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-variation-with-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 ' 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 ' 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 use 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 and one field marine data set; the presented results confirm that AD-IDLSM can create ADCIGs with higher spatial resolution, better amplitude fidelity, and fewer migration artifacts compared with 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.