Seismic Forward Modeling
Forward modeling is crucial in seismic imaging. The finite-difference (FD) methods are the most popular numerical methods for its smaller memory cost and faster computing speed. However, traditional FD methods encounter sever numerical dispersion for high frequency wave or high velocity contrast model. Our goal is to design wave field simulation methods with low numerical dispersion and low numerical error especially in long term simulation. 2 new algorithms, named MNAD and PDRP, are developed.
1. The improved ONAD method based on the modified NAD operator (MNAD) for 2D Scalar Wave Equation.
1. Redesign of the spatial differential operator to approximate the high order spatial derivatives.
2. Adjusting the stencil to minimize the energy error.
1. Low energy error in long time simulation
Fig 1 Energy error of MNAD in contrast with 6 other methods is a 300s long term simulation of a simple harmonic wave field.
2. Low numerical dispersion
Fig 2 Numerical dispersion relation of MNAD in contrast with 3 other methods. (Closer to 1 means the numerical velocity is closer to the real velocity).
Fig 3 Wave field snapshot of MNAD in contrast with 3 other methods. (MNAD generates no visible numerical dispersion).
3. High computational efficiency
The computational speed of MNAD, measured by CPU time, is about 4.32 times and 1.43 times comparing with the 4th-order Lax-Wendroff correction (LWC) method and the optimal nearly analytical discretized method (ONADM).
2. Numerical dispersion minimized nearly analytic discrete (DMNAD) scheme
Wave number domain optimizing combined with the nearly analytic discrete operator.
1. Low numerical error especially in long time simulation
Fig. 4 Numerical error of DMNAD in contrast with 5 other methods is a 300s long term simulation of a simple harmonic wave field.
2. Even lower numerical dispersion than MNAD, outperforming traditional high-order methods like LWC24.
Fig 5 The ratio R of the numerical phase velocity to the phase velocity versus the sampling rate Sp for the 6 methods when the Courant number.
3. More than 30% of computational efficiency promotion comparing to MNAD.
Yushu Chen, Guojie Song, Zhihui Xue, Hao Jing, Haohuan Fu, and Guangwen Yang, "An improved ONAD Method for 2D Scalar Wave Equation in Heterogeneous Media Based on the Modified NAD Operator", Geophysics, 79: doi: 10.1190/GEO2014-0092.1 (in press) .
Yushu Chen, Guojie Song, Zhihui Xue, Hao Jing, Haohuan Fu, and Guangwen Yang, "An improved ONAD algorithm based on a modified nearly analytic discrete operator for solving 2D scalar wave equation", SEG Technical Program Expanded Abstracts 2013. 3569-3573.
Yushu Chen,4th year PhD.student,Tsinghua University
Dajia Peng,1st year PhD.student,Tsinghua University