利用有限元解波动方程求取初至时间
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摘要
叠前逆时偏移需要计算成像点的初至时间。射线追踪法因为计算效率高,常被用作旅行时的计算,但难以处理速度剧变和非规则网格情形。常用的有限元法在求解波动方程时,也会像有限差分法一样存在数据频散问题。本文采用有限元解波动方程获取地震波初至时间,与一般有限元法的主要区别在于利用集中质量矩阵压制时间频散使波前形态保真,并给出了根据震源子波第一极值出现时间求初至时间的方法。数值实验结果表明该方法能适用于非规则网格和速度剧变界面情形。
Prestack reverse time migration requires computing the first breaks time of imaging points. The ray-tracing approach is usually used for the computation of travel time because of higher computational efficiency, but difficult to handle the rapid velocity variation and irregular grid. Common-used finite-element algorithm also has same data dispersion problem as the finite-difference algorithm when solving the wave equation. Different from the common finite-element algorithm, the finite-element algorithm presented in the paper for solving the wave equation and gaining seismic first breaks time is using lumped mass matrix to suppress time dispersion,which makes the feature of wavefront hi-fi. The paper gives the method for computation of first breaks time according to first extreme appearing time of source wavelet. The numeric simulation results showed that the approach is suitable for the irregular grid and rapid-changed velocity interface.
Prestack reverse time migration requires computing the first breaks time of imaging points. The ray-tracing approach is usually used for the computation of travel time because of higher computational efficiency, but difficult to handle the rapid velocity variation and irregular grid. Common-used finite-element algorithm also has same data dispersion problem as the finite-difference algorithm when solving the wave equation. Different from the common finite-element algorithm, the finite-element algorithm presented in the paper for solving the wave equation and gaining seismic first breaks time is using lumped mass matrix to suppress time dispersion,which makes the feature of wavefront hi-fi. The paper gives the method for computation of first breaks time according to first extreme appearing time of source wavelet. The numeric simulation results showed that the approach is suitable for the irregular grid and rapid-changed velocity interface.
引文
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[2]Chang WFand Mc Mechan G A·Reverse-ti me migra-tion of offset vertical seismic profiling data using the excitation-ti me i maging condition·Geophysics,1986,67~84
[3]Vidale J E·Finite-difference calculation of travelti-mes·Bull Seis Soc Am,1988,2062~2076
[4]Trier J and Symes W Wand Upwind finite-difference calculation of travelti mes·Geophysics,1991,812~821
[5]Qin F,Luo Y,Olsen K B et al·Finite-difference so-lution of the eikonal equation along expanding wave-fronts·Geophysics,1992,478~487
[6]Fei T·Eli mination of numerical dispersion in fi-nite-difference modeling and migration by flux-corrected transport·Ph Dthesis,Colorado School of Mines,1994
[7]王勖成.有限单元法.北京:清华大学出版社,2003
[8]谢里夫R E,吉尔达特L P·勘探地震学·北京:石油工业出版社,1999
[9]Marfurt KJ.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equa-tions·Geophysics,1984,49:533~549
[10]监凯维奇O C·有限元法·北京:科学出版社,1985
[2]Chang WFand Mc Mechan G A·Reverse-ti me migra-tion of offset vertical seismic profiling data using the excitation-ti me i maging condition·Geophysics,1986,67~84
[3]Vidale J E·Finite-difference calculation of travelti-mes·Bull Seis Soc Am,1988,2062~2076
[4]Trier J and Symes W Wand Upwind finite-difference calculation of travelti mes·Geophysics,1991,812~821
[5]Qin F,Luo Y,Olsen K B et al·Finite-difference so-lution of the eikonal equation along expanding wave-fronts·Geophysics,1992,478~487
[6]Fei T·Eli mination of numerical dispersion in fi-nite-difference modeling and migration by flux-corrected transport·Ph Dthesis,Colorado School of Mines,1994
[7]王勖成.有限单元法.北京:清华大学出版社,2003
[8]谢里夫R E,吉尔达特L P·勘探地震学·北京:石油工业出版社,1999
[9]Marfurt KJ.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equa-tions·Geophysics,1984,49:533~549
[10]监凯维奇O C·有限元法·北京:科学出版社,1985
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