3D frequency-domain seismic modeling with a Parallel BLR multifrontal direct solver

Three-dimensional frequency-domain full waveform inversion (FWI) of fixed-spread data can be efficiently performed in the visco-acoustic approximation when seismic modeling is based on a sparse direct solver. We present a parallel algebraic Block Low-Rank (BLR) multifrontal solver which provides an approximate solution of the time-harmonic wave equation with a reduced operation count, memory demand, and volume of communication relative to the full-rank solver. We analyze the parallel efficiency and the accuracy of the solver with a realistic FWI case study from the Valhall oil field.

[1]  K. Marfurt.  Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations , 1984 .

[2]  Jan H. Kommedal,et al.  3D Waveform Inversion on Valhall Wide-azimuth OBC , 2009 .

[3]  Jean-Yves L'Excellent,et al.  Improving Multifrontal Methods by Means of Block Low-Rank Representations , 2015, SIAM J. Sci. Comput..

[4]  Olav I. Barkved,et al.  Thematic Set: Full waveform inversion: the next leap forward in imaging at Valhall , 2010 .

[5]  John K. Reid,et al.  The Multifrontal Solution of Indefinite Sparse Symmetric Linear , 1983, TOMS.

[6]  Patrick R. Amestoy,et al.  3D frequency-domain seismic modeling with a Block Low-Rank algebraic multifrontal direct solver , 2013 .

[7]  M. N. Toksoz,et al.  Seismic wave attenuation , 1981 .

[8]  W. Hackbusch.  A Sparse Matrix Arithmetic Based on $\Cal H$-Matrices. Part I: Introduction to ${\Cal H}$-Matrices , 1999, Computing.

[9]  Ludovic Métivier,et al.  Computationally efficient three-dimensional acoustic finite-difference frequency-domain seismic modeling in vertical transversely isotropic media with sparse direct solver , 2014 .

[10]  Jianlin Xia,et al.  On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver , 2011 .

[11]  Robert Schreiber,et al.  A New Implementation of Sparse Gaussian Elimination , 1982, TOMS.

[12]  Patrick R. Amestoy,et al.  Efficient 3D frequency-domain full-waveform inversion of ocean-bottom cable data with sparse block low-rank direct solver: a real data case study from the North Sea , 2015 .

[13]  Wolfgang Hackbusch,et al.  A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices , 1999, Computing.

[14]  Jean Virieux,et al.  An overview of full-waveform inversion in exploration geophysics , 2009 .

[15]  Jianlin Xia,et al.  Superfast Multifrontal Method for Large Structured Linear Systems of Equations , 2009, SIAM J. Matrix Anal. Appl..

[16]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[17]  R. Pratt.  Seismic waveform inversion in the frequency domain; Part 1, Theory and verification in a physical scale model , 1999 .

[18]  Mario Bebendorf,et al.  Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems , 2008 .

[19]  Olav I. Barkved,et al.  Business Impact of Full Waveform Inversion At Valhall , 2010 .