Linearized waveform inversion for vertical transversely isotropic elastic media: Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs. Seismic migration aims at obtaining structural images of subsurface geologic discontinuities. More specifically, seismic migration estimates the reflectivity function (stacked average reflectivity or pre-stack angle-dependent reflectivity) from seismic reflection data. On the other hand, seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations. Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters. Although there exist many differences, pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.

Usually, seismic migration and inversion techniques assume an acoustic or isotropic elastic medium. Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property. We present a linearized waveform inversion (LWI) scheme for weakly anisotropic elastic media with vertical transversely isotropic (VTI) symmetry. It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations (△V_p0/V_p0, △V_s0/V_s0, △ϵ, △δ) from the long-wavelength reference model. Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration. We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method. The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images. We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters. Especially, the Thomsen parameter δ is the most difficult to resolve. We also analyze the multi-parameter crosstalk using scattering radiation patterns.

The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.