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《Geophysical Prospecting For Petrole》 2003-04
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Fraction expansion time-distance equation of reflection wave and its accuracy analysis

Liu Yang (CNPC Geophysical Key Lab, University of Petroleum, Beijing, 102200, China)  
Based on Taylor series expansion of time-distance equation of reflection wave in horizontal layered media, fraction expansion time-distance equation was derived. Then, hyperbolic time-distance equation, Taylor series expansion four-order time-distance equation and fraction expansion two-order time-distance equation were compared on three typical velocity models, which showed that fraction expansion two-order equation has the highest accuracy. Further, Taylor series expansion six-order equation, fraction expansion two-order equation and fraction expansion four-order equation were compared based on the same models, which indicated that fraction expansion two-order equation is characterized by the least dependence on models and the best stability. The signification of parameters of fraction expansion two-order equation was analyzed using vertically linear velocity model, expression of velocity gradient was derived, and a conclusion was drawn that velocity gradient generally increases with the increase of depth. With the advantage of higher accuracy, better stability and univocal parameters, fraction expansion two-order time-distance equation can be utilized to process seismic data of large offset.
【CateGory Index】: P631.4
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