The finite frequency kernel function calculation based on Gassian beam theory
Shou-Jin WANG1, Peng-Gui Jing2, Jie-Xiong CAI1
1. Academy of Petroleum Geophysical Exploration Technology,SINOPEC,Nanjing 025111,China 2. Branch of Geological Exploration,SINOPEC,Chengdu 610041,China
In comparison with the routine ray tomographic velocity model construction,the tomographic velocity model construction based on undulation theory considers the belt limitation property of the wave,and hence it has higher inversion resolution.The core of the undulation theory tomography lies in the calculation of the wave route (finite frequency kernel function).This paper introduces in detail a method for calculation of finite frequency kernel function based on Gassian beam operator,analyzes the effect of the initial width and the emergence angle interval of the Gassian beam on the calculation precision.To overcome the defect of the relatively large error at the near-source place of the Gassian beam,the authors put forward improved beam parameters so as to raise the near-source precision.This paper also analyzes in detail the effect of initial beam width and angle interval on the improved Gassian beam and the focussing characteristics of the improved Gassian beam.Digital calculation example has verified the feasibility of this method in calculation of finite frequency kernel function.Its calculation efficiency is relatively high and it can process kernel function of the inflection wave.
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