The author has systematically summarized and derived the advanced theory of continuous complex potential wavelet transform mentioned in many papers abroad and put forward the analytical expression of continuous complex potential wavelet transform of gravity field caused by an inclined prism source. Cauchy wavelet transform of gravity field due to homogeneous gravity sources is equivalent to combination of upward continuation with derivatives of gravity field of any order and obeys a double scaling law. The geometry, depth and dip of causative sources can be simultaneously inverted using wavelet transform coefficients modulus along modulus maximal lines. Conclusions are tested on lots of synthetic modeling field sources by self reliantly written programs. Continuous complex potential wavelet transform provides a new kind of approach and is useful to automation processing, inversion and interpretation of magnetic and gravity fields.
[1] Alexandrescu M,Gilbert D,Hulot G, et. al.Detection of geomagnetic jerks using wavelet analysis[J].J Geophys Res, 1995,100: 12557-12572.
[2] Moreau F,Gilber D,Holschneider M,et al.Identification of sources of potential fields with the continuous wavelet transform: Basic theory[J].J Geophys Res,1999,104: 5003-5013.
[3] Hornby P,Boschetti F,Horovitz F G.Analysis of potential field data in the wavelet domain[J].Geophys J Int,1999,137: 175-196.
[4] sailhac P,Galdeano A,Gilbert D,et al.Identification of sources of potential fields with the continuous wavelet transform: Complex wavelets and application to aeromagnetic profiles in French Guiana[J].J Geophys Res, 2000,105:19455-19475.
[5] Martelet G,Sailhac P,Moreau F,et al.Characterization of geological boundaries using 1-D wavelet transform on gravity data: Theory and application to the Himalayas[J].Geophysics, 2001,66(4):1116-1129.
[6] 陈玉东.利用位场连续复小波变换识辨磁场源(上)[J].物探与化探计算技术,2003,25(2):113-118.
[7] 陈玉东.利用位场连续复小波变换识辨磁场源(下)[J].物探与化探计算技术,2003,25(3).
[8] Thompson D T. EULDPH: A new technique for making computer-assisted depth estimates from magnetic data[J].Geophysics, 1982,47(1):31-37.
[9] Reid B A, Allsop J M,Granser H, et al.Magnetic interpretation in three dimensions using Euler deconvolution[J].Geophysics, 1990,55(1), 80-91 .
[10] Barbosa C F V,Silva J B C,Medeiros E W, et al. Stability analysis and improvement of structural index estimation in Euler deconvolution[J].Geophysics,1999,64(1): 48-60.
[11] 姚天任,孙洪.现代数字信号处理[M].武汉:华中科技大学出版社,2001.212.
[12] 崔锦泰.小波分析论[M].西安:西安交通大学出版社,2001. 81.
[13] 许惠平,Haagmans R H N,deBrnoue A J Th,等.球面小波分析技术及其在全球重力模型中的应用[J].物探与化探,2001,25(1):8-13.
[14] 耿喜哲,刘天佑,丁艳红,等.小波神经网络在重磁资料反演中的应用前景[J].物探与化探,2001,25(2):102-108.
[15] 李健,周云轩,许惠平.重力场数据处理中小波母函数的选择[J].物探与化探,2001,25(6):410-417.