重力位场小波多尺度分解性质的分析与应用

Property analysis and application of multi-scale wavelet decomposition of gravity potential field

小波多尺度分解是重力位场分离的常用方法之一,其最大的优点是突破了传统的二分重力异常的理念,实现了重力异常的多重分解,但对其性质及其存在的局限性还未进行系统研究。为了更好地指导实践,本文从基于剖面和格网的重力位场小波多尺度分解的定义出发,阐述了低阶小波细节不变准则等3个重要性质,通过设计简单和复杂两类典型理论模型,分析了小波多尺度定义及性质,并在应用实例中与插值切割法进行了对比。结果表明,小波多尺度分解可以实现重力位场多层分离并推估源体埋深,同时针对本文指出的异常尺度混叠和比例系数难以确定等局限,给出了改进思路。以上基础研究工作,可为重力位场资料的处理和解释提供一定参考。

Multi-scale wavelet decomposition is one of the common methods for gravity potential field separation.The biggest advantage is that it breaks through the traditional concept of dichotomy gravity anomalies and achieves the multiple decomposition of gravity anomalies.However,no systematic study has been carried out on the limitations and properties of the multi-scale wavelet decomposition.To systematically investigate the multi-scale wavelet decomposition and provide guidance for its practical application,this study,starting from the definition of multi-scale wavelet decomposition of gravity potential field based on profiles and grids,expounded three important properties such as the criterion that low-order wavelet keeps details invariant.Then,it analyzed the definition and properties of multi-scale wavelet by designing simple and complex theoretical models.Afterward,this study compared the multi-scale wavelet decomposition with the interpolation cutting method using field data.The results show that multi-scale wavelet decomposition can achieve multi-layer separation of gravity potential field and estimate the burial depths of source bodies.In addition,the multi-scale wavelet decomposition can provide some ideas for solving the limitations pointed out in this study,such as abnormal scale aliasing and difficulty with the determination of scale coefficients.The above basic research can provide a certain degree of references for the processing and interpretation of gravitational potential field data.