Elastic full-waveform inversion for VTI media: A synthetic parameterization study

Abstract

One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform elastic FWI for a synthetic 2D VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent surface data are generated by a finite-difference code. We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate inverse Hessian matrix, computed using the L-BFGS-B algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy in the deeper part of the section, the model is updated primarily with reflection data. An oblique displacement source, which excites sufficiently intensive shear waves in the conventional offset range, helps provide more accurate updates in the Shear-wave vertical velocity, especially in the shallow layers. We test three model parameterizations, which exhibit different radiation patterns and, therefore, create different parameter trade-offs. Whereas most examples are for a constant-density model, we also generate a density field using Gardner's relationship and invert for the density along with the velocity parameters. The parameterizations that combine velocities and anisotropy coefficients generally yield superior results to the one that includes only velocities, provided that a reasonably accurate initial model is available.

3D waveform inversion of downhole microseismic data for transversely isotropic media

“…This choice of parameters helps reduce trade‐offs in WI, in particular when waves travel mostly near the horizontal direction (Alkhalifah and Plessix ; Kamath et al . ).…”

“…The derivatives of the objective function with respect to the stiffness coefficients c ijkl are given by Liu and Tromp (), Jarillo Michel and Tsvankin () and Kamath et al . (): where u and ψ are the forward and adjoint displacement fields, respectively. Closed‐form 3D expressions for the inversion gradient can be found in the .…”

“…The parameterization includes the P-wave horizontal velocity (V hor ), S-wave vertical velocity (V S0 ), anellipticity coefficient η and Thomsen parameter ε, which are specified on a rectangular grid. This choice of parameters helps reduce trade-offs in WI, in particular when waves travel mostly near the horizontal direction (Alkhalifah and Plessix 2014;Kamath et al 2017). The gradient of the objective function with respect to the medium parameters is obtained using the adjoint-state method.…”

“…The main benefit of WI is an increase in parameter resolution achieved by incorporating phase and amplitude information into the datafitting procedure. The WI gradient can be efficiently computed with just two modelling simulations using the adjoint-state method (Fichtner, Bunge and Igel 2006;Plessix 2006;Kamath, Tsvankin and Díaz 2017).…”

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

“…Over the past three decades, most FWI techniques have been designed to recover only a P-wave velocity model because of the high computational cost (e.g., Gauthier et al, 1986;Pratt, 1999). The recent progress in high-performance computing and the improvement in data acquisition resulted in the extension of FWI to 2D and 3D acoustic and elastic transverse isotropic media with a vertical axis of symmetry (VTI) (e.g., Warner et al, 2013;Operto et al, 2014;Wu and Alkhalifah, 2016;Kamath et al, 2017). This extension has resulted in challenges related to the trade-offs between the model parameters in our inversion process.…”