Analysis And Optimization Of A Finite Frequency Ray Tracing Method Based On Kirchhoff Integral

Seismic ray tracing is one of the important means of seismic numerical calculation.The traditional ray tracing method is based on the high frequency asymptotic theory.With the high frequency approximation(or far field approximation),the ray path follows Snell law and is only affected by the medium on the ray path,thus ignoring the effect of the medium and structure in the Fresnel zone around the path when the seismic wave frequency is limited.The traditional calculation of frequency limited ray is based on the frequency-dependent eikonal equation.The process is complex,and all of frequency in the frequency range needs to be calculated.The wavelength-smooth method,which considered the effect of medium in the Fresnel zone on the ray path,is essentially a ray calculation under high frequency approximation.The method is simple and easy to calculate based on Kirchhoff integral's frequency limited ray tracing method and transmission wave field represented by Kirchhoff integral.However,there are many approximations and omissions in the process of the method implementation,and there are some problems such as the impact on the results is not analyzed,and the selection of parameters is not quantified.The full Kirchhoff frequency limited ray tracing with all terms of the Kirchhoff integral is given for the above problems,and the frequency and the weighted range change with the frequency band width are given when the two terms with the same amplitude are quantifiable.The following results were achieved:1.The finite frequency ray tracing method based on the full Kirchhoff integral is given,which proves that ignoring the frequency correlation of Kirchhoff integral has a significant impact on the result.Compared with the original Kirchhoff limited frequency ray tracing,it contains more perfect wave field information.2.The selection of quantifiable frequency band width is given,including the relation between the frequency band width parameter and the weighted range and the relation between the frequency and frequency band width when the two terms are equal in amplitude,which provides a quantifiable and accurate basis for the selection of parameters.Based on the results of multiple numerical simulations,the full-kirchhoff integral frequency limited ray tracing is more comprehensive than the frequency limited ray tracing wave field information which omits the frequency-related terms,and the travel time simulation is more accurate.The quantization of the bandwidth parameter can help to carry out more comprehensive and scientific parameter selection for the calculation of different problems and models.