Q-compensated least-squares reverse time migration in viscoelastic media using the fractional viscoelastic wave equation

Seismic images play a crucial role in seismic processing and significantly impact the subsequent seismic interpretation. As intrinsic attributes of actual subsurface media, attenuation and elastic effects stand as pivotal factors necessitating consideration within the imaging process. Currently, Q-compensated least-squares reverse time migration (QELSRTM) based on viscoelastic media primarily depends on employing standard linear solids (SLS) to simulate seismic data. The coupling of amplitude attenuation in the wave field and phase dispersion, as derived from the conventional SLS-based method, exerts an impact on the precision of imaging. Recently, the employment of the fractional viscoelastic wave equation for simulating attenuation and elasticity effects in viscoelastic media has demonstrated commendable efficacy, notably in the realm of Q-compensated reverse time migration. To enhance imaging accuracy, we further develop an LSRTM-based approach grounded in fractional-order viscoelastic equations. We first employ the fractional viscoelastic wave equation to generate data that exhibits a close resemblance to real seismic observations. Subsequently, we simultaneously calculate the demigration operator and its related adjoint operator. Lastly, we utilize the conjugate gradient method based on this equation to iteratively update the migration model. Due to the advantages of fractional-order equations in decoupling amplitude attenuation and phase dispersion, implementing QELSRTM is easier with fractional-order equations than with the SLS-based method. Numerical experiments on 2D synthetic models are used to test that QELSRTM can further improve the accuracy of imaging by introducing the Q compensation.