FWI inversion sensitivities of elastic stiffness coefficients in fractured media: numerical modelling

Wenyong Pan, Kristopher A. Innanen, Gary F. Margrave, Junxiao Li, Xinding Fang, Mike C. Fehler

In the companion paper, we give the analytic expressions of the 3D scattering patterns (3D Frchet derivative) due to the perturbations of different elastic constants. And in this paper, we perform several 2D numerical examples to verify and understand the analytic scattering patterns. Firstly, we consider an elastic and isotropic local inclusion embedded in the elastic and isotropic background. The numerical results of the scattering patterns due to the perturbations of elastic constants c11 and c44 (and Lam constants and ) are analyzed and compared to the analytic results. Then we consider a transverse isotropic (HTI or VTI) local inclusion embedded in the elastic and isotropic background. We give the numerical results of P-P and P-SV scattering patterns due to the perturbations of c11, c13, c33 and c44 respectively. These numerical results are consistent with the analytic results. The x and z components of the scattering patterns and the inversion sensitivity kernels in acoustic, elastic and anisotropic media (HTI or VTI) are also given for comparison.