摘要
Some new imaging formulas for seismic reflection wave and theirtheoretical 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 reflected wave is given. Multi-reflection and filter of formations are considered in inversion formulas. Prob-lems in classical convolution model and wave equation are illustrated. All these inversion formulas can be used to image underground medium by wavelet transform and method of '3-basic colors'. Different colors mean different media.
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 reflected wave is given. Multi-reflection and filter of formations are considered in inversion formulas. Problems in classical convolution model and wave equation are illustrated. All these inversion formulas can be used to image underground medium by wavelet transform and method of “3-basic colors”. Different colors mean different media.
基金
CNSF (Grant No. 69575010). The author would like to thank ZhaoQiangji of Daqing Oil Field for providing physical data and Chen Pin in Department of Computer Science of Shandong University for color drawing.
