复小波变换反演重力异常

对国外最新研究位场连续复小波变换理论的一系列文章进行了系统归纳、推导与总结,推出了板状体重力场的小波变换系数解析式.对齐次场源形成的重力场进行柯西小波变换,等效于重力场向上延拓和求导两种运算相结合,并服从小波变换双尺度定律.利用小波变换系数模沿极值轴线的变化特征同时反演重力场源的几何形状、埋深、倾角.独立编写了所有程序,并对不同理论模型进行了大量计算,对所有结果进行了分析与讨论.此法为重力场反演提供了一条新的途径,实用于重磁资料自动化处理、反演与解释.

INVERSION OF GRAVITY ANOMALY WITH CONTINUOUS COMPLEX POTENTIAL WAVELET TRANSFORM

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.