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模拟弹性波传播问题时,PML作为FDTD中至关重要的一个环节,其性能的好坏会直接关系到波场模拟的稳定性和准确度,在随钻声波测井有限差分数值模拟时,由于钻铤占据了井眼大部分空间且将井眼内流体分成极薄的两部分(半径约27 mm),使得数值模拟时需要极细的网格,从而使得时间步长极小,时间迭代步数变多,累计数值误差增大;介质之间的波阻抗差异大(流体和钻铤之间的波阻抗差异超过30倍),对边界处的吸收性能要求高。采用FDTD模拟这种特殊环境中的波场时,累计的数值误差及不佳的吸收效果会导致数值不稳定,这是一个亟待解决的问题,本文首次针对随钻声波测井的复杂井身结构引起的模式波复杂的情况,系统地分析了现今流行的几种PML方法(分裂式PML(SPML),多轴PML(MPML),非分裂式PML(NPML)及复频变换PML(CFSPML))的吸收效果及各自的优缺点,比较了各种PML在随钻声波测井数值模拟中的适应性.结果表明,相比SPML和MPML,NPML和CFS-PML能够更有效地吸收来自计算边界的反射导波;SPML,MPML和NPML在长的模拟时间时会出现数值不稳定现象,而MPML的稳定性可以通过微调参数得到改善,针对分析结果,首次提出在FDTD方法中采用CFS-PML来消除随钻声波测井数值模拟时的数值不稳定及改善吸收效果。为了得到随钻声波测井数值模拟中的CFS-PML的最优化参数,利用并行机计算了数千个三维模型。对典型随钻情形,二次项衰减剖面的最大值应为一倍的d_0。线性频移因子和尺度因子的最大值的优选范围与PML层的厚度有关。对一般地层而言,如果PML层的厚度为十个网格,利用最优化的参数,可以得到的全局误差小于百分之一,且该误差会随PML层厚度的增加而降低。
When simulating the propagation problem of elastic wave, PML is an important link in FDTD. Its performance will be directly related to the stability and accuracy of wavefield simulation. In the finite difference numerical simulation of LWD acoustic logging, The drill collar takes up most of the wellbore space and divides the fluid within the wellbore into two very thin sections (about 27 mm radius) that allow very fine grids for numerical simulations, resulting in extremely small time steps and iterative time The number increases, the accumulated numerical error increases; the wave impedance difference between the media is large (the wave impedance difference between the fluid and the drill collars exceeds 30 times), and the absorbing performance at the boundary is high. When using FDTD to simulate the wave field in this special environment, the accumulated numerical errors and poor absorption results in unstable values. This is an urgent problem to be solved. For the first time, this paper is aimed at the complicated well structure of acoustic logging while drilling (SPML), multi-axis PML (MPML), non-split PML (NPML) and complex frequency transform PML (CFSPML) are systematically analyzed in this paper. , And their respective advantages and disadvantages, and compared the applicability of various PMLs in the numerical simulation of LWD acoustic logging.The results show that compared with SPML and MPML, NPML and CFS-PML can more effectively absorb data from the calculated boundary Reflected waveguides; SPML, MPML and NPML appear numerical instability in a long simulation time, while the stability of MPML can be improved by fine tuning parameters. For the first time, we propose to eliminate CFML by using CFS-PML in the FDTD method Numerical Simulation of LWD Logging is Unstable and Improves Absorption. In order to obtain the optimal parameters of CFS-PML in the acoustic simulation of LWD, thousands of three-dimensional models were calculated using parallel machines. For a typical case of drilling, the maximum of the quadratic term attenuation profile should be d_0. The preferred range of the maximum value of the linear frequency shift factor and the scale factor is related to the thickness of the PML layer. For general strata, if the thickness of the PML layer is ten meshes, the global error that can be obtained using the optimized parameters is less than one percent, and the error will decrease as the thickness of the PML layer increases.