2D声波频率域数值模拟中几种有限差分方法的对比分析
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摘要
频率域数值模拟是频率域全波形反演的基础,在地震波场数值模拟中占有重要地位.相对于时间域数值模拟,频率域数值模拟具有两个明显的优势:没有时间累计误差,适合于并行计算.然而,严重的数值频散和巨大的内存损耗是阻碍其应用的两大瓶颈.为解决这两个问题,基于有限差分方法,学者提出了多种差分格式,如优化9点、15点、17点以及25点差分格式.本文从频散关系、计算效率和存储量三个方面,对比、分析了以上四种差分方法.基于2D声波方程,通过在均匀模型、层状模型以及Marmousi模型上的应用效果,对每种方法的优缺点进行了总结,为高精度数值模拟和声波频率域全波形反演提供方法选择上的参考.
Frequency-domain numerical modeling is the basis of full waveform inversion,which is very important in seismic wave modeling.Compared with conventional time domain forward modeling,frequency-space domain forward modeling has two advantages:no time accumulated error;suitable for parallel cmputation.However,there are two problems with this modeling method;severe grid dispersion and huge memory consumption which have restricted its application to a large extent.Finite-differencing method is effective to achieve the simulation in the frequency-domain.To overcome the disadvantages,based on the finite-differencing,scholars proposed optimal 9-point,15-point,17-point and 25-point scheme.Based on the frequency domain 2D acoustic equation,these methods are applied in the homogeneous model,the single layer model and Marmousi model,then the results are compared and analyzed.By the comparisons of above methods from the point of dispersion,efficiency and computer memory of numerical simulation,we summarize the advantages and disadvantages of the methods,which gives the selection and reference to the following high precision numerical simulation and frequency domain full waveform inversion,
引文
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