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《Oil Geophysical Prospecting》 1991-02
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Approximation of Zoeppritz equation and its application,

Zheng Xiaodong:  
It is proposed that the approximate representation of Zoeppritz equation can be written in the form of power series.In the approximate representation, P-wave is expressed as the even power series of rayparameter p, and S-wave as the odd power series. In other words, the representation includes Aki, Richards and Shuey's formulas which are widely used in present seismic exploration.The representation has simpler form, more definite geophysical meaning and clearer lithology relation than the others. The representation has two very distinct properties. First, P-wave and S-wave are identified or separated off easily. Second, coefficients (A_n~R and A_n~T) of the rower series are the functions of medium density ρ, P-wave velocity α and S-wave velocity β; the base of power series is the function of incident angle i; and the constant terms (A_o~R and A_o~T) are just the reflectoin coefficient and transmission coefficient in the case of vertical incident wave.Consequently, with the use of curve fitting method, the inversion of all seismic lithologic parameters can be easy achieved, and zero-offset section can be obtained. Furthermore, using this approximate representation,we can know some new reflected and transmitted wave properties besides old ones, and extract 28 new AVO characteristic sections from conventional CDP gathers.
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