Diffraction-angle filtering of gradient for acoustic full-waveform inversion

Seismic full-waveform inversion (FWI) estimates subsurface velocity structures by reducing data misfit between observed and modeled data. Simultaneous matching of transmitted and reflected waves in seismic FWI causes different updates of different wavenumber components of a given model depending on the diffraction angle between incident and diffracted rays. Motivated by the inverse-scattering imaging condition and elastic FWI, we have applied a diffraction-angle filtering technique in acoustic FWI, which enables us to separate transmission and reflection energy in the partial derivative wavefields. Diffraction-angle filtering is applied to the virtual source, which is the model parameter perturbation acting as a source for the partial derivative wavefields. Diffraction-angle filtering consists of two diffraction-angle filters (DAFs), DAF-I and DAF-II. The former is derived from the particle acceleration of the incident wavefields and suppresses energies at either small or large diffraction angles by changing the sign of the weighting factor. DAF-I is exactly identical to the conventional inverse scattering approach. The DAF-II is derived from the artificial shear strain of the incident P-wave and additionally suppresses energies at intermediate diffraction angles. With this mechanism, we can design various types of diffraction-angle filtering to control the updates of wavenumber components of the misfit gradient with respect to the P-wave velocity. Using the synthetic Marmousi-II data and real ocean-bottom seismic data from the North Sea, we determined that diffraction-angle filtering enables us to control low-, intermediate-, and high-wavenumber components of the gradient direction.