Abstract：With reference to Gauss and Newton's method revised by Redshaw, I put forward a new method for interval velocity inversion using VSP first break time. The assumption is made that the earth is horizontally layered medium where velocity is constant in each layer, whose depth is derived from well loggrog data. This method is essentially a model iteration technique. Mathematically, it is a restricted nonlinear least square optimization problem with multiple factors. Proper mathematical transform can make the restricted optimization problem unrestricted. However, no existing generalized theory can confirm the existence, uniquence and stability of the solution of the nonlinear optimization problem; and no method can estimate exact inversion error that results from observation data error. 95% confidence interval is estimated using error theory of linear inversion problem. How observation data influences on inversion result is analysed respectively by putting random error into both the first break time of synthetic VSP data and the positions of sources and receivers. It is further analysed how inversion result is influenced by shallow geophone vacancy, dipping formation and inaccurate layering depth. This inversion method is tested respectively by adopting synthetic and real VSP data. The inversion results of two sets of offset VSP data from the same well show that this inversion method can provide proper interval velocity for VSP-CDP stack and migration of offset VSP data.
陈信平. 由VSP初至时间反演层速度的算法和误差估计[J]. 石油地球物理勘探, 1992, 27(6): 744-752.
Chen Xinping . Method for interval velocity inversion using VSP first break time and the error estimation. OGP, 1992, 27(6): 744-752.
