Elastic multiple-scattering wavefields modeling and imaging via a vector-reflectivity formulation

Inverse problems for reflector imaging are often formulated using Born-type linearised scattering operators, which describe only single-scattering interactions and therefore provide an incomplete representation of elastic wave physics. We introduce a vector-reflectivity formulation of the elastic wave equation for multiple-scattering wavefields modelling and imaging. A key property of the proposed formulation is that both nonlinear and linearised wave propagation operators with respect to the vector-reflectivity have the ability to represent elastic multiple-scattering wavefields in the smooth background velocity models. Based on this vector-reflectivity formulation, we develop a matrix-free Gauss--Newton inversion method for imaging of elastic multiple-scattering wavefields. Numerical experiments show that the proposed vector-reflectivity formulation accurately models elastic multiple-scattering wavefields and improves reflector imaging of faults and steeply dipping structures compared with conventional linearised elastic inversion. The results also show that the truncated Gauss--Newton scheme converges faster than the L-BFGS method when measured by the number of equivalent wave-equation solutions.