Effect of borehole variations on borehole compensated sonic logging(BCSL) based on 2D finite-difference method(FDM)

The slowness time of BCSL was numerically calculated in different lithology of the formation and in borehole variations using 2D FDM.The correction curve of the slowness time was obtained using linear bivariateregression method.It was shown that the lithology of the formation can have certain effect on slowness time of BCSL.The compensated ability of BCSL is different when the borehole varies.When the diameter of the borehole is constant,the compensated ability is getting gradually worse with the increase of the borehole enlargement along the axis.The ability is the worst when the slowness time is the largest,then the compensated ability begins to improve gradually.When the length of the borehole enlargement or cave-in along borehole axis is constant,the compensated ability is getting worse with the increase of the diameter of the borehole enlargement or the decrease of the diameter of the borehole cave-in.The linear bivariateregression method in this paper is proved better than the method of traditional arithmetic average.