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| 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 |
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Abstract 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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Received: 14 December 2017
Published: 20 February 2019
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The accuracy of Green function with different initial beam width and angular spacing
a—effects of different initial beam widths on the accuracy of Green function;b—effects of different angle intervals on the accuracy of Green function
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Error comparison of 20 Hz Green function of GB、analytical solution
a—20 Hz Green function analytical solution;b—20 Hz Green function GB solution;c—error of two solution;d—horizon slice of the error
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Effect of beam width and angular spacing for modified GB
a—beam width effect;b—angular spacing effect
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Comparison of Green function with conventional GB and modified GB
a—normal beam parameter Gaussian beam;b—improved beam parameter Gaussian beam;c—the improved beam parameters are compared with the conventional Gaussian beam
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Layer model with high and low velocity
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Beam width variation when single beam propagating layer model
a—conventional beam;b—modified beam
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Weight coefficient of 0~50 Hz GB
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Kernel function and error of analysis solution and GB solution
a—20 Hz analysis kernel function;b—20 Hz GB solution kernel function;c—error of analysis solution and GB solution;d—error slice of analysic solution and GB solution
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Frequency-limited kernel function and error between analysis and GB solution
a—5~25 Hz analysis kernel function;b—5~25 Hz GB kernel;c—horizon slice of kernel function of two methods
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Kernel function of constant velocity gradien
a—frequency-limited kernel function;b—vertical slice of kernel function
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Dingshan velocity model and frequency-limited kernel function by GB method
a—Dingshan velocity model;b—kernel function from source point to reflect point and from reflect point to detector point
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