重力场实数尺度小波分解及其应用

重力异常的多尺度分解是利用重力资料进行地质解释的重要环节,以往的小波多尺度分解,其小波细节尺度都是2的正整数次幂,这虽然非常有效,但在某些情况下,细节还是不够细致.因此,本文提出用无理数槡2的正整数次幂为尺度细节进行多尺度分解,以便取关于地壳三维密度结构的更多细节.中国陆地布格重力异常的实例表明,该方法得到的异常细节更为细致,新增加的无理尺度小波细节为我们提取了更多地壳构造信息,可对地质构造解释发挥更有力的作用.

The production and application of irrational scale wavelet details for gravity field

Multi scale decomposition of gravity anomaly is the key step for gravity data geological interpretation. But in previous multi scale wavelet decomposition the wavelet detail scale is based on 2 to the power of positive integer, which proved to be effective in many cases, but in some cases the details are not delicate enough. In this paper multi scale wavelet decomposition was carried out based on irrational number √ 2 to the power of positive integer, in order to obtain better information about crustal density structures.The Mallat and Daubechies methods are still employed for wavelet multi scale decomposition, and only the selected scale varies. The irrational number √ 2 to the power of positive integer can be introduced for multi scale wavelet decomposition.Applying the irrational decomposition method presented in this paper, re-decomposition was performed with 1st-7th order wavelet scale for the Bouguer gravity anomaly of Chinese mainland, among which the 2nd, 4th and 6th order wavelet details were the irrational scale details. The result demonstrates the conventional 4th order approximation of conventional decomposition and the 7th order approximation with the method presented in this paper. By comparison we can find that the 7th approximation results are in accordance with the conventional 4th decomposition results, which demonstrates the presented method's correctness and coherence. This 7th order wavelet details reveal more delicate characterization of gravity anomaly of Chinese mainland, which will play an active role in geological interpretation.In view of the wavelet multi scale decomposition result of Bouguer anomaly of Chinese mainland, we can conclude that irrational scale wavelet decomposition gets more delicate wavelet details than that from conventional decomposition, which is favorable for practical application. These two methods can get similar approximation results, which reflects the coherence as a whole.