Second-order optimization for multiparameter reflection waveform inversion in acoustic VTI media

SUMMARY The seismic wave velocity in subsurface formations typically varies both spatially and directionally, resulting in a heterogeneous and anisotropic medium. To successfully image complex structures and potential reservoirs using multichannel seismic data, high-resolution interval velocity models are required. However, most controlled-source seismic recordings lack wide-angle signals, such as diving and refracted waves that propagate through deep formations. Consequently, geophysicists rely on the traveltimes and waveforms of reflections or back-scatterings in finite-frequency and finite-offset seismograms to estimate velocity and account for possible anisotropy. Recently, wave-equation based reflection waveform inversion (RWI) has emerged as an active research topic due to its ability to recover intermediate-wavelength model components that cannot be retrieved in reflection traveltime tomography. Nevertheless, the widely used gradient-type local optimization suffers from multiparameter trade-off and slow convergence of RWI in anisotropic media. Analysis of the Fréchet derivative reveals that the sensitivity of reflections to changes in long-to-intermediate wavelengths of the anisotropic velocities is jointly controlled by the specular reflection on the interface and the radiation pattern of scattered fields concerning the model parameters along the wave paths. Anatomy of the approximate Hessian reveals characteristics of parameter coupling and spatial resolution in the context of multiparameter RWI, inspiring the development of a matrix-free Gauss–Newton algorithm based on the second-order adjoint-state method for large-scale applications. Synthetic and real data examples demonstrate that the proposed approach can appropriately handle overburden heterogeneities and anisotropies, and thus improve imaging of underlying complex structures such as dipping and small-scale faults in the deep parts.