Simultaneous estimation of velocity and density in acoustic multiparameter full-waveform inversion using an improved scattering-integral approach

Abstract

Density is known to be difficult to reconstruct in multiparameter full-waveform inversion (FWI). This difficulty results from the similarity of the diffraction patterns of velocity and density at small scattering angles. In addition, the sensitivities of seismic data with respect to velocity and density have different orders of magnitude which make the inversion ill-conditioned. The inverse Hessian has been shown to mitigate the coupling effects and rescale the magnitudes of different parameters, such that reliable updates for all parameters are available. We have investigated the possibility of simultaneous estimations of velocity and density in acoustic media using the truncated Gauss-Newton method. The model updates are calculated using a matrix-free conjugate gradient solution of the Gauss-Newton normal equation. The gradients of the misfit function with respect to the model parameters and the Hessian-vector products are computed using an improved scattering-integral approach. To give some insights into the trade-off effects between velocity and density, and the imaging resolution in FWI, the sensitivity kernels of both parameters are numerically calculated in homogeneous background models, and their spatial distributions and characteristics are analyzed. The synthetic experiments on a canonical inclusion model and the 2004 BP model confirm that, in cases in which the Gauss-Newton approximate Hessian, especially its off-diagonal blocks, is accurately taken into account, the truncated Gauss-Newton method can effectively mitigate the trade-off effects between velocity and density and provide accelerated convergence rate. Hence, well-resolved velocity and density models are expected.

On the role of density and attenuation in three-dimensional multiparameter viscoacoustic VTI frequency-domain FWI: an OBC case study from the North Sea

“…There have been several investigations to assess either the feasibility of density or impedance (Jeong et al 2012;Przebindowska et al 2012;Bai & Yingst 2014;Qin & Lambaré 2016;Yang et al 2016b) or attenuation (e.g. Hicks & Pratt 2001;Askan et al 2007;Malinowski et al 2011;Kamei & Pratt 2013;Kurzmann et al 2013;Takam Takougang & Calvert 2013;Stopin et al 2016) imaging by FWI.…”

“…Moreover, as the radiation pattern can be seen as a θ -dependent weighting operator in the FWI misfit gradient, the high wavenumbers of the density model will tend to be updated before the smaller ones and hence will break down the scale continuation from the low wavenumbers to the higher ones fostered by the frequency continuation in the data space. This prompts Yang et al (2016b) to design an FWI pre-conditioner which balances the effects of the density radiation pattern.…”

Quantitative imaging using ultrasonic tomography based on full waveform inversion

“…More details of the Hessian used to improve the descent direction and the smoothing regularization constraint can be found in [189,195,196]. Noticeable artifacts are observed from both imaging in the experiment.…”

“…In this chapter, the SI method proposed by Liu et al [187] evaluates kernel-vector products in equation (8.6) by accumulating decomposed vector-scalar product without explicitly calculating the matrix (see equation (8.14)). It needs to be noted that the SI method is a useful alternative, which is not a replacement of the AS method [189].…”

“…Based on the same model perturbation, a larger sensitivity kernel for a parameter denotes a larger sensitivity of the data to this parameter. The frequency-domain sensitivity kernels of velocity and density in the homogeneous background can be given by [189]   …”