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本文重点讨论在振幅谱估计准确的情况下,采用不同相位谱子波作为实际估计子波进行线性最小二乘反演,并对结果进行分析。除子波相位外,所有其它影响反演结果的因素均忽略。稀疏反射系数模型(块状波阻抗模型)反演结果表明:(1)使用不同相位谱子波进行反演,其反演结果合成的记录与原始记录都非常匹配,但反演的反射系数和声波阻抗结果与真实模型有差异;(2)反演结果的可靠程度主要与不同相位子波z变换的根的分布有关,当估计子波与真实子波Z变换的根的分布仅在单位圆附近有差异时,反演的反射系数和声波阻抗与真实模型很接近;(3)尽管反演前后地震记录都匹配了,并且评价反演结果好坏的柯西准则或改进柯西准则(反演参数没有进行自适应处理)已经达到了最优(最小),但反演结果与真实模型仍存在较大差异。最后,针对子波相位估计不准可能导致反演效果较差这个问题,我们提出采用求L1范数、丰度、变分、柯西准则(反演参数进行了自适应处理)或/和改进柯西准则(反演参数进行了自适应处理)的最优值或次优值作为评价准则的一种解决办法,理论上得到了好的效果。
This article focuses on the use of different phase spectral wavelets as the actual estimated wavelet in the case of accurate estimation of the amplitude spectrum linear least squares inversion and analysis of the results. With the exception of the wavelet phase, all other factors that affect the inversion result are ignored. The inversion results of the sparse reflection coefficient model (bulk impedance model) show that: (1) The inversion using different phase spectral wavelets, the inversion result of the synthesis of the record and the original record are very close, but the inversion of the reflection coefficient and the sound wave (2) The reliability of the inversion results is mainly related to the root distribution of z-transform of different phase wavelets.When the distribution of the root of z-transform between estimated wavelet and true wavelet is only near the unit circle When there is difference, the reflection coefficient and acoustic impedance of the inversion are very close to the real model. (3) Although the seismic record before and after the inversion are matched, and the Cauchy criterion or the Cauchy criterion Parameter is not adaptive) has reached the optimal (minimum), but the inversion results and real models are still quite different. Finally, in order to solve the problem that the estimation of wavelet phase is not accurate, which can lead to the poor inversion result, we propose to use L1 norm, abundance, variational, Cauchy criterion (the inversion parameters are adaptively processed) and / or improve Cauchy criterion (the inversion parameters are adaptively processed), the optimal value or sub-optimal value as a criterion for evaluation of a solution, the theory has been good results.