Building seismic velocity and attenuation models using Hessian-based multiparameter viscoacoustic full waveform inversion

Abstract:

While velocity tomographic model provides a means to demystify the deep Earth structure, the seismic attenuation model can provide independent and complementary constraints on the subsurface structure. Recent developments on fractional viscoacoustic modeling and its associated Fréchet kernel computation enables incorporating the seismic attenuation into the multiparameter full waveform inversion (FWI) in a classic gradient-based fashion. In this FWI process, however, both kinetic and dynamic information in the seismic data could be attributed to either velocity or attenuation heterogeneity. Consequently, the data-synthetic residual introduced by one model parameter is often mistakenly assigned to another, which leads to the notorious crosstalk (or trade-off) problem between velocity and attenuation. To deal with this problem, we integrate the information of the 2nd-order Fréchet derivative, i.e., the Hessian, into the multiparameter viscoacoustic FWI workflow via a Newton-CG framework. At each iteration, we approximate the gradient preconditioned by the inverse Hessian by solving a linear system using a conjugate gradient internal loop. In particular, the Hessian-vector multiplication in the internal loop is conducted in a matrix-free fashion using the 2nd-order adjoint-state method, which guarantees the computational feasibility of our algorithm. The numerical experiment suggests that this Hessian-based multiparameter FWI can significantly mitigate the crosstalk, and shed light upon simultaneous inversion for both velocity and attenuation models.