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1、 The inversion of interval velocities For a horizontally layered model, the rms velocity from the surface to the bottom of layer n is defined by:(1)2=1=12and (2)=1The simple linear relation between the squared interval velocities and the squared rms velocities in expressions 1and2 proposes a practic
2、al choice of data and model parameters. Let the data vector d contain the squared rms velocities picked from the velocity analysis:d= , (3) 21, 22, 2 and let m be the unknown squared interval velocitiesm= , (4) 21, 22, 2 where n is the number of picked rms velocities.The relation between the squared
3、 picked rms velocities in d and the unknown squared interval velocities in m can be written asd=Gm (5)where G is an integral or summation operator with dimension , in this paper ,we consider the case that .1=2=So the matrix G will be follow:=(1 0 0 0 0 012 12 0 0 0 0. . . . . . 1 1 1 1 . . . 1)Objec
4、t Function ： 在此处键入公式。+ = + (6)()=22()()2= + =1(1=1)(1=1) =12let()=0we can get the following form: (+2)=Then we solve the linear equation by the Cholesky decomposition method.This is the result of one trace :Figure 1 The interval velocities obtained from the dix formula (red lines),the blue lines is the result of the inversion.
