TY - JOUR

T1 - Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

AU - Chu, Chunlei

AU - Stoffa, Paul L.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Stoffa would like to acknowledge the King Abdullah University of Science and Technology (KAUST) for their support of his research. We are grateful to associate editor Jeff Shragge and the reviewers for their constructive comments which helped significantly improve the original manuscript. We also thank ConocoPhillips for permission to publish this work.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2012/7

Y1 - 2012/7

N2 - Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.

AB - Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.

UR - http://hdl.handle.net/10754/598096

UR - http://mr.crossref.org/iPage?doi=10.1190%2Fgeo2011-0415.1

UR - http://www.scopus.com/inward/record.url?scp=84864098970&partnerID=8YFLogxK

U2 - 10.1190/GEO2011-0415.1

DO - 10.1190/GEO2011-0415.1

M3 - Article

VL - 77

SP - T117-T123

JO - GEOPHYSICS

JF - GEOPHYSICS

SN - 0016-8033

IS - 4

ER -