Angle-dependent image-domain least-squares migration through analytical point spread functions

Image-domain least-squares migration (IDLSM) is an established approach to recover high-fidelity seismic images of subsurface reflectors; this is achieved by removing the blurring effects of the Hessian operator in the standard migration approach with the help of so-called point spread functions (PSFs). However, most of the existing IDLSM approaches recover an angle-independent image of the subsurface reflectors, which is not suitable for subsequent amplitude versus angle (AVA) analysis. To overcome this limitation, we have developed an angle-dependent IDLSM approach, denoted as AD-IDLSM, which can recover a high-fidelity and high-resolution angle-dependent reflectivity image of subsurface reflectors. The problem is formulated here as an angle-dependent image-domain inversion with PSFs computed by means of full-wave Green's function. More specifically, we derive an analytical expression to compute angle-dependent PSFs by means of a wave-equation-based Kirchhoff migration (WEBKM) engine, where a localization assumption is made in both spatial directions to decrease the computational cost and memory overhead. The amplitude and traveltime of the Green's functions involved in the WEBKM approach are estimated by the excitation-amplitude and excitation-time of the full-wave wavefield. The scattering angle is then approximately estimated from the Poynting vector of the excitation-time field. To stabilize the solution of AD-IDLSM, we utilize a regularization scheme that applies a second derivative along the direction of the reflection angle of angle-domain common-image gathers (ADCIGs) to ensure continuity in the amplitude variations versus angle and suppress migration artifacts. We demonstrate the effectiveness of the AD-IDLSM approach through two synthetic data and a field marine dataset; the presented results confirm that AD-IDLSM can create ADCIGs with higher spatial resolution, better amplitude-fidelity, and fewer migration artifacts, compared to those obtained by its migration counterpart. Moreover, AD-IDLSM amplitude variations with angle are shown to closely resemble the theoretical AVA curve of the reflectors.