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.