This study proposes an elastic finite difference(FD)time domain method with variable grids in three-dimensional cylindrical coordinates.The calculations will diverge and become less accurate by conventional cylindrical FD as the grid size gradually becomes more extensive with the increasing radius.To prevent grids from being too coarse in far fields,we compensate for the grid cell inflation by refining the grid step in the azimuthal direction.The variable grid FD in the cylindrical coordinate systems has a higher efficiency in solving acoustic logging while drilling(LWD)problems because the grid boundaries are consistent with those of the drill collar and the borehole.The proposed algorithm saves approximately 94％of the FD grids,80％of the computation time,and memory with a higher calculation accuracy than the FD on rectangular grids for the same models.We also calculate the acoustic LWD responses of the fluid-filled borehole intersecting with fractures.Reflections are generated at the fractures,which can be equivalent to an additional scattering source.The mode conversions between the collar and the Stoneley waves are revealed.The Stoneley spectra are more sensitive to the fracture.Finally,the logs in a heterogeneous formation with two reflectors far from the borehole are modeled,and a means of estimating the azimuth of geological interfaces from reflections is proposed.

Pan Yue;He Xiao;Chen Hao;Wang Xiu-Ming

State Key Laboratory of Acoustics,Institute of Acoustics,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China;Beijing Engineering Research Center of Sea Deep Drilling and Exploration,Beijing 100190,China

应用地球物理（英文版）

[1]Pan Yue;He Xiao;Chen Hao;Wang Xiu-Ming-.Acoustic field simulations of logging while drilling by cylindrical finite difference with variable grids)[J].应用地球物理（英文版）,2022(01):11-28

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