Estimation of elastic constants for HTI media using Gauss-Newton and full-Newton multiparameter full-waveform inversion

Abstract

In seismic full-waveform inversion (FWI), subsurface parameters are estimated by iteratively minimizing the difference between the modeled and the observed data. We have considered the problem of estimating the elastic constants of a fractured medium using multiparameter FWI and modeling naturally fractured reservoirs as equivalent anisotropic media. Multiparameter FWI, although promising, remains exposed to a range of challenges, one being the parameter crosstalk problem resulting from the overlap of Fréchet derivative wavefields. Parameter crosstalk is strongly influenced by the form of the scattering pattern for each parameter. We have derived 3D radiation patterns associated with scattering from a range of elastic constants in general anisotropic media. Then, we developed scattering patterns specific to a horizontal transverse isotropic (HTI) medium to draw conclusions about parameter crosstalk in FWI. Bare gradients exhibit crosstalk, as well as artifacts caused by doubly scattered energy in the data residuals. The role of the multiparameter Gauss-Newton (GN) Hessian in suppressing parameter crosstalk is revealed. We have found that the second-order term in the multiparameter Hessian, which is associated with multiparameter second-order scattering effects, can be constructed with the adjoint-state technique. We have examined the analytic scattering patterns for HTI media with a 2D numerical example. We have examined the roles played by the first-and second-order terms in multiparameter Hessian to suppress parameter crosstalk and second-order scattering artifacts numerically. We have also compared the multiparameter GN and full-Newton methods as methods for determining the elastic constants in HTI media with a two-block-layer model.

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

“…One can also simultaneously update all parameters in one stage. This strategy requires proper gradient preconditioning using the second-order derivatives of the objective function, specifically the Hessian matrix (Pratt et al, 1998;Pan et al, 2016). However, the size of the Hessian matrix makes this computationally challenging .…”

Optimal full-waveform inversion strategy for marine data in azimuthally rotated elastic orthorhombic media

“…The angular dependency of PDW from the incidence P-wave in an isotropic background medium can be approximated as follows (Aki and Richards, 1980;Oh and Alkhalifah, 2016a;Pan et al, 2016):…”

“…Because the gradient direction of each parameter is determined by the zero-lag crosscorrelation between PDW and residual wavefields , the radiation pattern of the PDW for each parameter determines which part of data contribute in recovering that parameter. Based on the definition of angle in the radiation-pattern plot, the diffraction patterns (Tarantola, 1986;Pan et al, 2016;Rusmanugroho et al, 2017), the reflection patterns Alkhalifah and Plessix, 2014;Oh and Alkhalifah, 2016a), and the transmission patterns He and Plessix, 2016;Kamath and Tsvankin, 2016) are used to find an optimal parameterization that has less trade-off among parameters. Because we focus on reflections from predominately horizontal and the diving waves from velocity variations along the vertical direction, we rely on the reflection (for a horizontal reflector) patterns in this paper.…”

“…Another simple anisotropic model is the horizontal transverse isotropic (HTI) model, which includes vertically aligned fracture networks (Tsvankin, 2012). Pan et al (2016) examine the Gauss-Newton approach to invert for HTI parameters.…”

Estimation of elastic constants in HTI media using Gauss-Newton and Full-Newton multi-parameter full waveform inversion

“…The multiparameter approximate HessianH is essential in overcoming the crosstalk difficulty in multiparameter FWI Pan et al, 2015b). As we discussed in the previous section, the similarity of the Fréchet derivative wavefields with respect to different physical parameters gives rise to the crosstalk problem.…”