A second-order preconditioner for Newton updates in seismic full waveform inversion

Kris Innanen

ABSTRACT

Newton updates (i.e., the updates invoked in the most general forms of seismic full waveform inversion) are intrinsically nonlinear, in the sense that they invoke the data twice, once in the gradient and once in the inverse Hessian. However, a simple univariate example demonstrates that its nonlinear nature is not used advantageously in inversion. This can be fixed by introducing a formal parameter λ to the nonlinear part of the inverse Hessian, and determining a value for it which correctly implements second order nonlinearity. The approach extends without requiring any additional conceptual leaps to a multidimensional scalar full waveform inversion problem, provided that development makes use of a nonlinear sensitivity expression such as that developed in a companion report.

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