New imaging method for seismic reflection wave and its theoretical basis

Some new imaging formulas for seismic reflection wave and their theoretical basis are given. Phenomena of wave propagation should be characterized by instantaneous spectrum and expressed by complex function of three variables (time, space and frequency) in mathematics. Various physical parameters of medium are also complex functions of two variables (space and frequency). The relationship between reflection coefficient of medium and spectrum of r eflected wave is given. Multi-reflection and filter of formations are consi dered in inversion formulas. Problems in classical convolution model and wa ve equation are illustrated. All these inversion formulas can be used to im age underground medium by wavelet transform and method of "3-basic colors". Different colors mean different media.