Approximate inversion of the wave-equation Hessian via randomized matrix probing
Author(s)Letourneau, Pierre-David; Demanet, Laurent; Calandra, Henri
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We present a method for approximately inverting the Hessian of full waveform inversion as a dip-dependent and scale-dependent amplitude correction. The terms in the expansion of this correction are determined by least-squares fitting from a handful of applications of the Hessian to random models — a procedure called matrix probing. We show numerical indications that randomness is important for generating a robust preconditioner, i.e., one that works regardless of the model to be corrected. To be successful, matrix probing requires an accurate determination of the nullspace of the Hessian, which we propose to implement as a local dip-dependent mask in curvelet space. Numerical experiments show that the novel preconditioner fits 70% of the inverse Hessian (in Frobenius norm) for the 1-parameter acoustic 2D Marmousi model.
DepartmentMassachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences; Massachusetts Institute of Technology. Department of Mathematics
SEG Technical Program Expanded Abstracts 2012
Society of Exploration Geophysicists
Letourneau, Pierre-David, Laurent Demanet, and Henri Calandra. “Approximate Inversion of the Wave-Equation Hessian via Randomized Matrix Probing.” SEG Technical Program Expanded Abstracts 2012 (September 2012).
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