further optimize the standard modules,this again saves computation substantially.Some comuter examples with Synthetic data have been given,which lead to excellent results.