The precision analysis and algorithm improvement in Lie algebra depth integral of one-way seismic wave
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摘要: 本文在利用拟微分算子和象征理论研究单程波传播规律的基础上,详细分析了单平方根算子李代数深度积分存在的问题,利用改进的算法对单平方根算子进行大步长延拓,计算其李代数积分和指数映射,得到地震波走时的解析表达式.对方法改进前后李代数积分象征中系数校正情况和线性横向变速介质中走时的计算误差进行了对比,数值算例表明,改进后的方法收敛更快,减少了计算时间且提高了计算精度.Abstract: Based on the research of the propagation rules of one-way seismic wave using pseudo differential operator and the symbol theory, we analyze the existing problems in Lie algebra depth integral of single square root operator in detail. Making use of the improved algorithm to perform large-step extrapolation of single square root operator and calculating Lie algebra integral and exponential mapping, we can finally obtain the analytical expression of seismic travel time. Besides, we compare the coefficient corrections in symbol of Lie algebra integral and calculation error in medium with laterally linear velocity variation before and after algorithm modification. The numerical examples prove that the improved algorithm converges faster, reduces the computing time and improves the numerical precision.
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