A new parameterization for frequency-domain elastic full waveform inversion for VTI media

Abstract

Abstract To improve full waveform inversion (FWI) results for 2-D vertical transverse isotropic (VTI) media, we propose a new parameterization scheme that is based on Lame constants. In the new parameterization approach, elastic constants of C11, C13, C33, and C44 are replaced with Lame constants and newly introduced parameters of ξ1 and ξ2 for anisotropic properties. Multi-parametric inversion for elastic VTI media has been conducted using a two-step sequential inversion strategy, in which primary parameters (that are well inverted) are inverted first, and secondary parameters are inverted using the inverted primary parameters. In the conventional VTI parameterization approach, C33 and C44 are regarded as the primary parameters, whereas in the new parameterization approach, Lame constants are primary parameters. The new parameterization scheme is distinguished from the conventional VTI parameterization approach in scattering patterns of partial derivative wavefields with respect to primary parameters. Scattering patterns of Lame constants are similar to those of the isotropic case. Because Lame constants are well inverted in the isotropic case, they may also be well inverted in the new parameterization. On the other hand, we do not expect any direct improvements for anisotropic properties because ξ1 and ξ2 produce the same scattering patterns as those of C11 and C13. Gradient directions for a two-layered model show that we can improve the resolution of gradient direction for μ (one of the primary parameters). Although ξ1 and ξ2 of the new parameterization retain characteristics of C11 and C13 in the conventional parameterization, improved primary parameters (Lame constants) affect anisotropic parameters positively. Consequently, inversion results for all of the parameters can be improved. Numerical examples indicate that the new parameterization scheme provides more reliable inversion results than the conventional and sequential inversion approaches. In addition, the new parameterization approach exhibits higher degrees of computational efficiency than the sequential inversion approach because it involves simultaneous inversion of all parameters and does not require an additional inversion stage. Our new parameterization scheme can therefore overcome the intrinsic disadvantages of elastic inversion for VTI media. In applying the new parameterization to real seismic data, it is necessary to increase its applicability to noisy and low-frequency missing data and it also needs to be extended to 3-D case.