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《Chinese Journal of Geophysics》 1990-01
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A NEW MODEL PARAMETERIZATION METHOD FOR INVERSION OF 3-DIMENSIONAL VELOCITY STRUCTURE

ZHU LU-PEI ZENG RONG-SHENG (Institute of Geophysics, State Scismological Bureau)LIU FU-TIAN (Institute of Geophysics, Academia Sinica)  
In this paper an important step in the inversion of 3-dimensional velocity structure, the model parameterization, has been discussed and a new parameterization method has been developed. Instead of dividing the model into rectangular blocks, we discretize the model in spatial frequency domain by expanding the perturbation of wave slowness within the area of study into Fourier series and the coefficients of the series can be evaluated by linearized inversion of travel time residuals. A simple form of frequency domain expansion formula, in 3-dimensional space has been derived by using Fourier transformation theory. The difference between discretizing models in the space domain and in the spatial frequency domain is analysed and the advantages of the latter are emphasized.Over-parameterization in space domain will distort the inverted solutions, but this can be effectively avoided by the frequency domain expansion parameterization which discretizes the model in spatial frequency domain. The new parameterization method also makes it possible to over-parameterize the model without limiting the resolving power of the observational system. The final representation includes not only the stable solutions but also the resolving power of the data in earch direction.In order to test the feasibility of the new method, a numerical simulation has been devised. The reulsts confirm the analysis given above.
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